-Error Estimates of the Extrapolated Crank-Nicolson Discontinuous Galerkin Approximations for Nonlinear Sobolev Equations

Directory of Open Access Journals (Sweden)

Lee HyunYoung

2010-01-01

Full Text Available We analyze discontinuous Galerkin methods with penalty terms, namely, symmetric interior penalty Galerkin methods, to solve nonlinear Sobolev equations. We construct finite element spaces on which we develop fully discrete approximations using extrapolated Crank-Nicolson method. We adopt an appropriate elliptic-type projection, which leads to optimal error estimates of discontinuous Galerkin approximations in both spatial direction and temporal direction.

Super-convergence of Discontinuous Galerkin Method Applied to the Navier-Stokes Equations

Science.gov (United States)

Atkins, Harold L.

2009-01-01

The practical benefits of the hyper-accuracy properties of the discontinuous Galerkin method are examined. In particular, we demonstrate that some flow attributes exhibit super-convergence even in the absence of any post-processing technique. Theoretical analysis suggest that flow features that are dominated by global propagation speeds and decay or growth rates should be super-convergent. Several discrete forms of the discontinuous Galerkin method are applied to the simulation of unsteady viscous flow over a two-dimensional cylinder. Convergence of the period of the naturally occurring oscillation is examined and shown to converge at 2p+1, where p is the polynomial degree of the discontinuous Galerkin basis. Comparisons are made between the different discretizations and with theoretical analysis.

Discontinuous Galerkin finite element method with anisotropic local grid refinement for inviscid compressible flows

NARCIS (Netherlands)

van der Vegt, Jacobus J.W.; van der Ven, H.

1998-01-01

A new discretization method for the three-dimensional Euler equations of gas dynamics is presented, which is based on the discontinuous Galerkin finite element method. Special attention is paid to an efficient implementation of the discontinuous Galerkin method that minimizes the number of flux

Modeling shallow water flows using the discontinuous Galerkin method

CERN Document Server

Khan, Abdul A

2014-01-01

Replacing the Traditional Physical Model Approach Computational models offer promise in improving the modeling of shallow water flows. As new techniques are considered, the process continues to change and evolve. Modeling Shallow Water Flows Using the Discontinuous Galerkin Method examines a technique that focuses on hyperbolic conservation laws and includes one-dimensional and two-dimensional shallow water flows and pollutant transports. Combines the Advantages of Finite Volume and Finite Element Methods This book explores the discontinuous Galerkin (DG) method, also known as the discontinuous finite element method, in depth. It introduces the DG method and its application to shallow water flows, as well as background information for implementing and applying this method for natural rivers. It considers dam-break problems, shock wave problems, and flows in different regimes (subcritical, supercritical, and transcritical). Readily Adaptable to the Real World While the DG method has been widely used in the fie...

Discontinuous Galerkin methods for plasma physics in the scrape-off layer of tokamaks

International Nuclear Information System (INIS)

Michoski, C.; Meyerson, D.; Isaac, T.; Waelbroeck, F.

2014-01-01

A new parallel discontinuous Galerkin solver, called ArcOn, is developed to describe the intermittent turbulent transport of filamentary blobs in the scrape-off layer (SOL) of fusion plasma. The model is comprised of an elliptic subsystem coupled to two convection-dominated reaction–diffusion–convection equations. Upwinding is used for a class of numerical fluxes developed to accommodate cross product driven convection, and the elliptic solver uses SIPG, NIPG, IIPG, Brezzi, and Bassi–Rebay fluxes to formulate the stiffness matrix. A novel entropy sensor is developed for this system, designed for a space–time varying artificial diffusion/viscosity regularization algorithm. Some numerical experiments are performed to show convergence order on manufactured solutions, regularization of blob/streamer dynamics in the SOL given unstable parameterizations, long-time stability of modon (or dipole drift vortex) solutions arising in simulations of drift-wave turbulence, and finally the formation of edge mode turbulence in the scrape-off layer under turbulent saturation conditions

L2-Error Estimates of the Extrapolated Crank-Nicolson Discontinuous Galerkin Approximations for Nonlinear Sobolev Equations

Directory of Open Access Journals (Sweden)

Hyun Young Lee

2010-01-01

Full Text Available We analyze discontinuous Galerkin methods with penalty terms, namely, symmetric interior penalty Galerkin methods, to solve nonlinear Sobolev equations. We construct finite element spaces on which we develop fully discrete approximations using extrapolated Crank-Nicolson method. We adopt an appropriate elliptic-type projection, which leads to optimal ℓ∞(L2 error estimates of discontinuous Galerkin approximations in both spatial direction and temporal direction.

hpGEM -- A software framework for discontinuous Galerkin finite element methods

NARCIS (Netherlands)

Pesch, L.; Bell, A.; Sollie, W.E.H.; Ambati, V.R.; Bokhove, Onno; van der Vegt, Jacobus J.W.

2006-01-01

hpGEM, a novel framework for the implementation of discontinuous Galerkin finite element methods, is described. We present structures and methods that are common for many (discontinuous) finite element methods and show how we have implemented the components as an object-oriented framework. This

A Streaming Language Implementation of the Discontinuous Galerkin Method

Science.gov (United States)

Barth, Timothy; Knight, Timothy

2005-01-01

We present a Brook streaming language implementation of the 3-D discontinuous Galerkin method for compressible fluid flow on tetrahedral meshes. Efficient implementation of the discontinuous Galerkin method using the streaming model of computation introduces several algorithmic design challenges. Using a cycle-accurate simulator, performance characteristics have been obtained for the Stanford Merrimac stream processor. The current Merrimac design achieves 128 Gflops per chip and the desktop board is populated with 16 chips yielding a peak performance of 2 Teraflops. Total parts cost for the desktop board is less than $20K. Current cycle-accurate simulations for discretizations of the 3-D compressible flow equations yield approximately 40-50% of the peak performance of the Merrimac streaming processor chip. Ongoing work includes the assessment of the performance of the same algorithm on the 2 Teraflop desktop board with a target goal of achieving 1 Teraflop performance.

A second order discontinuous Galerkin method for advection on unstructured triangular meshes

NARCIS (Netherlands)

Geijselaers, Hubertus J.M.; Huetink, Han

2003-01-01

In this paper the advection of element data which are linearly distributed inside the elements is addressed. Across element boundaries the data are assumed discontinuous. The equations are discretized by the Discontinuous Galerkin method. For stability and accuracy at large step sizes (large values

Analysis and development of adjoint-based h-adaptive direct discontinuous Galerkin method for the compressible Navier-Stokes equations

Science.gov (United States)

Cheng, Jian; Yue, Huiqiang; Yu, Shengjiao; Liu, Tiegang

2018-06-01

In this paper, an adjoint-based high-order h-adaptive direct discontinuous Galerkin method is developed and analyzed for the two dimensional steady state compressible Navier-Stokes equations. Particular emphasis is devoted to the analysis of the adjoint consistency for three different direct discontinuous Galerkin discretizations: including the original direct discontinuous Galerkin method (DDG), the direct discontinuous Galerkin method with interface correction (DDG(IC)) and the symmetric direct discontinuous Galerkin method (SDDG). Theoretical analysis shows the extra interface correction term adopted in the DDG(IC) method and the SDDG method plays a key role in preserving the adjoint consistency. To be specific, for the model problem considered in this work, we prove that the original DDG method is not adjoint consistent, while the DDG(IC) method and the SDDG method can be adjoint consistent with appropriate treatment of boundary conditions and correct modifications towards the underlying output functionals. The performance of those three DDG methods is carefully investigated and evaluated through typical test cases. Based on the theoretical analysis, an adjoint-based h-adaptive DDG(IC) method is further developed and evaluated, numerical experiment shows its potential in the applications of adjoint-based adaptation for simulating compressible flows.

Tensor-product preconditioners for higher-order space-time discontinuous Galerkin methods

Science.gov (United States)

Diosady, Laslo T.; Murman, Scott M.

2017-02-01

A space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equations. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high-order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.

Tensor-Product Preconditioners for Higher-Order Space-Time Discontinuous Galerkin Methods

Science.gov (United States)

Diosady, Laslo T.; Murman, Scott M.

2016-01-01

space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equat ions. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.

Discontinuous Galerkin Approaches for Stokes Flow and Flow in Porous Media

Science.gov (United States)

Lehmann, Ragnar; Kaus, Boris; Lukacova, Maria

2014-05-01

Firstly, we present results of a study comparing two different numerical approaches for solving the Stokes equations with strongly varying viscosity: the continuous Galerkin (i.e., FEM) and the discontinuous Galerkin (DG) method. Secondly, we show how the latter method can be extended and applied to flow in porous media governed by Darcy's law. Nonlinearities in the viscosity or other material parameters can lead to discontinuities in the velocity-pressure solution that may not be approximated well with continuous elements. The DG method allows for discontinuities across interior edges of the underlying mesh. Furthermore, depending on the chosen basis functions, it naturally enforces local mass conservation, i.e., in every mesh cell. Computationally, it provides the capability to locally adapt the polynomial degree and needs communication only between directly adjacent mesh cells making it highly flexible and easy to parallelize. The methods are compared for several geophysically relevant benchmarking setups and discussed with respect to speed, accuracy, computational efficiency.

Implementation of the entropy viscosity method with the discontinuous Galerkin method

KAUST Repository

Zingan, Valentin

2013-01-01

The notion of entropy viscosity method introduced in Guermond and Pasquetti [21] is extended to the discontinuous Galerkin framework for scalar conservation laws and the compressible Euler equations. © 2012 Elsevier B.V.

A discontinuous Galerkin method on kinetic flocking models

OpenAIRE

Tan, Changhui

2014-01-01

We study kinetic representations of flocking models. They arise from agent-based models for self-organized dynamics, such as Cucker-Smale and Motsch-Tadmor models. We prove flocking behavior for the kinetic descriptions of flocking systems, which indicates a concentration in velocity variable in infinite time. We propose a discontinuous Galerkin method to treat the asymptotic $\\delta$-singularity, and construct high order positive preserving scheme to solve kinetic flocking systems.

Fourier two-level analysis for higher dimensional discontinuous Galerkin discretisation

NARCIS (Netherlands)

P.W. Hemker (Piet); M.H. van Raalte (Marc)

2002-01-01

textabstractIn this paper we study the convergence of a multigrid method for the solution of a two-dimensional linear second order elliptic equation, discretized by discontinuous Galerkin (DG) methods. For the Baumann-Oden and for the symmetric DG method, we give a detailed analysis of the

A Level Set Discontinuous Galerkin Method for Free Surface Flows

DEFF Research Database (Denmark)

Grooss, Jesper; Hesthaven, Jan

2006-01-01

We present a discontinuous Galerkin method on a fully unstructured grid for the modeling of unsteady incompressible fluid flows with free surfaces. The surface is modeled by embedding and represented by a levelset. We discuss the discretization of the flow equations and the level set equation...

A conservative local discontinuous Galerkin method for the solution of nonlinear Schr(o)dinger equation in two dimensions

Institute of Scientific and Technical Information of China (English)

ZHANG RongPei; YU XiJun; LI MingJun; LI XiangGui

2017-01-01

In this study,we present a conservative local discontinuous Galerkin (LDG) method for numerically solving the two-dimensional nonlinear Schr(o)dinger (NLS) equation.The NLS equation is rewritten as a firstorder system and then we construct the LDG formulation with appropriate numerical flux.The mass and energy conserving laws for the semi-discrete formulation can be proved based on different choices of numerical fluxes such as the central,alternative and upwind-based flux.We will propose two kinds of time discretization methods for the semi-discrete formulation.One is based on Crank-Nicolson method and can be proved to preserve the discrete mass and energy conservation.The other one is Krylov implicit integration factor (ⅡF) method which demands much less computational effort.Various numerical experiments are presented to demonstrate the conservation law of mass and energy,the optimal rates of convergence,and the blow-up phenomenon.

Clearance gap flow: Simulations by discontinuous Galerkin method and experiments

Czech Academy of Sciences Publication Activity Database

Hála, Jindřich; Luxa, Martin; Bublík, O.; Prausová, H.; Vimmr, J.

2016-01-01

Roč. 92, May (2016), 02073-02073 ISSN 2100-014X. [EFM14 – Experimental Fluid Mechanics 2014. Český Krumlov, 18.11.2014-21.11.2014] Institutional support: RVO:61388998 Keywords : compressible fluid flow * narrow channel flow * discontinuous Galerkin finite element method Subject RIV: BK - Fluid Dynamics

Discontinuous Galerkin Approximations for Computing Electromagnetic Bloch Modes in Photonic Crystals

NARCIS (Netherlands)

Lu, Zhongjie; Cesmelioglu, A.; van der Vegt, Jacobus J.W.; Xu, Yan

We analyze discontinuous Galerkin finite element discretizations of the Maxwell equations with periodic coefficients. These equations are used to model the behavior of light in photonic crystals, which are materials containing a spatially periodic variation of the refractive index commensurate with

Discontinuous Galerkin finite element methods for hyperbolic nonconservative partial differential equations

NARCIS (Netherlands)

Rhebergen, Sander; Bokhove, Onno; van der Vegt, Jacobus J.W.

We present space- and space-time discontinuous Galerkin finite element (DGFEM) formulations for systems containing nonconservative products, such as occur in dispersed multiphase flow equations. The main criterium we pose on the formulation is that if the system of nonconservative partial

Spacetime Discontinuous Galerkin FEM: Spectral Response

International Nuclear Information System (INIS)

Abedi, R; Omidi, O; Clarke, P L

2014-01-01

Materials in nature demonstrate certain spectral shapes in terms of their material properties. Since successful experimental demonstrations in 2000, metamaterials have provided a means to engineer materials with desired spectral shapes for their material properties. Computational tools are employed in two different aspects for metamaterial modeling: 1. Mircoscale unit cell analysis to derive and possibly optimize material's spectral response; 2. macroscale to analyze their interaction with conventional material. We compare two different approaches of Time-Domain (TD) and Frequency Domain (FD) methods for metamaterial applications. Finally, we discuss advantages of the TD method of Spacetime Discontinuous Galerkin finite element method (FEM) for spectral analysis of metamaterials

A spectral hybridizable discontinuous Galerkin method for elastic-acoustic wave propagation

Science.gov (United States)

Terrana, S.; Vilotte, J. P.; Guillot, L.

2018-04-01

We introduce a time-domain, high-order in space, hybridizable discontinuous Galerkin (DG) spectral element method (HDG-SEM) for wave equations in coupled elastic-acoustic media. The method is based on a first-order hyperbolic velocity-strain formulation of the wave equations written in conservative form. This method follows the HDG approach by introducing a hybrid unknown, which is the approximation of the velocity on the elements boundaries, as the only globally (i.e. interelement) coupled degrees of freedom. In this paper, we first present a hybridized formulation of the exact Riemann solver at the element boundaries, taking into account elastic-elastic, acoustic-acoustic and elastic-acoustic interfaces. We then use this Riemann solver to derive an explicit construction of the HDG stabilization function τ for all the above-mentioned interfaces. We thus obtain an HDG scheme for coupled elastic-acoustic problems. This scheme is then discretized in space on quadrangular/hexahedral meshes using arbitrary high-order polynomial basis for both volumetric and hybrid fields, using an approach similar to the spectral element methods. This leads to a semi-discrete system of algebraic differential equations (ADEs), which thanks to the structure of the global conservativity condition can be reformulated easily as a classical system of first-order ordinary differential equations in time, allowing the use of classical explicit or implicit time integration schemes. When an explicit time scheme is used, the HDG method can be seen as a reformulation of a DG with upwind fluxes. The introduction of the velocity hybrid unknown leads to relatively simple computations at the element boundaries which, in turn, makes the HDG approach competitive with the DG-upwind methods. Extensive numerical results are provided to illustrate and assess the accuracy and convergence properties of this HDG-SEM. The approximate velocity is shown to converge with the optimal order of k + 1 in the L2-norm

Discontinuous Petrov–Galerkin method with optimal test functions for thin-body problems in solid mechanics

KAUST Repository

Niemi, Antti H.; Bramwell, Jamie A.; Demkowicz, Leszek F.

2011-01-01

We study the applicability of the discontinuous Petrov-Galerkin (DPG) variational framework for thin-body problems in structural mechanics. Our numerical approach is based on discontinuous piecewise polynomial finite element spaces for the trial

A study on discontinuous Galerkin finite element methods for elliptic problems

NARCIS (Netherlands)

Janivita Joto Sudirham, J.J.S.; Sudirham, J.J.; van der Vegt, Jacobus J.W.; van Damme, Rudolf M.J.

2003-01-01

In this report we study several approaches of the discontinuous Galerkin finite element methods for elliptic problems. An important aspect in these formulations is the use of a lifting operator, for which we present an efficient numerical approximation technique. Numerical experiments for two

Discontinuous Galerkin finite element methods for hyperbolic nonconservative partial differential equations

NARCIS (Netherlands)

Rhebergen, Sander; Bokhove, Onno; van der Vegt, Jacobus J.W.

2008-01-01

We present space- and space-time discontinuous Galerkin finite element (DGFEM) formulations for systems containing nonconservative products, such as occur in dispersed multiphase flow equations. The main criterium we pose on the weak formulation is that if the system of nonconservative partial

Planet-disc interactions with Discontinuous Galerkin Methods using GPUs

Science.gov (United States)

Velasco Romero, David A.; Veiga, Maria Han; Teyssier, Romain; Masset, Frédéric S.

2018-05-01

We present a two-dimensional Cartesian code based on high order discontinuous Galerkin methods, implemented to run in parallel over multiple GPUs. A simple planet-disc setup is used to compare the behaviour of our code against the behaviour found using the FARGO3D code with a polar mesh. We make use of the time dependence of the torque exerted by the disc on the planet as a mean to quantify the numerical viscosity of the code. We find that the numerical viscosity of the Keplerian flow can be as low as a few 10-8r2Ω, r and Ω being respectively the local orbital radius and frequency, for fifth order schemes and resolution of ˜10-2r. Although for a single disc problem a solution of low numerical viscosity can be obtained at lower computational cost with FARGO3D (which is nearly an order of magnitude faster than a fifth order method), discontinuous Galerkin methods appear promising to obtain solutions of low numerical viscosity in more complex situations where the flow cannot be captured on a polar or spherical mesh concentric with the disc.

A second order discontinuous Galerkin fast sweeping method for Eikonal equations

Science.gov (United States)

Li, Fengyan; Shu, Chi-Wang; Zhang, Yong-Tao; Zhao, Hongkai

2008-09-01

In this paper, we construct a second order fast sweeping method with a discontinuous Galerkin (DG) local solver for computing viscosity solutions of a class of static Hamilton-Jacobi equations, namely the Eikonal equations. Our piecewise linear DG local solver is built on a DG method developed recently [Y. Cheng, C.-W. Shu, A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations, Journal of Computational Physics 223 (2007) 398-415] for the time-dependent Hamilton-Jacobi equations. The causality property of Eikonal equations is incorporated into the design of this solver. The resulting local nonlinear system in the Gauss-Seidel iterations is a simple quadratic system and can be solved explicitly. The compactness of the DG method and the fast sweeping strategy lead to fast convergence of the new scheme for Eikonal equations. Extensive numerical examples verify efficiency, convergence and second order accuracy of the proposed method.

Fourier two-level analysis for discontinuous Galerkin discretization with linear elements

NARCIS (Netherlands)

P.W. Hemker (Piet); W. Hoffmann; M.H. van Raalte (Marc)

2002-01-01

textabstractIn this paper we study the convergence of a multigrid method for the solution of a linear second order elliptic equation, discretized by discontinuous Galerkin (DG) methods, and we give a detailed analysis of the convergence fordifferent block-relaxation strategies. In addition to an

An H1(Ph)-Coercive Discontinuous Galerkin Formulation for the Poisson Problem : 1-D Analysis

NARCIS (Netherlands)

Van der Zee, K.G.; Van Brummelen, E.H.

2005-01-01

Discontinuous Galerkin (DG) methods are finite element techniques for the solution of partial differential equations. They allow shape functions which are discontinuous across inter-element edges. In principle, DG methods are ideally suited for hp-adaptivity, as they handle nonconforming meshes and

Adaptive mixed-hybrid and penalty discontinuous Galerkin method for two-phase flow in heterogeneous media

KAUST Repository

Hou, Jiangyong

2016-02-05

In this paper, we present a hybrid method, which consists of a mixed-hybrid finite element method and a penalty discontinuous Galerkin method, for the approximation of a fractional flow formulation of a two-phase flow problem in heterogeneous media with discontinuous capillary pressure. The fractional flow formulation is comprised of a wetting phase pressure equation and a wetting phase saturation equation which are coupled through a total velocity and the saturation affected coefficients. For the wetting phase pressure equation, the continuous mixed-hybrid finite element method space can be utilized due to a fundamental property that the wetting phase pressure is continuous. While it can reduce the computational cost by using less degrees of freedom and avoiding the post-processing of velocity reconstruction, this method can also keep several good properties of the discontinuous Galerkin method, which are important to the fractional flow formulation, such as the local mass balance, continuous normal flux and capability of handling the discontinuous capillary pressure. For the wetting phase saturation equation, the penalty discontinuous Galerkin method is utilized due to its capability of handling the discontinuous jump of the wetting phase saturation. Furthermore, an adaptive algorithm for the hybrid method together with the centroidal Voronoi Delaunay triangulation technique is proposed. Five numerical examples are presented to illustrate the features of proposed numerical method, such as the optimal convergence order, the accurate and efficient velocity approximation, and the applicability to the simulation of water flooding in oil field and the oil-trapping or barrier effect phenomena.

Adaptive mixed-hybrid and penalty discontinuous Galerkin method for two-phase flow in heterogeneous media

KAUST Repository

Hou, Jiangyong; Chen, Jie; Sun, Shuyu; Chen, Zhangxin

2016-01-01

In this paper, we present a hybrid method, which consists of a mixed-hybrid finite element method and a penalty discontinuous Galerkin method, for the approximation of a fractional flow formulation of a two-phase flow problem in heterogeneous media with discontinuous capillary pressure. The fractional flow formulation is comprised of a wetting phase pressure equation and a wetting phase saturation equation which are coupled through a total velocity and the saturation affected coefficients. For the wetting phase pressure equation, the continuous mixed-hybrid finite element method space can be utilized due to a fundamental property that the wetting phase pressure is continuous. While it can reduce the computational cost by using less degrees of freedom and avoiding the post-processing of velocity reconstruction, this method can also keep several good properties of the discontinuous Galerkin method, which are important to the fractional flow formulation, such as the local mass balance, continuous normal flux and capability of handling the discontinuous capillary pressure. For the wetting phase saturation equation, the penalty discontinuous Galerkin method is utilized due to its capability of handling the discontinuous jump of the wetting phase saturation. Furthermore, an adaptive algorithm for the hybrid method together with the centroidal Voronoi Delaunay triangulation technique is proposed. Five numerical examples are presented to illustrate the features of proposed numerical method, such as the optimal convergence order, the accurate and efficient velocity approximation, and the applicability to the simulation of water flooding in oil field and the oil-trapping or barrier effect phenomena.

Two-level Fourier analysis of a multigrid approach for discontinuous Galerkin discretisation

NARCIS (Netherlands)

P.W. Hemker (Piet); W. Hoffmann; M.H. van Raalte (Marc)

2002-01-01

textabstractIn this paper we study a multigrid method for the solution of a linear second order elliptic equation, discretized by discontinuous Galerkin (DG) methods, andwe give a detailed analysis of the convergence for different block-relaxation strategies.We find that point-wise

A stable and high-order accurate discontinuous Galerkin based splitting method for the incompressible Navier-Stokes equations

Science.gov (United States)

Piatkowski, Marian; Müthing, Steffen; Bastian, Peter

2018-03-01

In this paper we consider discontinuous Galerkin (DG) methods for the incompressible Navier-Stokes equations in the framework of projection methods. In particular we employ symmetric interior penalty DG methods within the second-order rotational incremental pressure correction scheme. The major focus of the paper is threefold: i) We propose a modified upwind scheme based on the Vijayasundaram numerical flux that has favourable properties in the context of DG. ii) We present a novel postprocessing technique in the Helmholtz projection step based on H (div) reconstruction of the pressure correction that is computed locally, is a projection in the discrete setting and ensures that the projected velocity satisfies the discrete continuity equation exactly. As a consequence it also provides local mass conservation of the projected velocity. iii) Numerical results demonstrate the properties of the scheme for different polynomial degrees applied to two-dimensional problems with known solution as well as large-scale three-dimensional problems. In particular we address second-order convergence in time of the splitting scheme as well as its long-time stability.

A high-order discontinuous Galerkin method for wave propagation through coupled elastic-acoustic media

International Nuclear Information System (INIS)

Wilcox, Lucas C.; Stadler, Georg; Burstedde, Carsten; Ghattas, Omar

2010-01-01

We introduce a high-order discontinuous Galerkin (dG) scheme for the numerical solution of three-dimensional (3D) wave propagation problems in coupled elastic-acoustic media. A velocity-strain formulation is used, which allows for the solution of the acoustic and elastic wave equations within the same unified framework. Careful attention is directed at the derivation of a numerical flux that preserves high-order accuracy in the presence of material discontinuities, including elastic-acoustic interfaces. Explicit expressions for the 3D upwind numerical flux, derived as an exact solution for the relevant Riemann problem, are provided. The method supports h-non-conforming meshes, which are particularly effective at allowing local adaptation of the mesh size to resolve strong contrasts in the local wavelength, as well as dynamic adaptivity to track solution features. The use of high-order elements controls numerical dispersion, enabling propagation over many wave periods. We prove consistency and stability of the proposed dG scheme. To study the numerical accuracy and convergence of the proposed method, we compare against analytical solutions for wave propagation problems with interfaces, including Rayleigh, Lamb, Scholte, and Stoneley waves as well as plane waves impinging on an elastic-acoustic interface. Spectral rates of convergence are demonstrated for these problems, which include a non-conforming mesh case. Finally, we present scalability results for a parallel implementation of the proposed high-order dG scheme for large-scale seismic wave propagation in a simplified earth model, demonstrating high parallel efficiency for strong scaling to the full size of the Jaguar Cray XT5 supercomputer.

Long-time stability effects of quadrature and artificial viscosity on nodal discontinuous Galerkin methods for gas dynamics

Science.gov (United States)

Durant, Bradford; Hackl, Jason; Balachandar, Sivaramakrishnan

2017-11-01

Nodal discontinuous Galerkin schemes present an attractive approach to robust high-order solution of the equations of fluid mechanics, but remain accompanied by subtle challenges in their consistent stabilization. The effect of quadrature choices (full mass matrix vs spectral elements), over-integration to manage aliasing errors, and explicit artificial viscosity on the numerical solution of a steady homentropic vortex are assessed over a wide range of resolutions and polynomial orders using quadrilateral elements. In both stagnant and advected vortices in periodic and non-periodic domains the need arises for explicit stabilization beyond the numerical surface fluxes of discontinuous Galerkin spectral elements. Artificial viscosity via the entropy viscosity method is assessed as a stabilizing mechanism. It is shown that the regularity of the artificial viscosity field is essential to its use for long-time stabilization of small-scale features in nodal discontinuous Galerkin solutions of the Euler equations of gas dynamics. Supported by the Department of Energy Predictive Science Academic Alliance Program Contract DE-NA0002378.

The streamline upwind Petrov-Galerkin stabilising method for the numerical solution of highly advective problems

Directory of Open Access Journals (Sweden)

Carlos Humberto Galeano Urueña

2009-05-01

Full Text Available This article describes the streamline upwind Petrov-Galerkin (SUPG method as being a stabilisation technique for resolving the diffusion-advection-reaction equation by finite elements. The first part of this article has a short analysis of the importance of this type of differential equation in modelling physical phenomena in multiple fields. A one-dimensional description of the SUPG me- thod is then given to extend this basis to two and three dimensions. The outcome of a strongly advective and a high numerical complexity experiment is presented. The results show how the version of the implemented SUPG technique allowed stabilised approaches in space, even for high Peclet numbers. Additional graphs of the numerical experiments presented here can be downloaded from www.gnum.unal.edu.co.

Stability Analysis of Discontinuous Galerkin Approximations to the Elastodynamics Problem

KAUST Repository

Antonietti, Paola F.

2015-11-21

We consider semi-discrete discontinuous Galerkin approximations of both displacement and displacement-stress formulations of the elastodynamics problem. We prove the stability analysis in the natural energy norm and derive optimal a-priori error estimates. For the displacement-stress formulation, schemes preserving the total energy of the system are introduced and discussed. We verify our theoretical estimates on two and three dimensions test problems.

Stability Analysis of Discontinuous Galerkin Approximations to the Elastodynamics Problem

KAUST Repository

Antonietti, Paola F.; Ayuso de Dios, Blanca; Mazzieri, Ilario; Quarteroni, Alfio

2015-01-01

We consider semi-discrete discontinuous Galerkin approximations of both displacement and displacement-stress formulations of the elastodynamics problem. We prove the stability analysis in the natural energy norm and derive optimal a-priori error estimates. For the displacement-stress formulation, schemes preserving the total energy of the system are introduced and discussed. We verify our theoretical estimates on two and three dimensions test problems.

Numerical solution of the Navier-Stokes equations by discontinuous Galerkin method

Science.gov (United States)

Krasnov, M. M.; Kuchugov, P. A.; E Ladonkina, M.; E Lutsky, A.; Tishkin, V. F.

2017-02-01

Detailed unstructured grids and numerical methods of high accuracy are frequently used in the numerical simulation of gasdynamic flows in areas with complex geometry. Galerkin method with discontinuous basis functions or Discontinuous Galerkin Method (DGM) works well in dealing with such problems. This approach offers a number of advantages inherent to both finite-element and finite-difference approximations. Moreover, the present paper shows that DGM schemes can be viewed as Godunov method extension to piecewise-polynomial functions. As is known, DGM involves significant computational complexity, and this brings up the question of ensuring the most effective use of all the computational capacity available. In order to speed up the calculations, operator programming method has been applied while creating the computational module. This approach makes possible compact encoding of mathematical formulas and facilitates the porting of programs to parallel architectures, such as NVidia CUDA and Intel Xeon Phi. With the software package, based on DGM, numerical simulations of supersonic flow past solid bodies has been carried out. The numerical results are in good agreement with the experimental ones.

Discontinuous Galerkin finite element method for solving population density functions of cortical pyramidal and thalamic neuronal populations.

Science.gov (United States)

Huang, Chih-Hsu; Lin, Chou-Ching K; Ju, Ming-Shaung

2015-02-01

Compared with the Monte Carlo method, the population density method is efficient for modeling collective dynamics of neuronal populations in human brain. In this method, a population density function describes the probabilistic distribution of states of all neurons in the population and it is governed by a hyperbolic partial differential equation. In the past, the problem was mainly solved by using the finite difference method. In a previous study, a continuous Galerkin finite element method was found better than the finite difference method for solving the hyperbolic partial differential equation; however, the population density function often has discontinuity and both methods suffer from a numerical stability problem. The goal of this study is to improve the numerical stability of the solution using discontinuous Galerkin finite element method. To test the performance of the new approach, interaction of a population of cortical pyramidal neurons and a population of thalamic neurons was simulated. The numerical results showed good agreement between results of discontinuous Galerkin finite element and Monte Carlo methods. The convergence and accuracy of the solutions are excellent. The numerical stability problem could be resolved using the discontinuous Galerkin finite element method which has total-variation-diminishing property. The efficient approach will be employed to simulate the electroencephalogram or dynamics of thalamocortical network which involves three populations, namely, thalamic reticular neurons, thalamocortical neurons and cortical pyramidal neurons. Copyright © 2014 Elsevier Ltd. All rights reserved.

A Gas-kinetic Discontinuous Galerkin Method for Viscous Flow Equations

International Nuclear Information System (INIS)

Liu, Hongwei; Xu, Kun

2007-01-01

This paper presents a Runge-Kutta discontinuous Galerkin (RKDG) method for viscous flow computation. The construction of the RKDG method is based on a gas-kinetic formulation, which not only couples the convective and dissipative terms together, but also includes both discontinuous and continuous representation in the flux evaluation at the cell interface through a simple hybrid gas distribution function. Due to the intrinsic connection between the gaskinetic BGK model and the Navier-Stokes equations, the Navier-Stokes flux is automatically obtained by the present method. Numerical examples for both one dimensional (10) and two dimensional(20) compressible viscous flows are presented to demonstrate the accuracy and shock capturing capability of the current RKDG method

Discontinuous Galerkin Time-Domain Analysis of Power-Ground Planes Taking Into Account Decoupling Capacitors

KAUST Repository

Li, Ping; Jiang, Li Jun; Bagci, Hakan

2017-01-01

In this paper, a discontinuous Galerkin time-domain (DGTD) method is developed to analyze the power-ground planes taking into account the decoupling capacitors. In the presence of decoupling capacitors, the whole physical system can be split

Discontinuous Petrov-Galerkin method based on the optimal test space norm for one-dimensional transport problems

KAUST Repository

Niemi, Antti; Collier, Nathan; Calo, Victor M.

2011-01-01

We revisit the finite element analysis of convection dominated flow problems within the recently developed Discontinuous Petrov-Galerkin (DPG) variational framework. We demonstrate how test function spaces that guarantee numerical stability can

Study of flow over object problems by a nodal discontinuous Galerkin-lattice Boltzmann method

Science.gov (United States)

Wu, Jie; Shen, Meng; Liu, Chen

2018-04-01

The flow over object problems are studied by a nodal discontinuous Galerkin-lattice Boltzmann method (NDG-LBM) in this work. Different from the standard lattice Boltzmann method, the current method applies the nodal discontinuous Galerkin method into the streaming process in LBM to solve the resultant pure convection equation, in which the spatial discretization is completed on unstructured grids and the low-storage explicit Runge-Kutta scheme is used for time marching. The present method then overcomes the disadvantage of standard LBM for depending on the uniform meshes. Moreover, the collision process in the LBM is completed by using the multiple-relaxation-time scheme. After the validation of the NDG-LBM by simulating the lid-driven cavity flow, the simulations of flows over a fixed circular cylinder, a stationary airfoil and rotating-stationary cylinders are performed. Good agreement of present results with previous results is achieved, which indicates that the current NDG-LBM is accurate and effective for flow over object problems.

ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics

Science.gov (United States)

Fambri, F.; Dumbser, M.; Köppel, S.; Rezzolla, L.; Zanotti, O.

2018-03-01

We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved spacetimes. In this paper we assume the background spacetime to be given and static, i.e. we make use of the Cowling approximation. The governing partial differential equations are solved via a new family of fully-discrete and arbitrary high-order accurate path-conservative discontinuous Galerkin (DG) finite-element methods combined with adaptive mesh refinement and time accurate local timestepping. In order to deal with shock waves and other discontinuities, the high-order DG schemes are supplemented with a novel a-posteriori subcell finite-volume limiter, which makes the new algorithms as robust as classical second-order total-variation diminishing finite-volume methods at shocks and discontinuities, but also as accurate as unlimited high-order DG schemes in smooth regions of the flow. We show the advantages of this new approach by means of various classical two- and three-dimensional benchmark problems on fixed spacetimes. Finally, we present a performance and accuracy comparisons between Runge-Kutta DG schemes and ADER high-order finite-volume schemes, showing the higher efficiency of DG schemes.

Topology Optimization of Nano-Mechanical Cantilever Sensors Using a C0 Discontinuous Galerkin-Type Approach

DEFF Research Database (Denmark)

Marhadi, Kun Saptohartyadi; Evgrafov, Anton; Sørensen, Mads Peter

2011-01-01

We demonstrate the use of a C0 discontinuous Galerkin method for topology optimization of nano-mechanical sensors, namely temperature, surface stress, and mass sensors. The sensors are modeled using classical thin plate theory, which requires C1 basis functions in the standard finite element method...

Finite element and discontinuous Galerkin methods for transient wave equations

CERN Document Server

Cohen, Gary

2017-01-01

This monograph presents numerical methods for solving transient wave equations (i.e. in time domain). More precisely, it provides an overview of continuous and discontinuous finite element methods for these equations, including their implementation in physical models, an extensive description of 2D and 3D elements with different shapes, such as prisms or pyramids, an analysis of the accuracy of the methods and the study of the Maxwell’s system and the important problem of its spurious free approximations. After recalling the classical models, i.e. acoustics, linear elastodynamics and electromagnetism and their variational formulations, the authors present a wide variety of finite elements of different shapes useful for the numerical resolution of wave equations. Then, they focus on the construction of efficient continuous and discontinuous Galerkin methods and study their accuracy by plane wave techniques and a priori error estimates. A chapter is devoted to the Maxwell’s system and the important problem ...

Optimal convergence of discontinuous Galerkin methods for continuum modeling of supply chain networks

KAUST Repository

Zhang, Shuhua; Sun, Shuyu; Yang, Hongtao

2014-01-01

A discontinuous Galerkin method is considered to simulate materials flow in a supply chain network problem which is governed by a system of conservation laws. By means of a novel interpolation and superclose analysis technique, the optimal and superconvergence error estimates are established under two physically meaningful assumptions on the connectivity matrix. Numerical examples are presented to validate the theoretical results. © 2014 Elsevier Ltd. All rights reserved.

Optimal convergence of discontinuous Galerkin methods for continuum modeling of supply chain networks

KAUST Repository

Zhang, Shuhua

2014-09-01

A discontinuous Galerkin method is considered to simulate materials flow in a supply chain network problem which is governed by a system of conservation laws. By means of a novel interpolation and superclose analysis technique, the optimal and superconvergence error estimates are established under two physically meaningful assumptions on the connectivity matrix. Numerical examples are presented to validate the theoretical results. © 2014 Elsevier Ltd. All rights reserved.

Application of discontinuous Galerkin method for solving a compressible five-equation two-phase flow model

Science.gov (United States)

Saleem, M. Rehan; Ali, Ishtiaq; Qamar, Shamsul

2018-03-01

In this article, a reduced five-equation two-phase flow model is numerically investigated. The formulation of the model is based on the conservation and energy exchange laws. The model is non-conservative and the governing equations contain two equations for the mass conservation, one for the over all momentum and one for the total energy. The fifth equation is the energy equation for one of the two phases that includes a source term on the right hand side for incorporating energy exchange between the two fluids in the form of mechanical and thermodynamical works. A Runge-Kutta discontinuous Galerkin finite element method is applied to solve the model equations. The main attractive features of the proposed method include its formal higher order accuracy, its nonlinear stability, its ability to handle complicated geometries, and its ability to capture sharp discontinuities or strong gradients in the solutions without producing spurious oscillations. The proposed method is robust and well suited for large-scale time-dependent computational problems. Several case studies of two-phase flows are presented. For validation and comparison of the results, the same model equations are also solved by using a staggered central scheme. It was found that discontinuous Galerkin scheme produces better results as compared to the staggered central scheme.

Numerical Evaluation of P-Multigrid Method for the Solution of Discontinuous Galerkin Discretizations of Diffusive Equations

Science.gov (United States)

Atkins, H. L.; Helenbrook, B. T.

2005-01-01

This paper describes numerical experiments with P-multigrid to corroborate analysis, validate the present implementation, and to examine issues that arise in the implementations of the various combinations of relaxation schemes, discretizations and P-multigrid methods. The two approaches to implement P-multigrid presented here are equivalent for most high-order discretization methods such as spectral element, SUPG, and discontinuous Galerkin applied to advection; however it is discovered that the approach that mimics the common geometric multigrid implementation is less robust, and frequently unstable when applied to discontinuous Galerkin discretizations of di usion. Gauss-Seidel relaxation converges 40% faster than block Jacobi, as predicted by analysis; however, the implementation of Gauss-Seidel is considerably more expensive that one would expect because gradients in most neighboring elements must be updated. A compromise quasi Gauss-Seidel relaxation method that evaluates the gradient in each element twice per iteration converges at rates similar to those predicted for true Gauss-Seidel.

The direct Discontinuous Galerkin method for the compressible Navier-Stokes equations on arbitrary grids

Science.gov (United States)

Yang, Xiaoquan; Cheng, Jian; Liu, Tiegang; Luo, Hong

2015-11-01

The direct discontinuous Galerkin (DDG) method based on a traditional discontinuous Galerkin (DG) formulation is extended and implemented for solving the compressible Navier-Stokes equations on arbitrary grids. Compared to the widely used second Bassi-Rebay (BR2) scheme for the discretization of diffusive fluxes, the DDG method has two attractive features: first, it is simple to implement as it is directly based on the weak form, and therefore there is no need for any local or global lifting operator; second, it can deliver comparable results, if not better than BR2 scheme, in a more efficient way with much less CPU time. Two approaches to perform the DDG flux for the Navier- Stokes equations are presented in this work, one is based on conservative variables, the other is based on primitive variables. In the implementation of the DDG method for arbitrary grid, the definition of mesh size plays a critical role as the formation of viscous flux explicitly depends on the geometry. A variety of test cases are presented to demonstrate the accuracy and efficiency of the DDG method for discretizing the viscous fluxes in the compressible Navier-Stokes equations on arbitrary grids.

h-multigrid agglomeration based solution strategies for discontinuous Galerkin discretizations of incompressible flow problems

Science.gov (United States)

Botti, L.; Colombo, A.; Bassi, F.

2017-10-01

In this work we exploit agglomeration based h-multigrid preconditioners to speed-up the iterative solution of discontinuous Galerkin discretizations of the Stokes and Navier-Stokes equations. As a distinctive feature h-coarsened mesh sequences are generated by recursive agglomeration of a fine grid, admitting arbitrarily unstructured grids of complex domains, and agglomeration based discontinuous Galerkin discretizations are employed to deal with agglomerated elements of coarse levels. Both the expense of building coarse grid operators and the performance of the resulting multigrid iteration are investigated. For the sake of efficiency coarse grid operators are inherited through element-by-element L2 projections, avoiding the cost of numerical integration over agglomerated elements. Specific care is devoted to the projection of viscous terms discretized by means of the BR2 dG method. We demonstrate that enforcing the correct amount of stabilization on coarse grids levels is mandatory for achieving uniform convergence with respect to the number of levels. The numerical solution of steady and unsteady, linear and non-linear problems is considered tackling challenging 2D test cases and 3D real life computations on parallel architectures. Significant execution time gains are documented.

Analysis of the discontinuous Petrov-Galerkin method with optimal test functions for the Reissner-Mindlin plate bending model

KAUST Repository

Calo, Victor M.; Collier, Nathan; Niemi, Antti H.

2014-01-01

We analyze the discontinuous Petrov-Galerkin (DPG) method with optimal test functions when applied to solve the Reissner-Mindlin model of plate bending. We prove that the hybrid variational formulation underlying the DPG method is well-posed (stable

Discontinuous Galerkin finite element methods for hyperbolic nonconservative partial differential equations

International Nuclear Information System (INIS)

Rhebergen, S.; Bokhove, O.; Vegt, J.J.W. van der

2008-01-01

We present space- and space-time discontinuous Galerkin finite element (DGFEM) formulations for systems containing nonconservative products, such as occur in dispersed multiphase flow equations. The main criterium we pose on the weak formulation is that if the system of nonconservative partial differential equations can be transformed into conservative form, then the formulation must reduce to that for conservative systems. Standard DGFEM formulations cannot be applied to nonconservative systems of partial differential equations. We therefore introduce the theory of weak solutions for nonconservative products into the DGFEM formulation leading to the new question how to define the path connecting left and right states across a discontinuity. The effect of different paths on the numerical solution is investigated and found to be small. We also introduce a new numerical flux that is able to deal with nonconservative products. Our scheme is applied to two different systems of partial differential equations. First, we consider the shallow water equations, where topography leads to nonconservative products, in which the known, possibly discontinuous, topography is formally taken as an unknown in the system. Second, we consider a simplification of a depth-averaged two-phase flow model which contains more intrinsic nonconservative products

Discontinuous Galerkin method for computing gravitational waveforms from extreme mass ratio binaries

International Nuclear Information System (INIS)

Field, Scott E; Hesthaven, Jan S; Lau, Stephen R

2009-01-01

Gravitational wave emission from extreme mass ratio binaries (EMRBs) should be detectable by the joint NASA-ESA LISA project, spurring interest in analytical and numerical methods for investigating EMRBs. We describe a discontinuous Galerkin (dG) method for solving the distributionally forced 1+1 wave equations which arise when modeling EMRBs via the perturbation theory of Schwarzschild black holes. Despite the presence of jump discontinuities in the relevant polar and axial gravitational 'master functions', our dG method achieves global spectral accuracy, provided that we know the instantaneous position, velocity and acceleration of the small particle. Here these variables are known, since we assume that the particle follows a timelike geodesic of the Schwarzschild geometry. We document the results of several numerical experiments testing our method, and in our concluding section discuss the possible inclusion of gravitational self-force effects.

Lagrangian Particle Tracking in a Discontinuous Galerkin Method for Hypersonic Reentry Flows in Dusty Environments

Science.gov (United States)

Ching, Eric; Lv, Yu; Ihme, Matthias

2017-11-01

Recent interest in human-scale missions to Mars has sparked active research into high-fidelity simulations of reentry flows. A key feature of the Mars atmosphere is the high levels of suspended dust particles, which can not only enhance erosion of thermal protection systems but also transfer energy and momentum to the shock layer, increasing surface heat fluxes. Second-order finite-volume schemes are typically employed for hypersonic flow simulations, but such schemes suffer from a number of limitations. An attractive alternative is discontinuous Galerkin methods, which benefit from arbitrarily high spatial order of accuracy, geometric flexibility, and other advantages. As such, a Lagrangian particle method is developed in a discontinuous Galerkin framework to enable the computation of particle-laden hypersonic flows. Two-way coupling between the carrier and disperse phases is considered, and an efficient particle search algorithm compatible with unstructured curved meshes is proposed. In addition, variable thermodynamic properties are considered to accommodate high-temperature gases. The performance of the particle method is demonstrated in several test cases, with focus on the accurate prediction of particle trajectories and heating augmentation. Financial support from a Stanford Graduate Fellowship and the NASA Early Career Faculty program are gratefully acknowledged.

Sharp Penalty Term and Time Step Bounds for the Interior Penalty Discontinuous Galerkin Method for Linear Hyperbolic Problems

NARCIS (Netherlands)

Geevers, Sjoerd; van der Vegt, J.J.W.

2017-01-01

We present sharp and sucient bounds for the interior penalty term and time step size to ensure stability of the symmetric interior penalty discontinuous Galerkin (SIPDG) method combined with an explicit time-stepping scheme. These conditions hold for generic meshes, including unstructured

The development of high performance numerical simulation code for transient groundwater flow and reactive solute transport problems based on local discontinuous Galerkin method

International Nuclear Information System (INIS)

Suzuki, Shunichi; Motoshima, Takayuki; Naemura, Yumi; Kubo, Shin; Kanie, Shunji

2009-01-01

The authors develop a numerical code based on Local Discontinuous Galerkin Method for transient groundwater flow and reactive solute transport problems in order to make it possible to do three dimensional performance assessment on radioactive waste repositories at the earliest stage possible. Local discontinuous Galerkin Method is one of mixed finite element methods which are more accurate ones than standard finite element methods. In this paper, the developed numerical code is applied to several problems which are provided analytical solutions in order to examine its accuracy and flexibility. The results of the simulations show the new code gives highly accurate numeric solutions. (author)

Adaptive discontinuous Galerkin methods for non-linear reactive flows

CERN Document Server

Uzunca, Murat

2016-01-01

The focus of this monograph is the development of space-time adaptive methods to solve the convection/reaction dominated non-stationary semi-linear advection diffusion reaction (ADR) equations with internal/boundary layers in an accurate and efficient way. After introducing the ADR equations and discontinuous Galerkin discretization, robust residual-based a posteriori error estimators in space and time are derived. The elliptic reconstruction technique is then utilized to derive the a posteriori error bounds for the fully discrete system and to obtain optimal orders of convergence. As coupled surface and subsurface flow over large space and time scales is described by (ADR) equation the methods described in this book are of high importance in many areas of Geosciences including oil and gas recovery, groundwater contamination and sustainable use of groundwater resources, storing greenhouse gases or radioactive waste in the subsurface.

Discontinuous Galerkin methods and a posteriori error analysis for heterogenous diffusion problems

International Nuclear Information System (INIS)

Stephansen, A.F.

2007-12-01

In this thesis we analyse a discontinuous Galerkin (DG) method and two computable a posteriori error estimators for the linear and stationary advection-diffusion-reaction equation with heterogeneous diffusion. The DG method considered, the SWIP method, is a variation of the Symmetric Interior Penalty Galerkin method. The difference is that the SWIP method uses weighted averages with weights that depend on the diffusion. The a priori analysis shows optimal convergence with respect to mesh-size and robustness with respect to heterogeneous diffusion, which is confirmed by numerical tests. Both a posteriori error estimators are of the residual type and control the energy (semi-)norm of the error. Local lower bounds are obtained showing that almost all indicators are independent of heterogeneities. The exception is for the non-conforming part of the error, which has been evaluated using the Oswald interpolator. The second error estimator is sharper in its estimate with respect to the first one, but it is slightly more costly. This estimator is based on the construction of an H(div)-conforming Raviart-Thomas-Nedelec flux using the conservativeness of DG methods. Numerical results show that both estimators can be used for mesh-adaptation. (author)

Discontinuous Galerkin methods and a posteriori error analysis for heterogenous diffusion problems; Methodes de Galerkine discontinues et analyse d'erreur a posteriori pour les problemes de diffusion heterogene

Energy Technology Data Exchange (ETDEWEB)

Stephansen, A.F

2007-12-15

In this thesis we analyse a discontinuous Galerkin (DG) method and two computable a posteriori error estimators for the linear and stationary advection-diffusion-reaction equation with heterogeneous diffusion. The DG method considered, the SWIP method, is a variation of the Symmetric Interior Penalty Galerkin method. The difference is that the SWIP method uses weighted averages with weights that depend on the diffusion. The a priori analysis shows optimal convergence with respect to mesh-size and robustness with respect to heterogeneous diffusion, which is confirmed by numerical tests. Both a posteriori error estimators are of the residual type and control the energy (semi-)norm of the error. Local lower bounds are obtained showing that almost all indicators are independent of heterogeneities. The exception is for the non-conforming part of the error, which has been evaluated using the Oswald interpolator. The second error estimator is sharper in its estimate with respect to the first one, but it is slightly more costly. This estimator is based on the construction of an H(div)-conforming Raviart-Thomas-Nedelec flux using the conservativeness of DG methods. Numerical results show that both estimators can be used for mesh-adaptation. (author)

Multicomponent gas flow computations by a discontinuous Galerkin scheme using L2-projection of perfect gas EOS

Science.gov (United States)

Franchina, N.; Savini, M.; Bassi, F.

2016-06-01

A new formulation of multicomponent gas flow computation, suited to a discontinuous Galerkin discretization, is here presented and discussed. The original key feature is the use of L2-projection form of the (perfect gas) equation of state that allows all thermodynamic variables to span the same functional space. This choice greatly mitigates problems encountered by the front-capturing schemes in computing discontinuous flow field, retaining at the same time their conservation properties at the discrete level and ease of use. This new approach, combined with an original residual-based artificial dissipation technique, shows itself capable, through a series of tests illustrated in the paper, to both control the spurious oscillations of flow variables occurring in high-order accurate computations and reduce them increasing the degree of the polynomial representation of the solution. This result is of great importance in computing reacting gaseous flows, where the local accuracy of temperature and species mass fractions is crucial to the correct evaluation of the chemical source terms contained in the equations, even if the presence of the physical diffusivities somewhat brings relief to these problems. The present work can therefore also be considered, among many others already presented in the literature, as the authors' first step toward the construction of a new discontinuous Galerkin scheme for reacting gas mixture flows.

HP-multigrid as smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows. Part I. Multilevel Analysis

NARCIS (Netherlands)

van der Vegt, Jacobus J.W.; Rhebergen, Sander

2011-01-01

The hp-Multigrid as Smoother algorithm (hp-MGS) for the solution of higher order accurate space-(time) discontinuous Galerkin discretizations of advection dominated flows is presented. This algorithm combines p-multigrid with h-multigrid at all p-levels, where the h-multigrid acts as smoother in the

Discontinuous Galerkin Subgrid Finite Element Method for Heterogeneous Brinkman’s Equations

KAUST Repository

Iliev, Oleg P.

2010-01-01

We present a two-scale finite element method for solving Brinkman\\'s equations with piece-wise constant coefficients. This system of equations model fluid flows in highly porous, heterogeneous media with complex topology of the heterogeneities. We make use of the recently proposed discontinuous Galerkin FEM for Stokes equations by Wang and Ye in [12] and the concept of subgrid approximation developed for Darcy\\'s equations by Arbogast in [4]. In order to reduce the error along the coarse-grid interfaces we have added a alternating Schwarz iteration using patches around the coarse-grid boundaries. We have implemented the subgrid method using Deal.II FEM library, [7], and we present the computational results for a number of model problems. © 2010 Springer-Verlag Berlin Heidelberg.

Convergence of Discontinuous Galerkin Methods for Incompressible Two-Phase Flow in Heterogeneous Media

KAUST Repository

Kou, Jisheng; Sun, Shuyu

2013-01-01

A class of discontinuous Galerkin methods with interior penalties is presented for incompressible two-phase flow in heterogeneous porous media with capillary pressures. The semidiscrete approximate schemes for fully coupled system of two-phase flow are formulated. In highly heterogeneous permeable media, the saturation is discontinuous due to different capillary pressures, and therefore, the proposed methods incorporate the capillary pressures in the pressure equation instead of saturation equation. By introducing a coupling approach for stability and error estimates instead of the conventional separate analysis for pressure and saturation, the stability of the schemes in space and time and a priori hp error estimates are presented in the L2(H 1) for pressure and in the L∞(L2) and L2(H1) for saturation. Two time discretization schemes are introduced for effectively computing the discrete solutions. © 2013 Societ y for Industrial and Applied Mathematics.

A class of discontinuous Petrov–Galerkin methods. Part III: Adaptivity

KAUST Repository

Demkowicz, Leszek

2012-04-01

We continue our theoretical and numerical study on the Discontinuous Petrov-Galerkin method with optimal test functions in context of 1D and 2D convection-dominated diffusion problems and hp-adaptivity. With a proper choice of the norm for the test space, we prove robustness (uniform stability with respect to the diffusion parameter) and mesh-independence of the energy norm of the FE error for the 1D problem. With hp-adaptivity and a proper scaling of the norms for the test functions, we establish new limits for solving convection-dominated diffusion problems numerically: ε=10 -11 for 1D and ε=10 -7 for 2D problems. The adaptive process is fully automatic and starts with a mesh consisting of few elements only. © 2011 IMACS. Published by Elsevier B.V. All rights reserved.

Incorporation of exact boundary conditions into a discontinuous galerkin finite element method for accurately solving 2d time-dependent maxwell equations

KAUST Repository

Sirenko, Kostyantyn; Liu, Meilin; Bagci, Hakan

2013-01-01

A scheme that discretizes exact absorbing boundary conditions (EACs) to incorporate them into a time-domain discontinuous Galerkin finite element method (TD-DG-FEM) is described. The proposed TD-DG-FEM with EACs is used for accurately characterizing

An efficient discontinuous Galerkin finite element method for highly accurate solution of maxwell equations

KAUST Repository

Liu, Meilin

2012-08-01

A discontinuous Galerkin finite element method (DG-FEM) with a highly accurate time integration scheme for solving Maxwell equations is presented. The new time integration scheme is in the form of traditional predictor-corrector algorithms, PE CE m, but it uses coefficients that are obtained using a numerical scheme with fully controllable accuracy. Numerical results demonstrate that the proposed DG-FEM uses larger time steps than DG-FEM with classical PE CE) m schemes when high accuracy, which could be obtained using high-order spatial discretization, is required. © 1963-2012 IEEE.

An efficient discontinuous Galerkin finite element method for highly accurate solution of maxwell equations

KAUST Repository

Liu, Meilin; Sirenko, Kostyantyn; Bagci, Hakan

2012-01-01

A discontinuous Galerkin finite element method (DG-FEM) with a highly accurate time integration scheme for solving Maxwell equations is presented. The new time integration scheme is in the form of traditional predictor-corrector algorithms, PE CE m, but it uses coefficients that are obtained using a numerical scheme with fully controllable accuracy. Numerical results demonstrate that the proposed DG-FEM uses larger time steps than DG-FEM with classical PE CE) m schemes when high accuracy, which could be obtained using high-order spatial discretization, is required. © 1963-2012 IEEE.

On the time-stepping stability of continuous mass-lumped and discontinuous Galerkin finite elements for the 3D acoustic wave equation

NARCIS (Netherlands)

Zhebel, E.; Minisini, S.; Mulder, W.A.

2012-01-01

We solve the three-dimensional acoustic wave equation, discretized on tetrahedral meshes. Two methods are considered: mass-lumped continuous finite elements and the symmetric interior-penalty discontinuous Galerkin method (SIP-DG). Combining the spatial discretization with the leap-frog

A spectral multiscale hybridizable discontinuous Galerkin method for second order elliptic problems

KAUST Repository

Efendiev, Yalchin R.

2015-08-01

We design a multiscale model reduction framework within the hybridizable discontinuous Galerkin finite element method. Our approach uses local snapshot spaces and local spectral decomposition following the concept of Generalized Multiscale Finite Element Methods. We propose several multiscale finite element spaces on the coarse edges that provide a reduced dimensional approximation for numerical traces within the HDG framework. We provide a general framework for systematic construction of multiscale trace spaces. Using local snapshots, we avoid high dimensional representation of trace spaces and use some local features of the solution space in constructing a low dimensional trace space. We investigate the solvability and numerically study the performance of the proposed method on a representative number of numerical examples.

Divergence-Conforming Discontinuous Galerkin Methods and $C^0$ Interior Penalty Methods

KAUST Repository

Kanschat, Guido

2014-01-01

© 2014 Society for Industrial and Applied Mathematics. In this paper, we show that recently developed divergence-conforming methods for the Stokes problem have discrete stream functions. These stream functions in turn solve a continuous interior penalty problem for biharmonic equations. The equivalence is established for the most common methods in two dimensions based on interior penalty terms. Then, extensions of the concept to discontinuous Galerkin methods defined through lifting operators, for different weak formulations of the Stokes problem, and to three dimensions are discussed. Application of the equivalence result yields an optimal error estimate for the Stokes velocity without involving the pressure. Conversely, combined with a recent multigrid method for Stokes flow, we obtain a simple and uniform preconditioner for harmonic problems with simply supported and clamped boundary.

hp-version discontinuous Galerkin methods on polygonal and polyhedral meshes

CERN Document Server

Cangiani, Andrea; Georgoulis, Emmanuil H; Houston, Paul

2017-01-01

Over the last few decades discontinuous Galerkin finite element methods (DGFEMs) have been witnessed tremendous interest as a computational framework for the numerical solution of partial differential equations. Their success is due to their extreme versatility in the design of the underlying meshes and local basis functions, while retaining key features of both (classical) finite element and finite volume methods. Somewhat surprisingly, DGFEMs on general tessellations consisting of polygonal (in 2D) or polyhedral (in 3D) element shapes have received little attention within the literature, despite the potential computational advantages. This volume introduces the basic principles of hp-version (i.e., locally varying mesh-size and polynomial order) DGFEMs over meshes consisting of polygonal or polyhedral element shapes, presents their error analysis, and includes an extensive collection of numerical experiments. The extreme flexibility provided by the locally variable elemen t-shapes, element-sizes, and elemen...

Penyelesaian Numerik Persamaan Advection Dengan Radial Point Interpolation Method dan Integrasi Waktu Dengan Discontinuous Galerkin Method

Directory of Open Access Journals (Sweden)

Kresno Wikan Sadono

2016-12-01

Full Text Available Persamaan differensial banyak digunakan untuk menggambarkan berbagai fenomena dalam bidang sains dan rekayasa. Berbagai masalah komplek dalam kehidupan sehari-hari dapat dimodelkan dengan persamaan differensial dan diselesaikan dengan metode numerik. Salah satu metode numerik, yaitu metode meshfree atau meshless berkembang akhir-akhir ini, tanpa proses pembuatan elemen pada domain. Penelitian ini menggabungkan metode meshless yaitu radial basis point interpolation method (RPIM dengan integrasi waktu discontinuous Galerkin method (DGM, metode ini disebut RPIM-DGM. Metode RPIM-DGM diaplikasikan pada advection equation pada satu dimensi. RPIM menggunakan basis function multiquadratic function (MQ dan integrasi waktu diturunkan untuk linear-DGM maupun quadratic-DGM. Hasil simulasi menunjukkan, metode ini mendekati hasil analitis dengan baik. Hasil simulasi numerik dengan RPIM DGM menunjukkan semakin banyak node dan semakin kecil time increment menunjukkan hasil numerik semakin akurat. Hasil lain menunjukkan, integrasi numerik dengan quadratic-DGM untuk suatu time increment dan jumlah node tertentu semakin meningkatkan akurasi dibandingkan dengan linear-DGM.  [Title: Numerical solution of advection equation with radial basis interpolation method and discontinuous Galerkin method for time integration] Differential equation is widely used to describe a variety of phenomena in science and engineering. A variety of complex issues in everyday life can be modeled with differential equations and solved by numerical method. One of the numerical methods, the method meshfree or meshless developing lately, without making use of the elements in the domain. The research combines methods meshless, i.e. radial basis point interpolation method with discontinuous Galerkin method as time integration method. This method is called RPIM-DGM. The RPIM-DGM applied to one dimension advection equation. The RPIM using basis function multiquadratic function and time

Discontinuous Galerkin time-domain analysis of power/ground plate pairs with wave port excitation

KAUST Repository

Li, Ping; Jiang, Li Jun; Bagci, Hakan

2018-01-01

In this work, a discontinuous Galerkin time-domain method is developed to analyze the power/ground plate pairs taking into account arbitrarily shaped antipads. To implement proper source excitations over the antipads, the magnetic surface current expanded by the electric eigen-modes supported by the corresponding antipad is employed as the excitation. For irregularly shaped antipads, the eigen-modes are obtained by numerical approach. Accordingly, the methodology for the S-parameter extraction is derived based on the orthogonal properties of the different modes. Based on the approach, the transformation between different modes can be readily evaluated.

Discontinuous Galerkin time-domain analysis of power/ground plate pairs with wave port excitation

KAUST Repository

Li, Ping

2018-04-06

In this work, a discontinuous Galerkin time-domain method is developed to analyze the power/ground plate pairs taking into account arbitrarily shaped antipads. To implement proper source excitations over the antipads, the magnetic surface current expanded by the electric eigen-modes supported by the corresponding antipad is employed as the excitation. For irregularly shaped antipads, the eigen-modes are obtained by numerical approach. Accordingly, the methodology for the S-parameter extraction is derived based on the orthogonal properties of the different modes. Based on the approach, the transformation between different modes can be readily evaluated.

An upwind space-time conservation element and solution element scheme for solving dusty gas flow model

Directory of Open Access Journals (Sweden)

Asad Rehman

Full Text Available An upwind space-time conservation element and solution element (CE/SE scheme is extended to numerically approximate the dusty gas flow model. Unlike central CE/SE schemes, the current method uses the upwind procedure to derive the numerical fluxes through the inner boundary of conservation elements. These upwind fluxes are utilized to calculate the gradients of flow variables. For comparison and validation, the central upwind scheme is also applied to solve the same dusty gas flow model. The suggested upwind CE/SE scheme resolves the contact discontinuities more effectively and preserves the positivity of flow variables in low density flows. Several case studies are considered and the results of upwind CE/SE are compared with the solutions of central upwind scheme. The numerical results show better performance of the upwind CE/SE method as compared to the central upwind scheme. Keywords: Dusty gas flow, Solid particles, Upwind schemes, Rarefaction wave, Shock wave, Contact discontinuity

Discontinuous Petrov–Galerkin method with optimal test functions for thin-body problems in solid mechanics

KAUST Repository

Niemi, Antti H.

2011-02-01

We study the applicability of the discontinuous Petrov-Galerkin (DPG) variational framework for thin-body problems in structural mechanics. Our numerical approach is based on discontinuous piecewise polynomial finite element spaces for the trial functions and approximate, local computation of the corresponding \\'optimal\\' test functions. In the Timoshenko beam problem, the proposed method is shown to provide the best approximation in an energy-type norm which is equivalent to the L2-norm for all the unknowns, uniformly with respect to the thickness parameter. The same formulation remains valid also for the asymptotic Euler-Bernoulli solution. As another one-dimensional model problem we consider the modelling of the so called basic edge effect in shell deformations. In particular, we derive a special norm for the test space which leads to a robust method in terms of the shell thickness. Finally, we demonstrate how a posteriori error estimator arising directly from the discontinuous variational framework can be utilized to generate an optimal hp-mesh for resolving the boundary layer. © 2010 Elsevier B.V.

Resolution of the Vlasov-Maxwell system by PIC discontinuous Galerkin method on GPU with OpenCL

Directory of Open Access Journals (Sweden)

Crestetto Anaïs

2013-01-01

Full Text Available We present an implementation of a Vlasov-Maxwell solver for multicore processors. The Vlasov equation describes the evolution of charged particles in an electromagnetic field, solution of the Maxwell equations. The Vlasov equation is solved by a Particle-In-Cell method (PIC, while the Maxwell system is computed by a Discontinuous Galerkin method. We use the OpenCL framework, which allows our code to run on multicore processors or recent Graphic Processing Units (GPU. We present several numerical applications to two-dimensional test cases.

Discontinuous Galerkin methodology for Large-Eddy Simulations of wind turbine airfoils

DEFF Research Database (Denmark)

Frére, A.; Sørensen, Niels N.; Hillewaert, K.

2016-01-01

This paper aims at evaluating the potential of the Discontinuous Galerkin (DG) methodology for Large-Eddy Simulation (LES) of wind turbine airfoils. The DG method has shown high accuracy, excellent scalability and capacity to handle unstructured meshes. It is however not used in the wind energy...... sector yet. The present study aims at evaluating this methodology on an application which is relevant for that sector and focuses on blade section aerodynamics characterization. To be pertinent for large wind turbines, the simulations would need to be at low Mach numbers (M ≤ 0.3) where compressible...... at low and high Reynolds numbers and compares the results to state-of-the-art models used in industry, namely the panel method (XFOIL with boundary layer modeling) and Reynolds Averaged Navier-Stokes (RANS). At low Reynolds number (Re = 6 × 104), involving laminar boundary layer separation and transition...

Parallel discontinuous Galerkin FEM for computing hyperbolic conservation law on unstructured grids

Science.gov (United States)

Ma, Xinrong; Duan, Zhijian

2018-04-01

High-order resolution Discontinuous Galerkin finite element methods (DGFEM) has been known as a good method for solving Euler equations and Navier-Stokes equations on unstructured grid, but it costs too much computational resources. An efficient parallel algorithm was presented for solving the compressible Euler equations. Moreover, the multigrid strategy based on three-stage three-order TVD Runge-Kutta scheme was used in order to improve the computational efficiency of DGFEM and accelerate the convergence of the solution of unsteady compressible Euler equations. In order to make each processor maintain load balancing, the domain decomposition method was employed. Numerical experiment performed for the inviscid transonic flow fluid problems around NACA0012 airfoil and M6 wing. The results indicated that our parallel algorithm can improve acceleration and efficiency significantly, which is suitable for calculating the complex flow fluid.

A discontinuous Galerkin method for numerical pricing of European options under Heston stochastic volatility

Science.gov (United States)

Hozman, J.; Tichý, T.

2016-12-01

The paper is based on the results from our recent research on multidimensional option pricing problems. We focus on European option valuation when the price movement of the underlying asset is driven by a stochastic volatility following a square root process proposed by Heston. The stochastic approach incorporates a new additional spatial variable into this model and makes it very robust, i.e. it provides a framework to price a variety of options that is closer to reality. The main topic is to present the numerical scheme arising from the concept of discontinuous Galerkin methods and applicable to the Heston option pricing model. The numerical results are presented on artificial benchmarks as well as on reference market data.

Discontinuous Galerkin discretization and hp-refinement for the resolution of the neutron transport equation

International Nuclear Information System (INIS)

Fournier, Damien; Le-Tellier, Romain; Herbin, Raphaele

2013-01-01

This paper presents an hp-refinement method for a first order scalar transport reaction equation discretized by a discontinuous Galerkin method. First, the theoretical rates of convergence of h- and p-refinement are recalled and numerically tested. Then, in order to design some meshes, we propose two different estimators of the local error on the spatial domain. These quantities are analyzed and compared depending on the regularity of the solution so as to find the best way to lead the refinement process and the best strategy to choose between h- and p-refinement. Finally, the different possible refinement strategies are compared first on analytical examples and then on realistic applications for neutron transport in a nuclear reactor core. (authors)

An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry

Energy Technology Data Exchange (ETDEWEB)

Wintermeyer, Niklas [Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931 Köln (Germany); Winters, Andrew R., E-mail: awinters@math.uni-koeln.de [Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931 Köln (Germany); Gassner, Gregor J. [Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931 Köln (Germany); Kopriva, David A. [Department of Mathematics, The Florida State University, Tallahassee, FL 32306 (United States)

2017-07-01

We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretization exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving scheme we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretization of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem.

Analysis of an a posteriori error estimator for the transport equation with SN and discontinuous Galerkin discretizations

International Nuclear Information System (INIS)

Fournier, D.; Le Tellier, R.; Suteau, C.

2011-01-01

We present an error estimator for the S N neutron transport equation discretized with an arbitrary high-order discontinuous Galerkin method. As a starting point, the estimator is obtained for conforming Cartesian meshes with a uniform polynomial order for the trial space then adapted to deal with non-conforming meshes and a variable polynomial order. Some numerical tests illustrate the properties of the estimator and its limitations. Finally, a simple shielding benchmark is analyzed in order to show the relevance of the estimator in an adaptive process.

A hybrid time-domain discontinuous galerkin-boundary integral method for electromagnetic scattering analysis

KAUST Repository

Li, Ping; Shi, Yifei; Jiang, Lijun; Bagci, Hakan

2014-01-01

A scheme hybridizing discontinuous Galerkin time-domain (DGTD) and time-domain boundary integral (TDBI) methods for accurately analyzing transient electromagnetic scattering is proposed. Radiation condition is enforced using the numerical flux on the truncation boundary. The fields required by the flux are computed using the TDBI from equivalent currents introduced on a Huygens' surface enclosing the scatterer. The hybrid DGTDBI ensures that the radiation condition is mathematically exact and the resulting computation domain is as small as possible since the truncation boundary conforms to scatterer's shape and is located very close to its surface. Locally truncated domains can also be defined around each disconnected scatterer additionally reducing the size of the overall computation domain. Numerical examples demonstrating the accuracy and versatility of the proposed method are presented. © 2014 IEEE.

A hybrid time-domain discontinuous galerkin-boundary integral method for electromagnetic scattering analysis

KAUST Repository

Li, Ping

2014-05-01

A scheme hybridizing discontinuous Galerkin time-domain (DGTD) and time-domain boundary integral (TDBI) methods for accurately analyzing transient electromagnetic scattering is proposed. Radiation condition is enforced using the numerical flux on the truncation boundary. The fields required by the flux are computed using the TDBI from equivalent currents introduced on a Huygens\\' surface enclosing the scatterer. The hybrid DGTDBI ensures that the radiation condition is mathematically exact and the resulting computation domain is as small as possible since the truncation boundary conforms to scatterer\\'s shape and is located very close to its surface. Locally truncated domains can also be defined around each disconnected scatterer additionally reducing the size of the overall computation domain. Numerical examples demonstrating the accuracy and versatility of the proposed method are presented. © 2014 IEEE.

Discontinuous Petrov-Galerkin method based on the optimal test space norm for one-dimensional transport problems

KAUST Repository

Niemi, Antti

2011-05-14

We revisit the finite element analysis of convection dominated flow problems within the recently developed Discontinuous Petrov-Galerkin (DPG) variational framework. We demonstrate how test function spaces that guarantee numerical stability can be computed automatically with respect to the so called optimal test space norm by using an element subgrid discretization. This should make the DPG method not only stable but also robust, that is, uniformly stable with respect to the Ṕeclet number in the current application. The e_ectiveness of the algorithm is demonstrated on two problems for the linear advection-di_usion equation.

An hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations

KAUST Repository

Pani, Amiya K.

2010-06-06

In this article, a priori error bounds are derived for an hp-local discontinuous Galerkin (LDG) approximation to a parabolic integro-differential equation. It is shown that error estimates in L 2-norm of the gradient as well as of the potential are optimal in the discretizing parameter h and suboptimal in the degree of polynomial p. Due to the presence of the integral term, an introduction of an expanded mixed type Ritz-Volterra projection helps us to achieve optimal estimates. Further, it is observed that a negative norm estimate of the gradient plays a crucial role in our convergence analysis. As in the elliptic case, similar results on order of convergence are established for the semidiscrete method after suitably modifying the numerical fluxes. The optimality of these theoretical results is tested in a series of numerical experiments on two dimensional domains. © 2010 Springer Science+Business Media, LLC.

An hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations

KAUST Repository

Pani, Amiya K.; Yadav, Sangita

2010-01-01

In this article, a priori error bounds are derived for an hp-local discontinuous Galerkin (LDG) approximation to a parabolic integro-differential equation. It is shown that error estimates in L 2-norm of the gradient as well as of the potential are optimal in the discretizing parameter h and suboptimal in the degree of polynomial p. Due to the presence of the integral term, an introduction of an expanded mixed type Ritz-Volterra projection helps us to achieve optimal estimates. Further, it is observed that a negative norm estimate of the gradient plays a crucial role in our convergence analysis. As in the elliptic case, similar results on order of convergence are established for the semidiscrete method after suitably modifying the numerical fluxes. The optimality of these theoretical results is tested in a series of numerical experiments on two dimensional domains. © 2010 Springer Science+Business Media, LLC.

Propel: A Discontinuous-Galerkin Finite Element Code for Solving the Reacting Navier-Stokes Equations

Science.gov (United States)

Johnson, Ryan; Kercher, Andrew; Schwer, Douglas; Corrigan, Andrew; Kailasanath, Kazhikathra

2017-11-01

This presentation focuses on the development of a Discontinuous Galerkin (DG) method for application to chemically reacting flows. The in-house code, called Propel, was developed by the Laboratory of Computational Physics and Fluid Dynamics at the Naval Research Laboratory. It was designed specifically for developing advanced multi-dimensional algorithms to run efficiently on new and innovative architectures such as GPUs. For these results, Propel solves for convection and diffusion simultaneously with detailed transport and thermodynamics. Chemistry is currently solved in a time-split approach using Strang-splitting with finite element DG time integration of chemical source terms. Results presented here show canonical unsteady reacting flow cases, such as co-flow and splitter plate, and we report performance for higher order DG on CPU and GPUs.

Analysis of a combined mixed finite element and discontinuous Galerkin method for incompressible two-phase flow in porous media

KAUST Repository

Kou, Jisheng; Sun, Shuyu

2013-01-01

We analyze a combined method consisting of the mixed finite element method for pressure equation and the discontinuous Galerkin method for saturation equation for the coupled system of incompressible two-phase flow in porous media. The existence and uniqueness of numerical solutions are established under proper conditions by using a constructive approach. Optimal error estimates in L2(H1) for saturation and in L∞(H(div)) for velocity are derived. Copyright © 2013 John Wiley & Sons, Ltd.

Analysis of a combined mixed finite element and discontinuous Galerkin method for incompressible two-phase flow in porous media

KAUST Repository

Kou, Jisheng

2013-06-20

We analyze a combined method consisting of the mixed finite element method for pressure equation and the discontinuous Galerkin method for saturation equation for the coupled system of incompressible two-phase flow in porous media. The existence and uniqueness of numerical solutions are established under proper conditions by using a constructive approach. Optimal error estimates in L2(H1) for saturation and in L∞(H(div)) for velocity are derived. Copyright © 2013 John Wiley & Sons, Ltd.

Numerical simulation of the interaction between a nonlinear elastic structure and compressible flow by the discontinuous Galerkin method

Czech Academy of Sciences Publication Activity Database

Kosík, Adam; Feistauer, M.; Hadrava, Martin; Horáček, Jaromír

2015-01-01

Roč. 267, September (2015), s. 382-396 ISSN 0096-3003 R&D Projects: GA ČR(CZ) GAP101/11/0207 Institutional support: RVO:61388998 Keywords : discontinuous Galerkin method * nonlinear elasticity * compressible viscous flow * fluid–structure interaction Subject RIV: BI - Acoustics Impact factor: 1.345, year: 2015 http://www.sciencedirect.com/science/article/pii/S0096300315002453/pdfft?md5=02d46bc730e3a7fb8a5008aaab1da786&pid=1-s2.0-S0096300315002453-main.pdf

High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms

International Nuclear Information System (INIS)

Xing Yulong; Shu Chiwang

2006-01-01

Hyperbolic balance laws have steady state solutions in which the flux gradients are nonzero but are exactly balanced by the source term. In our earlier work [J. Comput. Phys. 208 (2005) 206-227; J. Sci. Comput., accepted], we designed a well-balanced finite difference weighted essentially non-oscillatory (WENO) scheme, which at the same time maintains genuine high order accuracy for general solutions, to a class of hyperbolic systems with separable source terms including the shallow water equations, the elastic wave equation, the hyperbolic model for a chemosensitive movement, the nozzle flow and a two phase flow model. In this paper, we generalize high order finite volume WENO schemes and Runge-Kutta discontinuous Galerkin (RKDG) finite element methods to the same class of hyperbolic systems to maintain a well-balanced property. Finite volume and discontinuous Galerkin finite element schemes are more flexible than finite difference schemes to treat complicated geometry and adaptivity. However, because of a different computational framework, the maintenance of the well-balanced property requires different technical approaches. After the description of our well-balanced high order finite volume WENO and RKDG schemes, we perform extensive one and two dimensional simulations to verify the properties of these schemes such as the exact preservation of the balance laws for certain steady state solutions, the non-oscillatory property for general solutions with discontinuities, and the genuine high order accuracy in smooth regions

A Reconstruction Approach to High-Order Schemes Including Discontinuous Galerkin for Diffusion

Science.gov (United States)

Huynh, H. T.

2009-01-01

We introduce a new approach to high-order accuracy for the numerical solution of diffusion problems by solving the equations in differential form using a reconstruction technique. The approach has the advantages of simplicity and economy. It results in several new high-order methods including a simplified version of discontinuous Galerkin (DG). It also leads to new definitions of common value and common gradient quantities at each interface shared by the two adjacent cells. In addition, the new approach clarifies the relations among the various choices of new and existing common quantities. Fourier stability and accuracy analyses are carried out for the resulting schemes. Extensions to the case of quadrilateral meshes are obtained via tensor products. For the two-point boundary value problem (steady state), it is shown that these schemes, which include most popular DG methods, yield exact common interface quantities as well as exact cell average solutions for nearly all cases.

A discontinuous galerkin time domain-boundary integral method for analyzing transient electromagnetic scattering

KAUST Repository

Li, Ping

2014-07-01

This paper presents an algorithm hybridizing discontinuous Galerkin time domain (DGTD) method and time domain boundary integral (BI) algorithm for 3-D open region electromagnetic scattering analysis. The computational domain of DGTD is rigorously truncated by analytically evaluating the incoming numerical flux from the outside of the truncation boundary through BI method based on the Huygens\\' principle. The advantages of the proposed method are that it allows the truncation boundary to be conformal to arbitrary (convex/ concave) scattering objects, well-separated scatters can be truncated by their local meshes without losing the physics (such as coupling/multiple scattering) of the problem, thus reducing the total mesh elements. Furthermore, low frequency waves can be efficiently absorbed, and the field outside the truncation domain can be conveniently calculated using the same BI formulation. Numerical examples are benchmarked to demonstrate the accuracy and versatility of the proposed method.

On discontinuous Galerkin and discrete ordinates approximations for neutron transport equation and the critical eigenvalue

International Nuclear Information System (INIS)

Asadzadeh, M.; Thevenot, L.

2010-01-01

The objective of this paper is to give a mathematical framework for a fully discrete numerical approach for the study of the neutron transport equation in a cylindrical domain (container model,). More specifically, we consider the discontinuous Galerkin (D G) finite element method for spatial approximation of the mono-energetic, critical neutron transport equation in an infinite cylindrical domain ??in R3 with a polygonal convex cross-section ? The velocity discretization relies on a special quadrature rule developed to give optimal estimates in discrete ordinate parameters compatible with the quasi-uniform spatial mesh. We use interpolation spaces and derive optimal error estimates, up to maximal available regularity, for the fully discrete scalar flux. Finally we employ a duality argument and prove superconvergence estimates for the critical eigenvalue.

Extending the Riemann-Solver-Free High-Order Space-Time Discontinuous Galerkin Cell Vertex Scheme (DG-CVS) to Solve Compressible Magnetohydrodynamics Equations

Science.gov (United States)

2016-06-08

Ideal Magnetohydrodynamics,” J. Com- put. Phys., Vol. 153, No. 2, 1999, pp. 334–352. [14] Tang, H.-Z. and Xu, K., “A high-order gas -kinetic method for...notwithstanding any other provision of law , no person shall be subject to any penalty for failing to comply with a collection of information if it does...Riemann-solver-free spacetime discontinuous Galerkin method for general conservation laws to solve compressible magnetohydrodynamics (MHD) equations. The

On the stability of projection methods for the incompressible Navier-Stokes equations based on high-order discontinuous Galerkin discretizations

Science.gov (United States)

Fehn, Niklas; Wall, Wolfgang A.; Kronbichler, Martin

2017-12-01

The present paper deals with the numerical solution of the incompressible Navier-Stokes equations using high-order discontinuous Galerkin (DG) methods for discretization in space. For DG methods applied to the dual splitting projection method, instabilities have recently been reported that occur for small time step sizes. Since the critical time step size depends on the viscosity and the spatial resolution, these instabilities limit the robustness of the Navier-Stokes solver in case of complex engineering applications characterized by coarse spatial resolutions and small viscosities. By means of numerical investigation we give evidence that these instabilities are related to the discontinuous Galerkin formulation of the velocity divergence term and the pressure gradient term that couple velocity and pressure. Integration by parts of these terms with a suitable definition of boundary conditions is required in order to obtain a stable and robust method. Since the intermediate velocity field does not fulfill the boundary conditions prescribed for the velocity, a consistent boundary condition is derived from the convective step of the dual splitting scheme to ensure high-order accuracy with respect to the temporal discretization. This new formulation is stable in the limit of small time steps for both equal-order and mixed-order polynomial approximations. Although the dual splitting scheme itself includes inf-sup stabilizing contributions, we demonstrate that spurious pressure oscillations appear for equal-order polynomials and small time steps highlighting the necessity to consider inf-sup stability explicitly.

On discontinuous Galerkin approach for atmospheric flow in the mesoscale with and without moisture

Directory of Open Access Journals (Sweden)

Dieter Schuster

2014-09-01

Full Text Available We present and discuss discontinuous Galerkin (DG schemes for dry and moist atmospheric flows in the mesoscale. We derive terrain-following coordinates on the sphere in strong-conservation form, which makes it possible to perform the computation on a Cartesian grid and yet conserves the momentum density on an f$f$-plane. A new DG model, i.e. DG-COSMO, is compared to the operational model COSMO of the Deutscher Wetterdienst (DWD. A simplified version of the suggested terrain-following coordinates is implemented in DG-COSMO and is compared against the DG dynamical core implemented within the DUNE framework, which uses unstructured grids to capture orography. Finally, a few idealised test cases, including 3d and moisture, are used for validation. In addition an estimate of efficiency for locally adaptive grids is derived for locally and non-locally occurring phenomena.

Accurate characterization of 3D diffraction gratings using time domain discontinuous Galerkin method with exact absorbing boundary conditions

KAUST Repository

Sirenko, Kostyantyn

2013-07-01

Exact absorbing and periodic boundary conditions allow to truncate grating problems\\' infinite physical domains without introducing any errors. This work presents exact absorbing boundary conditions for 3D diffraction gratings and describes their discretization within a high-order time-domain discontinuous Galerkin finite element method (TD-DG-FEM). The error introduced by the boundary condition discretization matches that of the TD-DG-FEM; this results in an optimal solver in terms of accuracy and computation time. Numerical results demonstrate the superiority of this solver over TD-DG-FEM with perfectly matched layers (PML)-based domain truncation. © 2013 IEEE.

CosmosDG: An hp-adaptive Discontinuous Galerkin Code for Hyper-resolved Relativistic MHD

Science.gov (United States)

Anninos, Peter; Bryant, Colton; Fragile, P. Chris; Holgado, A. Miguel; Lau, Cheuk; Nemergut, Daniel

2017-08-01

We have extended Cosmos++, a multidimensional unstructured adaptive mesh code for solving the covariant Newtonian and general relativistic radiation magnetohydrodynamic (MHD) equations, to accommodate both discrete finite volume and arbitrarily high-order finite element structures. The new finite element implementation, called CosmosDG, is based on a discontinuous Galerkin (DG) formulation, using both entropy-based artificial viscosity and slope limiting procedures for the regularization of shocks. High-order multistage forward Euler and strong-stability preserving Runge-Kutta time integration options complement high-order spatial discretization. We have also added flexibility in the code infrastructure allowing for both adaptive mesh and adaptive basis order refinement to be performed separately or simultaneously in a local (cell-by-cell) manner. We discuss in this report the DG formulation and present tests demonstrating the robustness, accuracy, and convergence of our numerical methods applied to special and general relativistic MHD, although we note that an equivalent capability currently also exists in CosmosDG for Newtonian systems.

CosmosDG: An hp -adaptive Discontinuous Galerkin Code for Hyper-resolved Relativistic MHD

Energy Technology Data Exchange (ETDEWEB)

Anninos, Peter; Lau, Cheuk [Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, CA 94550 (United States); Bryant, Colton [Department of Engineering Sciences and Applied Mathematics, Northwestern University, 2145 Sheridan Road, Evanston, Illinois, 60208 (United States); Fragile, P. Chris [Department of Physics and Astronomy, College of Charleston, 66 George Street, Charleston, SC 29424 (United States); Holgado, A. Miguel [Department of Astronomy and National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign, Urbana, Illinois, 61801 (United States); Nemergut, Daniel [Operations and Engineering Division, Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218 (United States)

2017-08-01

We have extended Cosmos++, a multidimensional unstructured adaptive mesh code for solving the covariant Newtonian and general relativistic radiation magnetohydrodynamic (MHD) equations, to accommodate both discrete finite volume and arbitrarily high-order finite element structures. The new finite element implementation, called CosmosDG, is based on a discontinuous Galerkin (DG) formulation, using both entropy-based artificial viscosity and slope limiting procedures for the regularization of shocks. High-order multistage forward Euler and strong-stability preserving Runge–Kutta time integration options complement high-order spatial discretization. We have also added flexibility in the code infrastructure allowing for both adaptive mesh and adaptive basis order refinement to be performed separately or simultaneously in a local (cell-by-cell) manner. We discuss in this report the DG formulation and present tests demonstrating the robustness, accuracy, and convergence of our numerical methods applied to special and general relativistic MHD, although we note that an equivalent capability currently also exists in CosmosDG for Newtonian systems.

CosmosDG: An hp -adaptive Discontinuous Galerkin Code for Hyper-resolved Relativistic MHD

International Nuclear Information System (INIS)

Anninos, Peter; Lau, Cheuk; Bryant, Colton; Fragile, P. Chris; Holgado, A. Miguel; Nemergut, Daniel

2017-01-01

We have extended Cosmos++, a multidimensional unstructured adaptive mesh code for solving the covariant Newtonian and general relativistic radiation magnetohydrodynamic (MHD) equations, to accommodate both discrete finite volume and arbitrarily high-order finite element structures. The new finite element implementation, called CosmosDG, is based on a discontinuous Galerkin (DG) formulation, using both entropy-based artificial viscosity and slope limiting procedures for the regularization of shocks. High-order multistage forward Euler and strong-stability preserving Runge–Kutta time integration options complement high-order spatial discretization. We have also added flexibility in the code infrastructure allowing for both adaptive mesh and adaptive basis order refinement to be performed separately or simultaneously in a local (cell-by-cell) manner. We discuss in this report the DG formulation and present tests demonstrating the robustness, accuracy, and convergence of our numerical methods applied to special and general relativistic MHD, although we note that an equivalent capability currently also exists in CosmosDG for Newtonian systems.

A discontinuous Galerkin method for P-wave modeling in tilted TI media

KAUST Repository

Amler, Thomas; Alkhalifah, Tariq Ali; Hoteit, Ibrahim

2014-01-01

The acoustic approximation is an efficient alternative to the equations of elastodynamics for modeling Pwave propagation in weakly anisotropic media. We present a stable discontinuous Galerkin (DG) method for solving the acoustic approximation in tilted TI media (acoustic TI approximation). The acoustic TI approximation is considered as a modification of the equations of elastodynamics from which a modified energy is derived. The modified energy is obtained by eliminating the shear stress in the coordinates determined by the tilt angle and finding an energy for the remaining unknowns. This construction is valid if the medium is not elliptically anisotropic, a requirement frequently found in the literature. In the fully discrete setting, the modified energy is also conserved in time the presence of sharp contrasts in material parameters. By construction, the scheme can be coupled to the (fully) acoustic wave equation in the same way as the equations of elastodynamics. Hence, the number of unknowns can be reduced in acoustic regions. Our numerical examples confirm the conservation of energy in the discrete setting and the stability of the scheme.

Discontinuous Petrov-Galerkin method based on the optimal test space norm for steady transport problems in one space dimension

KAUST Repository

Niemi, Antti

2013-05-01

We revisit the finite element analysis of convection-dominated flow problems within the recently developed Discontinuous Petrov-Galerkin (DPG) variational framework. We demonstrate how test function spaces that guarantee numerical stability can be computed automatically with respect to the optimal test space norm. This makes the DPG method not only stable but also robust, that is, uniformly stable with respect to the Péclet number in the current application. We employ discontinuous piecewise Bernstein polynomials as trial functions and construct a subgrid discretization that accounts for the singular perturbation character of the problem to resolve the corresponding optimal test functions. We also show that a smooth B-spline basis has certain computational advantages in the subgrid discretization. The overall effectiveness of the algorithm is demonstrated on two problems for the linear advection-diffusion equation. © 2011 Elsevier B.V.

Discontinuous Petrov-Galerkin method based on the optimal test space norm for steady transport problems in one space dimension

KAUST Repository

Niemi, Antti; Collier, Nathan; Calo, Victor M.

2013-01-01

We revisit the finite element analysis of convection-dominated flow problems within the recently developed Discontinuous Petrov-Galerkin (DPG) variational framework. We demonstrate how test function spaces that guarantee numerical stability can be computed automatically with respect to the optimal test space norm. This makes the DPG method not only stable but also robust, that is, uniformly stable with respect to the Péclet number in the current application. We employ discontinuous piecewise Bernstein polynomials as trial functions and construct a subgrid discretization that accounts for the singular perturbation character of the problem to resolve the corresponding optimal test functions. We also show that a smooth B-spline basis has certain computational advantages in the subgrid discretization. The overall effectiveness of the algorithm is demonstrated on two problems for the linear advection-diffusion equation. © 2011 Elsevier B.V.

An upwind space-time conservation element and solution element scheme for solving dusty gas flow model

Science.gov (United States)

Rehman, Asad; Ali, Ishtiaq; Qamar, Shamsul

An upwind space-time conservation element and solution element (CE/SE) scheme is extended to numerically approximate the dusty gas flow model. Unlike central CE/SE schemes, the current method uses the upwind procedure to derive the numerical fluxes through the inner boundary of conservation elements. These upwind fluxes are utilized to calculate the gradients of flow variables. For comparison and validation, the central upwind scheme is also applied to solve the same dusty gas flow model. The suggested upwind CE/SE scheme resolves the contact discontinuities more effectively and preserves the positivity of flow variables in low density flows. Several case studies are considered and the results of upwind CE/SE are compared with the solutions of central upwind scheme. The numerical results show better performance of the upwind CE/SE method as compared to the central upwind scheme.

Equivalence between the Energy Stable Flux Reconstruction and Filtered Discontinuous Galerkin Schemes

Science.gov (United States)

Zwanenburg, Philip; Nadarajah, Siva

2016-02-01

The aim of this paper is to demonstrate the equivalence between filtered Discontinuous Galerkin (DG) schemes and the Energy Stable Flux Reconstruction (ESFR) schemes, expanding on previous demonstrations in 1D [1] and for straight-sided elements in 3D [2]. We first derive the DG and ESFR schemes in strong form and compare the respective flux penalization terms while highlighting the implications of the fundamental assumptions for stability in the ESFR formulations, notably that all ESFR scheme correction fields can be interpreted as modally filtered DG correction fields. We present the result in the general context of all higher dimensional curvilinear element formulations. Through a demonstration that there exists a weak form of the ESFR schemes which is both discretely and analytically equivalent to the strong form, we then extend the results obtained for the strong formulations to demonstrate that ESFR schemes can be interpreted as a DG scheme in weak form where discontinuous edge flux is substituted for numerical edge flux correction. Theoretical derivations are then verified with numerical results obtained from a 2D Euler testcase with curved boundaries. Given the current choice of high-order DG-type schemes and the question as to which might be best to use for a specific application, the main significance of this work is the bridge that it provides between them. Clearly outlining the similarities between the schemes results in the important conclusion that it is always less efficient to use ESFR schemes, as opposed to the weak DG scheme, when solving problems implicitly.

High-order polygonal discontinuous Petrov-Galerkin (PolyDPG) methods using ultraweak formulations

Science.gov (United States)

Vaziri Astaneh, Ali; Fuentes, Federico; Mora, Jaime; Demkowicz, Leszek

2018-04-01

This work represents the first endeavor in using ultraweak formulations to implement high-order polygonal finite element methods via the discontinuous Petrov-Galerkin (DPG) methodology. Ultraweak variational formulations are nonstandard in that all the weight of the derivatives lies in the test space, while most of the trial space can be chosen as copies of $L^2$-discretizations that have no need to be continuous across adjacent elements. Additionally, the test spaces are broken along the mesh interfaces. This allows one to construct conforming polygonal finite element methods, termed here as PolyDPG methods, by defining most spaces by restriction of a bounding triangle or box to the polygonal element. The only variables that require nontrivial compatibility across elements are the so-called interface or skeleton variables, which can be defined directly on the element boundaries. Unlike other high-order polygonal methods, PolyDPG methods do not require ad hoc stabilization terms thanks to the crafted stability of the DPG methodology. A proof of convergence of the form $h^p$ is provided and corroborated through several illustrative numerical examples. These include polygonal meshes with $n$-sided convex elements and with highly distorted concave elements, as well as the modeling of discontinuous material properties along an arbitrary interface that cuts a uniform grid. Since PolyDPG methods have a natural a posteriori error estimator a polygonal adaptive strategy is developed and compared to standard adaptivity schemes based on constrained hanging nodes. This work is also accompanied by an open-source $\\texttt{PolyDPG}$ software supporting polygonal and conventional elements.

Automatically stable discontinuous Petrov-Galerkin methods for stationary transport problems: Quasi-optimal test space norm

KAUST Repository

Niemi, Antti H.

2013-12-01

We investigate the application of the discontinuous Petrov-Galerkin (DPG) finite element framework to stationary convection-diffusion problems. In particular, we demonstrate how the quasi-optimal test space norm improves the robustness of the DPG method with respect to vanishing diffusion. We numerically compare coarse-mesh accuracy of the approximation when using the quasi-optimal norm, the standard norm, and the weighted norm. Our results show that the quasi-optimal norm leads to more accurate results on three benchmark problems in two spatial dimensions. We address the problems associated to the resolution of the optimal test functions with respect to the quasi-optimal norm by studying their convergence numerically. In order to facilitate understanding of the method, we also include a detailed explanation of the methodology from the algorithmic point of view. © 2013 Elsevier Ltd. All rights reserved.

Automatically stable discontinuous Petrov-Galerkin methods for stationary transport problems: Quasi-optimal test space norm

KAUST Repository

Niemi, Antti H.; Collier, Nathan; Calo, Victor M.

2013-01-01

We investigate the application of the discontinuous Petrov-Galerkin (DPG) finite element framework to stationary convection-diffusion problems. In particular, we demonstrate how the quasi-optimal test space norm improves the robustness of the DPG method with respect to vanishing diffusion. We numerically compare coarse-mesh accuracy of the approximation when using the quasi-optimal norm, the standard norm, and the weighted norm. Our results show that the quasi-optimal norm leads to more accurate results on three benchmark problems in two spatial dimensions. We address the problems associated to the resolution of the optimal test functions with respect to the quasi-optimal norm by studying their convergence numerically. In order to facilitate understanding of the method, we also include a detailed explanation of the methodology from the algorithmic point of view. © 2013 Elsevier Ltd. All rights reserved.

Approximate tensor-product preconditioners for very high order discontinuous Galerkin methods

Science.gov (United States)

Pazner, Will; Persson, Per-Olof

2018-02-01

In this paper, we develop a new tensor-product based preconditioner for discontinuous Galerkin methods with polynomial degrees higher than those typically employed. This preconditioner uses an automatic, purely algebraic method to approximate the exact block Jacobi preconditioner by Kronecker products of several small, one-dimensional matrices. Traditional matrix-based preconditioners require O (p2d) storage and O (p3d) computational work, where p is the degree of basis polynomials used, and d is the spatial dimension. Our SVD-based tensor-product preconditioner requires O (p d + 1) storage, O (p d + 1) work in two spatial dimensions, and O (p d + 2) work in three spatial dimensions. Combined with a matrix-free Newton-Krylov solver, these preconditioners allow for the solution of DG systems in linear time in p per degree of freedom in 2D, and reduce the computational complexity from O (p9) to O (p5) in 3D. Numerical results are shown in 2D and 3D for the advection, Euler, and Navier-Stokes equations, using polynomials of degree up to p = 30. For many test cases, the preconditioner results in similar iteration counts when compared with the exact block Jacobi preconditioner, and performance is significantly improved for high polynomial degrees p.

An Online Generalized Multiscale Discontinuous Galerkin Method (GMsDGM) for Flows in Heterogeneous Media

KAUST Repository

Chung, Eric T.

2017-02-07

Offline computation is an essential component in most multiscale model reduction techniques. However, there are multiscale problems in which offline procedure is insufficient to give accurate representations of solutions, due to the fact that offline computations are typically performed locally and global information is missing in these offline information. To tackle this difficulty, we develop an online local adaptivity technique for local multiscale model reduction problems. We design new online basis functions within Discontinuous Galerkin method based on local residuals and some optimally estimates. The resulting basis functions are able to capture the solution efficiently and accurately, and are added to the approximation iteratively. Moreover, we show that the iterative procedure is convergent with a rate independent of physical scales if the initial space is chosen carefully. Our analysis also gives a guideline on how to choose the initial space. We present some numerical examples to show the performance of the proposed method.

Reactivity perturbation formulation for a discontinuous Galerkin-based transport solver and its use with adaptive mesh refinement

International Nuclear Information System (INIS)

Le Tellier, R.; Fournier, D.; Suteau, C.

2011-01-01

Within the framework of a Discontinuous Galerkin spatial approximation of the multigroup discrete ordinates transport equation, we present a generalization of the exact standard perturbation formula that takes into account spatial discretization-induced reactivity changes. It encompasses in two separate contributions the nuclear data-induced reactivity change and the reactivity modification induced by two different spatial discretizations. The two potential uses of such a formulation when considering adaptive mesh refinement are discussed, and numerical results on a simple two-group Cartesian two-dimensional benchmark are provided. In particular, such a formulation is shown to be useful to filter out a more accurate estimate of nuclear data-related reactivity effects from initial and perturbed calculations based on independent adaptation processes. (authors)

Advances in the discontinuous Galerkin method: Hybrid schemes and applications to the reactive infiltration instability in an upwelling compacting mantle

Science.gov (United States)

Schiemenz, Alan R.

High-order methods are emerging in the scientific computing community as superior alternatives to the classical finite difference, finite volume, and continuous finite element methods. The discontinuous Galerkin (DG) method in particular combines many of the positive features of all of these methods. This thesis presents two projects involving the DG method. First, a Hybrid scheme is presented, which implements DG areas where the solution is considered smooth, while dropping the order of the scheme elsewhere and implementing a finite volume scheme with high-order, non-oscillatory solution reconstructions suitable for unstructured mesh. Two such reconstructions from the ENO class are considered in the Hybrid. Successful numerical results are presented for nonlinear systems of conservation laws in one dimension. Second, the high-order discontinuous Galerkin and Fourier spectral methods are applied to an application modeling three-phase fluid flow through a porous medium, undergoing solid-fluid reaction due to the reactive infiltration instability (RII). This model incorporates a solid upwelling term and an equation to track the abundance of the reacting mineral orthopyroxene (opx). After validating the numerical discretization, results are given that provide new insight into the formation of melt channels in the Earth's mantle. Mantle heterogeneities are observed to be one catalyst for the development of melt channels, and the dissolution of opx produces interesting bifurcations in the melt channels. An alternative formulation is considered where the mass transfer rate relative to velocity is taken to be infinitely large. In this setting, the stiffest terms are removed, greatly reducing the cost of time integration.

PHYSICAL-CONSTRAINT-PRESERVING CENTRAL DISCONTINUOUS GALERKIN METHODS FOR SPECIAL RELATIVISTIC HYDRODYNAMICS WITH A GENERAL EQUATION OF STATE

Energy Technology Data Exchange (ETDEWEB)

Wu, Kailiang [School of Mathematical Sciences, Peking University, Beijing 100871 (China); Tang, Huazhong, E-mail: wukl@pku.edu.cn, E-mail: hztang@math.pku.edu.cn [HEDPS, CAPT and LMAM, School of Mathematical Sciences, Peking University, Beijing 100871 (China)

2017-01-01

The ideal gas equation of state (EOS) with a constant adiabatic index is a poor approximation for most relativistic astrophysical flows, although it is commonly used in relativistic hydrodynamics (RHD). This paper develops high-order accurate, physical-constraints-preserving (PCP), central, discontinuous Galerkin (DG) methods for the one- and two-dimensional special RHD equations with a general EOS. It is built on our theoretical analysis of the admissible states for RHD and the PCP limiting procedure that enforce the admissibility of central DG solutions. The convexity, scaling invariance, orthogonal invariance, and Lax–Friedrichs splitting property of the admissible state set are first proved with the aid of its equivalent form. Then, the high-order central DG methods with the PCP limiting procedure and strong stability-preserving time discretization are proved, to preserve the positivity of the density, pressure, specific internal energy, and the bound of the fluid velocity, maintain high-order accuracy, and be L {sup 1}-stable. The accuracy, robustness, and effectiveness of the proposed methods are demonstrated by several 1D and 2D numerical examples involving large Lorentz factor, strong discontinuities, or low density/pressure, etc.

Adaptive local basis set for Kohn–Sham density functional theory in a discontinuous Galerkin framework I: Total energy calculation

International Nuclear Information System (INIS)

Lin Lin; Lu Jianfeng; Ying Lexing; Weinan, E

2012-01-01

Kohn–Sham density functional theory is one of the most widely used electronic structure theories. In the pseudopotential framework, uniform discretization of the Kohn–Sham Hamiltonian generally results in a large number of basis functions per atom in order to resolve the rapid oscillations of the Kohn–Sham orbitals around the nuclei. Previous attempts to reduce the number of basis functions per atom include the usage of atomic orbitals and similar objects, but the atomic orbitals generally require fine tuning in order to reach high accuracy. We present a novel discretization scheme that adaptively and systematically builds the rapid oscillations of the Kohn–Sham orbitals around the nuclei as well as environmental effects into the basis functions. The resulting basis functions are localized in the real space, and are discontinuous in the global domain. The continuous Kohn–Sham orbitals and the electron density are evaluated from the discontinuous basis functions using the discontinuous Galerkin (DG) framework. Our method is implemented in parallel and the current implementation is able to handle systems with at least thousands of atoms. Numerical examples indicate that our method can reach very high accuracy (less than 1 meV) with a very small number (4–40) of basis functions per atom.

Optimal Strong-Stability-Preserving Runge–Kutta Time Discretizations for Discontinuous Galerkin Methods

KAUST Repository

Kubatko, Ethan J.; Yeager, Benjamin A.; Ketcheson, David I.

2013-01-01

Discontinuous Galerkin (DG) spatial discretizations are often used in a method-of-lines approach with explicit strong-stability-preserving (SSP) Runge–Kutta (RK) time steppers for the numerical solution of hyperbolic conservation laws. The time steps that are employed in this type of approach must satisfy Courant–Friedrichs–Lewy stability constraints that are dependent on both the region of absolute stability and the SSP coefficient of the RK method. While existing SSPRK methods have been optimized with respect to the latter, it is in fact the former that gives rise to stricter constraints on the time step in the case of RKDG stability. Therefore, in this work, we present the development of new “DG-optimized” SSPRK methods with stability regions that have been specifically designed to maximize the stable time step size for RKDG methods of a given order in one space dimension. These new methods represent the best available RKDG methods in terms of computational efficiency, with significant improvements over methods using existing SSPRK time steppers that have been optimized with respect to SSP coefficients. Second-, third-, and fourth-order methods with up to eight stages are presented, and their stability properties are verified through application to numerical test cases.

Optimal Strong-Stability-Preserving Runge–Kutta Time Discretizations for Discontinuous Galerkin Methods

KAUST Repository

Kubatko, Ethan J.

2013-10-29

Discontinuous Galerkin (DG) spatial discretizations are often used in a method-of-lines approach with explicit strong-stability-preserving (SSP) Runge–Kutta (RK) time steppers for the numerical solution of hyperbolic conservation laws. The time steps that are employed in this type of approach must satisfy Courant–Friedrichs–Lewy stability constraints that are dependent on both the region of absolute stability and the SSP coefficient of the RK method. While existing SSPRK methods have been optimized with respect to the latter, it is in fact the former that gives rise to stricter constraints on the time step in the case of RKDG stability. Therefore, in this work, we present the development of new “DG-optimized” SSPRK methods with stability regions that have been specifically designed to maximize the stable time step size for RKDG methods of a given order in one space dimension. These new methods represent the best available RKDG methods in terms of computational efficiency, with significant improvements over methods using existing SSPRK time steppers that have been optimized with respect to SSP coefficients. Second-, third-, and fourth-order methods with up to eight stages are presented, and their stability properties are verified through application to numerical test cases.

Implicit high-order discontinuous Galerkin method with HWENO type limiters for steady viscous flow simulations

Science.gov (United States)

Jiang, Zhen-Hua; Yan, Chao; Yu, Jian

2013-08-01

Two types of implicit algorithms have been improved for high order discontinuous Galerkin (DG) method to solve compressible Navier-Stokes (NS) equations on triangular grids. A block lower-upper symmetric Gauss-Seidel (BLU-SGS) approach is implemented as a nonlinear iterative scheme. And a modified LU-SGS (LLU-SGS) approach is suggested to reduce the memory requirements while retain the good convergence performance of the original LU-SGS approach. Both implicit schemes have the significant advantage that only the diagonal block matrix is stored. The resulting implicit high-order DG methods are applied, in combination with Hermite weighted essentially non-oscillatory (HWENO) limiters, to solve viscous flow problems. Numerical results demonstrate that the present implicit methods are able to achieve significant efficiency improvements over explicit counterparts and for viscous flows with shocks, and the HWENO limiters can be used to achieve the desired essentially non-oscillatory shock transition and the designed high-order accuracy simultaneously.

Runge-Kutta discontinuous Galerkin method using a new type of WENO limiters on unstructured meshes

Science.gov (United States)

Zhu, Jun; Zhong, Xinghui; Shu, Chi-Wang; Qiu, Jianxian

2013-09-01

In this paper we generalize a new type of limiters based on the weighted essentially non-oscillatory (WENO) finite volume methodology for the Runge-Kutta discontinuous Galerkin (RKDG) methods solving nonlinear hyperbolic conservation laws, which were recently developed in [32] for structured meshes, to two-dimensional unstructured triangular meshes. The key idea of such limiters is to use the entire polynomials of the DG solutions from the troubled cell and its immediate neighboring cells, and then apply the classical WENO procedure to form a convex combination of these polynomials based on smoothness indicators and nonlinear weights, with suitable adjustments to guarantee conservation. The main advantage of this new limiter is its simplicity in implementation, especially for the unstructured meshes considered in this paper, as only information from immediate neighbors is needed and the usage of complicated geometric information of the meshes is largely avoided. Numerical results for both scalar equations and Euler systems of compressible gas dynamics are provided to illustrate the good performance of this procedure.

Dynamic Mesh Adaptation for Front Evolution Using Discontinuous Galerkin Based Weighted Condition Number Mesh Relaxation

Energy Technology Data Exchange (ETDEWEB)

Greene, Patrick T. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Schofield, Samuel P. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Nourgaliev, Robert [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2016-06-21

A new mesh smoothing method designed to cluster mesh cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function being computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered elds, such as a volume fraction or index function, is provided. Results show that the low-order level set works equally well for the weight function as the actual level set. Meshes generated for a number of interface geometries are presented, including cases with multiple level sets. Dynamic cases for moving interfaces are presented to demonstrate the method's potential usefulness to arbitrary Lagrangian Eulerian (ALE) methods.

The hybridized Discontinuous Galerkin method for Implicit Large-Eddy Simulation of transitional turbulent flows

Science.gov (United States)

Fernandez, P.; Nguyen, N. C.; Peraire, J.

2017-05-01

We present a high-order Implicit Large-Eddy Simulation (ILES) approach for transitional aerodynamic flows. The approach encompasses a hybridized Discontinuous Galerkin (DG) method for the discretization of the Navier-Stokes (NS) equations, and a parallel preconditioned Newton-GMRES solver for the resulting nonlinear system of equations. The combination of hybridized DG methods with an efficient solution procedure leads to a high-order accurate NS solver that is competitive to alternative approaches, such as finite volume and finite difference codes, in terms of computational cost. The proposed approach is applied to transitional flows over the NACA 65-(18)10 compressor cascade and the Eppler 387 wing at Reynolds numbers up to 460,000. Grid convergence studies are presented and the required resolution to capture transition at different Reynolds numbers is investigated. Numerical results show rapid convergence and excellent agreement with experimental data. In short, this work aims to demonstrate the potential of high-order ILES for simulating transitional aerodynamic flows. This is illustrated through numerical results and supported by theoretical considerations.

Entropy stable high order discontinuous Galerkin methods for ideal compressible MHD on structured meshes

Science.gov (United States)

Liu, Yong; Shu, Chi-Wang; Zhang, Mengping

2018-02-01

We present a discontinuous Galerkin (DG) scheme with suitable quadrature rules [15] for ideal compressible magnetohydrodynamic (MHD) equations on structural meshes. The semi-discrete scheme is analyzed to be entropy stable by using the symmetrizable version of the equations as introduced by Godunov [32], the entropy stable DG framework with suitable quadrature rules [15], the entropy conservative flux in [14] inside each cell and the entropy dissipative approximate Godunov type numerical flux at cell interfaces to make the scheme entropy stable. The main difficulty in the generalization of the results in [15] is the appearance of the non-conservative "source terms" added in the modified MHD model introduced by Godunov [32], which do not exist in the general hyperbolic system studied in [15]. Special care must be taken to discretize these "source terms" adequately so that the resulting DG scheme satisfies entropy stability. Total variation diminishing / bounded (TVD/TVB) limiters and bound-preserving limiters are applied to control spurious oscillations. We demonstrate the accuracy and robustness of this new scheme on standard MHD examples.

An Entropy Stable h/p Non-Conforming Discontinuous Galerkin Method with the Summation-by-Parts Property

KAUST Repository

Friedrich, Lucas

2017-12-29

This work presents an entropy stable discontinuous Galerkin (DG) spectral element approximation for systems of non-linear conservation laws with general geometric (h) and polynomial order (p) non-conforming rectangular meshes. The crux of the proofs presented is that the nodal DG method is constructed with the collocated Legendre-Gauss-Lobatto nodes. This choice ensures that the derivative/mass matrix pair is a summation-by-parts (SBP) operator such that entropy stability proofs from the continuous analysis are discretely mimicked. Special attention is given to the coupling between nonconforming elements as we demonstrate that the standard mortar approach for DG methods does not guarantee entropy stability for non-linear problems, which can lead to instabilities. As such, we describe a precise procedure and modify the mortar method to guarantee entropy stability for general non-linear hyperbolic systems on h/p non-conforming meshes. We verify the high-order accuracy and the entropy conservation/stability of fully non-conforming approximation with numerical examples.

A non-linear optimal Discontinuous Petrov-Galerkin method for stabilising the solution of the transport equation

International Nuclear Information System (INIS)

Merton, S. R.; Smedley-Stevenson, R. P.; Pain, C. C.; Buchan, A. G.; Eaton, M. D.

2009-01-01

This paper describes a new Non-Linear Discontinuous Petrov-Galerkin (NDPG) method and application to the one-speed Boltzmann Transport Equation (BTE) for space-time problems. The purpose of the method is to remove unwanted oscillations in the transport solution which occur in the vicinity of sharp flux gradients, while improving computational efficiency and numerical accuracy. This is achieved by applying artificial dissipation in the solution gradient direction, internal to an element using a novel finite element (FE) Riemann approach. The amount of dissipation added acts internal to each element. This is done using a gradient-informed scaling of the advection velocities in the stabilisation term. This makes the method in its most general form non-linear. The method is designed to be independent of angular expansion framework. This is demonstrated for the both discrete ordinates (S N ) and spherical harmonics (P N ) descriptions of the angular variable. Results show the scheme performs consistently well in demanding time dependent and multi-dimensional radiation transport problems. (authors)

Incorporation of exact boundary conditions into a discontinuous galerkin finite element method for accurately solving 2d time-dependent maxwell equations

KAUST Repository

Sirenko, Kostyantyn

2013-01-01

A scheme that discretizes exact absorbing boundary conditions (EACs) to incorporate them into a time-domain discontinuous Galerkin finite element method (TD-DG-FEM) is described. The proposed TD-DG-FEM with EACs is used for accurately characterizing transient electromagnetic wave interactions on two-dimensional waveguides. Numerical results demonstrate the proposed method\\'s superiority over the TD-DG-FEM that employs approximate boundary conditions and perfectly matched layers. Additionally, it is shown that the proposed method can produce the solution with ten-eleven digit accuracy when high-order spatial basis functions are used to discretize the Maxwell equations as well as the EACs. © 1963-2012 IEEE.

Multiscale Capability in Rattlesnake using Contiguous Discontinuous Discretization of Self-Adjoint Angular Flux Equation

Energy Technology Data Exchange (ETDEWEB)

Zheng, Weixiong [Texas A & M Univ., College Station, TX (United States); Wang, Yaqi [Idaho National Lab. (INL), Idaho Falls, ID (United States); DeHart, Mark D. [Idaho National Lab. (INL), Idaho Falls, ID (United States)

2016-09-01

In this report, we present a new upwinding scheme for the multiscale capability in Rattlesnake, the MOOSE based radiation transport application. Comparing with the initial implementation of multiscale utilizing Lagrange multipliers to impose strong continuity of angular flux on interface of in-between subdomains, this scheme does not require the particular domain partitioning. This upwinding scheme introduces discontinuity of angular flux and resembles the classic upwinding technique developed for solving first order transport equation using discontinuous finite element method (DFEM) on the subdomain interfaces. Because this scheme restores the causality of radiation streaming on the interfaces, significant accuracy improvement can be observed with moderate increase of the degrees of freedom comparing with the continuous method over the entire solution domain. Hybrid SN-PN is implemented and tested with this upwinding scheme. Numerical results show that the angular smoothing required by Lagrange multiplier method is not necessary for the upwinding scheme.

A discontinuous Galerkin approach for conservative modeling of fully nonlinear and weakly dispersive wave transformations

Science.gov (United States)

Sharifian, Mohammad Kazem; Kesserwani, Georges; Hassanzadeh, Yousef

2018-05-01

This work extends a robust second-order Runge-Kutta Discontinuous Galerkin (RKDG2) method to solve the fully nonlinear and weakly dispersive flows, within a scope to simultaneously address accuracy, conservativeness, cost-efficiency and practical needs. The mathematical model governing such flows is based on a variant form of the Green-Naghdi (GN) equations decomposed as a hyperbolic shallow water system with an elliptic source term. Practical features of relevance (i.e. conservative modeling over irregular terrain with wetting and drying and local slope limiting) have been restored from an RKDG2 solver to the Nonlinear Shallow Water (NSW) equations, alongside new considerations to integrate elliptic source terms (i.e. via a fourth-order local discretization of the topography) and to enable local capturing of breaking waves (i.e. via adding a detector for switching off the dispersive terms). Numerical results are presented, demonstrating the overall capability of the proposed approach in achieving realistic prediction of nearshore wave processes involving both nonlinearity and dispersion effects within a single model.

Dynamic mesh adaptation for front evolution using discontinuous Galerkin based weighted condition number relaxation

International Nuclear Information System (INIS)

Greene, Patrick T.; Schofield, Samuel P.; Nourgaliev, Robert

2017-01-01

A new mesh smoothing method designed to cluster cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered fields, such as a volume fraction or index function, is provided. Results show that the low-order level set works equally well as the actual level set for mesh smoothing. Meshes generated for a number of interface geometries are presented, including cases with multiple level sets. Lastly, dynamic cases with moving interfaces show the new method is capable of maintaining a desired resolution near the interface with an acceptable number of relaxation iterations per time step, which demonstrates the method's potential to be used as a mesh relaxer for arbitrary Lagrangian Eulerian (ALE) methods.

Diffusion and dispersion characteristics of hybridized discontinuous Galerkin methods for under-resolved turbulence simulations

Science.gov (United States)

Moura, Rodrigo; Fernandez, Pablo; Mengaldo, Gianmarco

2017-11-01

We investigate the dispersion and diffusion characteristics of hybridized discontinuous Galerkin (DG) methods. This provides us with insights to develop robust and accurate high-order DG discretizations for under-resolved flow simulations. Using the eigenanalysis technique introduced in (Moura et al., JCP, 2015 and Mengaldo et al., Computers & Fluids, 2017), we present a dispersion-diffusion analysis for the linear advection-diffusion equation. The effect of the accuracy order, the Riemann flux and the viscous stabilization are investigated. Next, we examine the diffusion characteristics of hybridized DG methods for under-resolved turbulent flows. The implicit large-eddy simulation (iLES) of the inviscid and viscous Taylor-Green vortex (TGV) problems are considered to this end. The inviscid case is relevant in the limit of high Reynolds numbers Re , i.e. negligible molecular viscosity, while the viscous case explores the effect of Re on the accuracy and robustness of the simulations. The TGV cases considered here are particularly crucial to under-resolved turbulent free flows away from walls. We conclude the talk with a discussion on the connections between hybridized and standard DG methods for under-resolved flow simulations.

Hybrid Fourier pseudospectral/discontinuous Galerkin time-domain method for wave propagation

Science.gov (United States)

Pagán Muñoz, Raúl; Hornikx, Maarten

2017-11-01

The Fourier Pseudospectral time-domain (Fourier PSTD) method was shown to be an efficient way of modelling acoustic propagation problems as described by the linearized Euler equations (LEE), but is limited to real-valued frequency independent boundary conditions and predominantly staircase-like boundary shapes. This paper presents a hybrid approach to solve the LEE, coupling Fourier PSTD with a nodal Discontinuous Galerkin (DG) method. DG exhibits almost no restrictions with respect to geometrical complexity or boundary conditions. The aim of this novel method is to allow the computation of complex geometries and to be a step towards the implementation of frequency dependent boundary conditions by using the benefits of DG at the boundaries, while keeping the efficient Fourier PSTD in the bulk of the domain. The hybridization approach is based on conformal meshes to avoid spatial interpolation of the DG solutions when transferring values from DG to Fourier PSTD, while the data transfer from Fourier PSTD to DG is done utilizing spectral interpolation of the Fourier PSTD solutions. The accuracy of the hybrid approach is presented for one- and two-dimensional acoustic problems and the main sources of error are investigated. It is concluded that the hybrid methodology does not introduce significant errors compared to the Fourier PSTD stand-alone solver. An example of a cylinder scattering problem is presented and accurate results have been obtained when using the proposed approach. Finally, no instabilities were found during long-time calculation using the current hybrid methodology on a two-dimensional domain.

Discontinuous Galerkin modeling of the Columbia River's coupled estuary-plume dynamics

Science.gov (United States)

Vallaeys, Valentin; Kärnä, Tuomas; Delandmeter, Philippe; Lambrechts, Jonathan; Baptista, António M.; Deleersnijder, Eric; Hanert, Emmanuel

2018-04-01

The Columbia River (CR) estuary is characterized by high river discharge and strong tides that generate high velocity flows and sharp density gradients. Its dynamics strongly affects the coastal ocean circulation. Tidal straining in turn modulates the stratification in the estuary. Simulating the hydrodynamics of the CR estuary and plume therefore requires a multi-scale model as both shelf and estuarine circulations are coupled. Such a model has to keep numerical dissipation as low as possible in order to correctly represent the plume propagation and the salinity intrusion in the estuary. Here, we show that the 3D baroclinic discontinuous Galerkin finite element model SLIM 3D is able to reproduce the main features of the CR estuary-to-ocean continuum. We introduce new vertical discretization and mode splitting that allow us to model a region characterized by complex bathymetry and sharp density and velocity gradients. Our model takes into account the major forcings, i.e. tides, surface wind stress and river discharge, on a single multi-scale grid. The simulation period covers the end of spring-early summer of 2006, a period of high river flow and strong changes in the wind regime. SLIM 3D is validated with in-situ data on the shelf and at multiple locations in the estuary and compared with an operational implementation of SELFE. The model skill in the estuary and on the shelf indicate that SLIM 3D is able to reproduce the key processes driving the river plume dynamics, such as the occurrence of bidirectional plumes or reversals of the inner shelf coastal currents.

Multilevel preconditioners for discontinuous, Galerkin approximations of elliptic problems, with jump coefficients

KAUST Repository

Ayuso Dios, Blanca

2013-10-30

We introduce and analyze two-level and multilevel preconditioners for a family of Interior Penalty (IP) discontinuous Galerkin (DG) discretizations of second order elliptic problems with large jumps in the diffusion coefficient. Our approach to IPDG-type methods is based on a splitting of the DG space into two components that are orthogonal in the energy inner product naturally induced by the methods. As a result, the methods and their analysis depend in a crucial way on the diffusion coefficient of the problem. The analysis of the proposed preconditioners is presented for both symmetric and non-symmetric IP schemes; dealing simultaneously with the jump in the diffusion coefficient and the non-nested character of the relevant discrete spaces presents additional difficulties in the analysis, which precludes a simple extension of existing results. However, we are able to establish robustness (with respect to the diffusion coefficient) and near-optimality (up to a logarithmic term depending on the mesh size) for both two-level and BPX-type preconditioners, by using a more refined Conjugate Gradient theory. Useful by-products of the analysis are the supporting results on the construction and analysis of simple, efficient and robust two-level and multilevel preconditioners for non-conforming Crouzeix-Raviart discretizations of elliptic problems with jump coefficients. Following the analysis, we present a sequence of detailed numerical results which verify the theory and illustrate the performance of the methods. © 2013 American Mathematical Society.

Multilevel preconditioners for discontinuous, Galerkin approximations of elliptic problems, with jump coefficients

KAUST Repository

Ayuso Dios, Blanca; Holst, Michael; Zhu, Yunrong; Zikatanov, Ludmil

2013-01-01

We introduce and analyze two-level and multilevel preconditioners for a family of Interior Penalty (IP) discontinuous Galerkin (DG) discretizations of second order elliptic problems with large jumps in the diffusion coefficient. Our approach to IPDG-type methods is based on a splitting of the DG space into two components that are orthogonal in the energy inner product naturally induced by the methods. As a result, the methods and their analysis depend in a crucial way on the diffusion coefficient of the problem. The analysis of the proposed preconditioners is presented for both symmetric and non-symmetric IP schemes; dealing simultaneously with the jump in the diffusion coefficient and the non-nested character of the relevant discrete spaces presents additional difficulties in the analysis, which precludes a simple extension of existing results. However, we are able to establish robustness (with respect to the diffusion coefficient) and near-optimality (up to a logarithmic term depending on the mesh size) for both two-level and BPX-type preconditioners, by using a more refined Conjugate Gradient theory. Useful by-products of the analysis are the supporting results on the construction and analysis of simple, efficient and robust two-level and multilevel preconditioners for non-conforming Crouzeix-Raviart discretizations of elliptic problems with jump coefficients. Following the analysis, we present a sequence of detailed numerical results which verify the theory and illustrate the performance of the methods. © 2013 American Mathematical Society.

Bound-Preserving Discontinuous Galerkin Methods for Conservative Phase Space Advection in Curvilinear Coordinates

Energy Technology Data Exchange (ETDEWEB)

Mezzacappa, Anthony [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Endeve, Eirik [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Hauck, Cory D. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Xing, Yulong [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

2015-02-01

We extend the positivity-preserving method of Zhang & Shu [49] to simulate the advection of neutral particles in phase space using curvilinear coordinates. The ability to utilize these coordinates is important for non-equilibrium transport problems in general relativity and also in science and engineering applications with specific geometries. The method achieves high-order accuracy using Discontinuous Galerkin (DG) discretization of phase space and strong stabilitypreserving, Runge-Kutta (SSP-RK) time integration. Special care in taken to ensure that the method preserves strict bounds for the phase space distribution function f; i.e., f ϵ [0, 1]. The combination of suitable CFL conditions and the use of the high-order limiter proposed in [49] is su cient to ensure positivity of the distribution function. However, to ensure that the distribution function satisfies the upper bound, the discretization must, in addition, preserve the divergencefree property of the phase space ow. Proofs that highlight the necessary conditions are presented for general curvilinear coordinates, and the details of these conditions are worked out for some commonly used coordinate systems (i.e., spherical polar spatial coordinates in spherical symmetry and cylindrical spatial coordinates in axial symmetry, both with spherical momentum coordinates). Results from numerical experiments - including one example in spherical symmetry adopting the Schwarzschild metric - demonstrate that the method achieves high-order accuracy and that the distribution function satisfies the maximum principle.

Edge reconstruction in armchair phosphorene nanoribbons revealed by discontinuous Galerkin density functional theory.

Science.gov (United States)

Hu, Wei; Lin, Lin; Yang, Chao

2015-12-21

With the help of our recently developed massively parallel DGDFT (Discontinuous Galerkin Density Functional Theory) methodology, we perform large-scale Kohn-Sham density functional theory calculations on phosphorene nanoribbons with armchair edges (ACPNRs) containing a few thousands to ten thousand atoms. The use of DGDFT allows us to systematically achieve a conventional plane wave basis set type of accuracy, but with a much smaller number (about 15) of adaptive local basis (ALB) functions per atom for this system. The relatively small number of degrees of freedom required to represent the Kohn-Sham Hamiltonian, together with the use of the pole expansion the selected inversion (PEXSI) technique that circumvents the need to diagonalize the Hamiltonian, results in a highly efficient and scalable computational scheme for analyzing the electronic structures of ACPNRs as well as their dynamics. The total wall clock time for calculating the electronic structures of large-scale ACPNRs containing 1080-10,800 atoms is only 10-25 s per self-consistent field (SCF) iteration, with accuracy fully comparable to that obtained from conventional planewave DFT calculations. For the ACPNR system, we observe that the DGDFT methodology can scale to 5000-50,000 processors. We use DGDFT based ab initio molecular dynamics (AIMD) calculations to study the thermodynamic stability of ACPNRs. Our calculations reveal that a 2 × 1 edge reconstruction appears in ACPNRs at room temperature.

Analysis of the discontinuous Petrov-Galerkin method with optimal test functions for the Reissner-Mindlin plate bending model

KAUST Repository

Calo, Victor M.

2014-01-01

We analyze the discontinuous Petrov-Galerkin (DPG) method with optimal test functions when applied to solve the Reissner-Mindlin model of plate bending. We prove that the hybrid variational formulation underlying the DPG method is well-posed (stable) with a thickness-dependent constant in a norm encompassing the L2-norms of the bending moment, the shear force, the transverse deflection and the rotation vector. We then construct a numerical solution scheme based on quadrilateral scalar and vector finite elements of degree p. We show that for affine meshes the discretization inherits the stability of the continuous formulation provided that the optimal test functions are approximated by polynomials of degree p+3. We prove a theoretical error estimate in terms of the mesh size h and polynomial degree p and demonstrate numerical convergence on affine as well as non-affine mesh sequences. © 2013 Elsevier Ltd. All rights reserved.

A nodal discontinuous Galerkin approach to 3-D viscoelastic wave propagation in complex geological media

Science.gov (United States)

Lambrecht, L.; Lamert, A.; Friederich, W.; Möller, T.; Boxberg, M. S.

2018-03-01

A nodal discontinuous Galerkin (NDG) approach is developed and implemented for the computation of viscoelastic wavefields in complex geological media. The NDG approach combines unstructured tetrahedral meshes with an element-wise, high-order spatial interpolation of the wavefield based on Lagrange polynomials. Numerical fluxes are computed from an exact solution of the heterogeneous Riemann problem. Our implementation offers capabilities for modelling viscoelastic wave propagation in 1-D, 2-D and 3-D settings of very different spatial scale with little logistical overhead. It allows the import of external tetrahedral meshes provided by independent meshing software and can be run in a parallel computing environment. Computation of adjoint wavefields and an interface for the computation of waveform sensitivity kernels are offered. The method is validated in 2-D and 3-D by comparison to analytical solutions and results from a spectral element method. The capabilities of the NDG method are demonstrated through a 3-D example case taken from tunnel seismics which considers high-frequency elastic wave propagation around a curved underground tunnel cutting through inclined and faulted sedimentary strata. The NDG method was coded into the open-source software package NEXD and is available from GitHub.

An accurate discontinuous Galerkin method for solving point-source Eikonal equation in 2-D heterogeneous anisotropic media

Science.gov (United States)

Le Bouteiller, P.; Benjemaa, M.; Métivier, L.; Virieux, J.

2018-03-01

Accurate numerical computation of wave traveltimes in heterogeneous media is of major interest for a large range of applications in seismics, such as phase identification, data windowing, traveltime tomography and seismic imaging. A high level of precision is needed for traveltimes and their derivatives in applications which require quantities such as amplitude or take-off angle. Even more challenging is the anisotropic case, where the general Eikonal equation is a quartic in the derivatives of traveltimes. Despite their efficiency on Cartesian meshes, finite-difference solvers are inappropriate when dealing with unstructured meshes and irregular topographies. Moreover, reaching high orders of accuracy generally requires wide stencils and high additional computational load. To go beyond these limitations, we propose a discontinuous-finite-element-based strategy which has the following advantages: (1) the Hamiltonian formalism is general enough for handling the full anisotropic Eikonal equations; (2) the scheme is suitable for any desired high-order formulation or mixing of orders (p-adaptivity); (3) the solver is explicit whatever Hamiltonian is used (no need to find the roots of the quartic); (4) the use of unstructured meshes provides the flexibility for handling complex boundary geometries such as topographies (h-adaptivity) and radiation boundary conditions for mimicking an infinite medium. The point-source factorization principles are extended to this discontinuous Galerkin formulation. Extensive tests in smooth analytical media demonstrate the high accuracy of the method. Simulations in strongly heterogeneous media illustrate the solver robustness to realistic Earth-sciences-oriented applications.

Upwind differencing scheme for the equations of ideal magnetohydrodynamics

International Nuclear Information System (INIS)

Brio, M.; Wu, C.C.

1988-01-01

Recently, upwind differencing schemes have become very popular for solving hyperbolic partial differential equations, especially when discontinuities exist in the solutions. Among many upwind schemes successfully applied to the problems in gas dynamics, Roe's method stands out for its relative simplicity and clarity of the underlying physical model. In this paper, an upwind differencing scheme of Roe-type for the MHD equations is constructed. In each computational cell, the problem is first linearized around some averaged state which preserves the flux differences. Then the solution is advanced in time by computing the wave contributions to the flux at the cell interfaces. One crucial task of the linearization procedure is the construction of a Roe matrix. For the special case γ = 2, a Roe matrix in the form of a mean value Jacobian is found, and for the general case, a simple averaging procedure is introduced. All other necessary ingredients of the construction, which include eigenvalues, and a complete set of right eigenvectors of the Roe matrix and decomposition coefficients are presented. As a numerical example, we chose a coplanar MHD Riemann problem. The problem is solved by the newly constructed second-order upwind scheme as well as by the Lax-Friedrichs, the Lax-Wendroff, and the flux-corrected transport schemes. The results demonstrate several advantages of the upwind scheme. In this paper, we also show that the MHD equations are nonconvex. This is a contrast to the general belief that the fast and slow waves are like sound waves in the Euler equations. As a consequence, the wave structure becomes more complicated; for example, compound waves consisting of a shock and attached to it a rarefaction wave of the same family can exist in MHD. copyright 1988 Academic Press, Inc

Congruence Approximations for Entrophy Endowed Hyperbolic Systems

Science.gov (United States)

Barth, Timothy J.; Saini, Subhash (Technical Monitor)

1998-01-01

Building upon the standard symmetrization theory for hyperbolic systems of conservation laws, congruence properties of the symmetrized system are explored. These congruence properties suggest variants of several stabilized numerical discretization procedures for hyperbolic equations (upwind finite-volume, Galerkin least-squares, discontinuous Galerkin) that benefit computationally from congruence approximation. Specifically, it becomes straightforward to construct the spatial discretization and Jacobian linearization for these schemes (given a small amount of derivative information) for possible use in Newton's method, discrete optimization, homotopy algorithms, etc. Some examples will be given for the compressible Euler equations and the nonrelativistic MHD equations using linear and quadratic spatial approximation.

A discontinous Galerkin finite element method with an efficient time integration scheme for accurate simulations

KAUST Repository

Liu, Meilin; Bagci, Hakan

2011-01-01

A discontinuous Galerkin finite element method (DG-FEM) with a highly-accurate time integration scheme is presented. The scheme achieves its high accuracy using numerically constructed predictor-corrector integration coefficients. Numerical results

Seismic wave propagation in fractured media: A discontinuous Galerkin approach

KAUST Repository

De Basabe, Jonás D.

2011-01-01

We formulate and implement a discontinuous Galekin method for elastic wave propagation that allows for discontinuities in the displacement field to simulate fractures or faults using the linear- slip model. We show numerical results using a 2D model with one linear- slip discontinuity and different frequencies. The results show a good agreement with analytic solutions. © 2011 Society of Exploration Geophysicists.

A class of discontinuous Petrov-Galerkin methods. Part IV: The optimal test norm and time-harmonic wave propagation in 1D

KAUST Repository

Zitelli, J.; Muga, Ignacio; Demkowicz, Leszek F.; Gopalakrishnan, Jayadeep; Pardo, David; Calo, Victor M.

2011-01-01

The phase error, or the pollution effect in the finite element solution of wave propagation problems, is a well known phenomenon that must be confronted when solving problems in the high-frequency range. This paper presents a new method with no phase errors for one-dimensional (1D) time-harmonic wave propagation problems using new ideas that hold promise for the multidimensional case. The method is constructed within the framework of the discontinuous Petrov-Galerkin (DPG) method with optimal test functions. We have previously shown that such methods select solutions that are the best possible approximations in an energy norm dual to any selected test space norm. In this paper, we advance by asking what is the optimal test space norm that achieves error reduction in a given energy norm. This is answered in the specific case of the Helmholtz equation with L2-norm as the energy norm. We obtain uniform stability with respect to the wave number. We illustrate the method with a number of 1D numerical experiments, using discontinuous piecewise polynomial hp spaces for the trial space and its corresponding optimal test functions computed approximately and locally. A 1D theoretical stability analysis is also developed. © 2010 Elsevier Inc.

A class of discontinuous Petrov-Galerkin methods. Part IV: The optimal test norm and time-harmonic wave propagation in 1D

KAUST Repository

Zitelli, J.

2011-04-01

The phase error, or the pollution effect in the finite element solution of wave propagation problems, is a well known phenomenon that must be confronted when solving problems in the high-frequency range. This paper presents a new method with no phase errors for one-dimensional (1D) time-harmonic wave propagation problems using new ideas that hold promise for the multidimensional case. The method is constructed within the framework of the discontinuous Petrov-Galerkin (DPG) method with optimal test functions. We have previously shown that such methods select solutions that are the best possible approximations in an energy norm dual to any selected test space norm. In this paper, we advance by asking what is the optimal test space norm that achieves error reduction in a given energy norm. This is answered in the specific case of the Helmholtz equation with L2-norm as the energy norm. We obtain uniform stability with respect to the wave number. We illustrate the method with a number of 1D numerical experiments, using discontinuous piecewise polynomial hp spaces for the trial space and its corresponding optimal test functions computed approximately and locally. A 1D theoretical stability analysis is also developed. © 2010 Elsevier Inc.

Discontinuous Galerkin Time-Domain Modeling of Graphene Nano-Ribbon Incorporating the Spatial Dispersion Effects

KAUST Repository

Li, Ping; Jiang, Li Jun; Bagci, Hakan

2018-01-01

It is well known that graphene demonstrates spatial dispersion properties, i.e., its conductivity is nonlocal and a function of spectral wave number (momentum operator) q. In this paper, to account for effects of spatial dispersion on transmission of high speed signals along graphene nano-ribbon (GNR) interconnects, a discontinuous Galerkin time-domain (DGTD) algorithm is proposed. The atomically-thick GNR is modeled using a nonlocal transparent surface impedance boundary condition (SIBC) incorporated into the DGTD scheme. Since the conductivity is a complicated function of q (and one cannot find an analytical Fourier transform pair between q and spatial differential operators), an exact time domain SIBC model cannot be derived. To overcome this problem, the conductivity is approximated by its Taylor series in spectral domain under low-q assumption. This approach permits expressing the time domain SIBC in the form of a second-order partial differential equation (PDE) in current density and electric field intensity. To permit easy incorporation of this PDE with the DGTD algorithm, three auxiliary variables, which degenerate the second-order (temporal and spatial) differential operators to first-order ones, are introduced. Regarding to the temporal dispersion effects, the auxiliary differential equation (ADE) method is utilized to eliminates the expensive temporal convolutions. To demonstrate the applicability of the proposed scheme, numerical results, which involve characterization of spatial dispersion effects on the transfer impedance matrix of GNR interconnects, are presented.

Discontinuous Galerkin Time-Domain Modeling of Graphene Nano-Ribbon Incorporating the Spatial Dispersion Effects

KAUST Repository

Li, Ping

2018-04-13

It is well known that graphene demonstrates spatial dispersion properties, i.e., its conductivity is nonlocal and a function of spectral wave number (momentum operator) q. In this paper, to account for effects of spatial dispersion on transmission of high speed signals along graphene nano-ribbon (GNR) interconnects, a discontinuous Galerkin time-domain (DGTD) algorithm is proposed. The atomically-thick GNR is modeled using a nonlocal transparent surface impedance boundary condition (SIBC) incorporated into the DGTD scheme. Since the conductivity is a complicated function of q (and one cannot find an analytical Fourier transform pair between q and spatial differential operators), an exact time domain SIBC model cannot be derived. To overcome this problem, the conductivity is approximated by its Taylor series in spectral domain under low-q assumption. This approach permits expressing the time domain SIBC in the form of a second-order partial differential equation (PDE) in current density and electric field intensity. To permit easy incorporation of this PDE with the DGTD algorithm, three auxiliary variables, which degenerate the second-order (temporal and spatial) differential operators to first-order ones, are introduced. Regarding to the temporal dispersion effects, the auxiliary differential equation (ADE) method is utilized to eliminates the expensive temporal convolutions. To demonstrate the applicability of the proposed scheme, numerical results, which involve characterization of spatial dispersion effects on the transfer impedance matrix of GNR interconnects, are presented.

A fully-coupled discontinuous Galerkin spectral element method for two-phase flow in petroleum reservoirs

Science.gov (United States)

Taneja, Ankur; Higdon, Jonathan

2018-01-01

A high-order spectral element discontinuous Galerkin method is presented for simulating immiscible two-phase flow in petroleum reservoirs. The governing equations involve a coupled system of strongly nonlinear partial differential equations for the pressure and fluid saturation in the reservoir. A fully implicit method is used with a high-order accurate time integration using an implicit Rosenbrock method. Numerical tests give the first demonstration of high order hp spatial convergence results for multiphase flow in petroleum reservoirs with industry standard relative permeability models. High order convergence is shown formally for spectral elements with up to 8th order polynomials for both homogeneous and heterogeneous permeability fields. Numerical results are presented for multiphase fluid flow in heterogeneous reservoirs with complex geometric or geologic features using up to 11th order polynomials. Robust, stable simulations are presented for heterogeneous geologic features, including globally heterogeneous permeability fields, anisotropic permeability tensors, broad regions of low-permeability, high-permeability channels, thin shale barriers and thin high-permeability fractures. A major result of this paper is the demonstration that the resolution of the high order spectral element method may be exploited to achieve accurate results utilizing a simple cartesian mesh for non-conforming geological features. Eliminating the need to mesh to the boundaries of geological features greatly simplifies the workflow for petroleum engineers testing multiple scenarios in the face of uncertainty in the subsurface geology.

Dual-scale Galerkin methods for Darcy flow

Science.gov (United States)

Wang, Guoyin; Scovazzi, Guglielmo; Nouveau, Léo; Kees, Christopher E.; Rossi, Simone; Colomés, Oriol; Main, Alex

2018-02-01

The discontinuous Galerkin (DG) method has found widespread application in elliptic problems with rough coefficients, of which the Darcy flow equations are a prototypical example. One of the long-standing issues of DG approximations is the overall computational cost, and many different strategies have been proposed, such as the variational multiscale DG method, the hybridizable DG method, the multiscale DG method, the embedded DG method, and the Enriched Galerkin method. In this work, we propose a mixed dual-scale Galerkin method, in which the degrees-of-freedom of a less computationally expensive coarse-scale approximation are linked to the degrees-of-freedom of a base DG approximation. We show that the proposed approach has always similar or improved accuracy with respect to the base DG method, with a considerable reduction in computational cost. For the specific definition of the coarse-scale space, we consider Raviart-Thomas finite elements for the mass flux and piecewise-linear continuous finite elements for the pressure. We provide a complete analysis of stability and convergence of the proposed method, in addition to a study on its conservation and consistency properties. We also present a battery of numerical tests to verify the results of the analysis, and evaluate a number of possible variations, such as using piecewise-linear continuous finite elements for the coarse-scale mass fluxes.

An adaptive simplex cut-cell method for high-order discontinuous Galerkin discretizations of elliptic interface problems and conjugate heat transfer problems

Science.gov (United States)

Sun, Huafei; Darmofal, David L.

2014-12-01

In this paper we propose a new high-order solution framework for interface problems on non-interface-conforming meshes. The framework consists of a discontinuous Galerkin (DG) discretization, a simplex cut-cell technique, and an output-based adaptive scheme. We first present a DG discretization with a dual-consistent output evaluation for elliptic interface problems on interface-conforming meshes, and then extend the method to handle multi-physics interface problems, in particular conjugate heat transfer (CHT) problems. The method is then applied to non-interface-conforming meshes using a cut-cell technique, where the interface definition is completely separate from the mesh generation process. No assumption is made on the interface shape (other than Lipschitz continuity). We then equip our strategy with an output-based adaptive scheme for an accurate output prediction. Through numerical examples, we demonstrate high-order convergence for elliptic interface problems and CHT problems with both smooth and non-smooth interface shapes.

The Discontinuous Galerkin Finite Element Method for Solving the MEG and the Combined MEG/EEG Forward Problem

Directory of Open Access Journals (Sweden)

Maria Carla Piastra

2018-02-01

Full Text Available In Electro- (EEG and Magnetoencephalography (MEG, one important requirement of source reconstruction is the forward model. The continuous Galerkin finite element method (CG-FEM has become one of the dominant approaches for solving the forward problem over the last decades. Recently, a discontinuous Galerkin FEM (DG-FEM EEG forward approach has been proposed as an alternative to CG-FEM (Engwer et al., 2017. It was shown that DG-FEM preserves the property of conservation of charge and that it can, in certain situations such as the so-called skull leakages, be superior to the standard CG-FEM approach. In this paper, we developed, implemented, and evaluated two DG-FEM approaches for the MEG forward problem, namely a conservative and a non-conservative one. The subtraction approach was used as source model. The validation and evaluation work was done in statistical investigations in multi-layer homogeneous sphere models, where an analytic solution exists, and in a six-compartment realistically shaped head volume conductor model. In agreement with the theory, the conservative DG-FEM approach was found to be superior to the non-conservative DG-FEM implementation. This approach also showed convergence with increasing resolution of the hexahedral meshes. While in the EEG case, in presence of skull leakages, DG-FEM outperformed CG-FEM, in MEG, DG-FEM achieved similar numerical errors as the CG-FEM approach, i.e., skull leakages do not play a role for the MEG modality. In particular, for the finest mesh resolution of 1 mm sources with a distance of 1.59 mm from the brain-CSF surface, DG-FEM yielded mean topographical errors (relative difference measure, RDM% of 1.5% and mean magnitude errors (MAG% of 0.1% for the magnetic field. However, if the goal is a combined source analysis of EEG and MEG data, then it is highly desirable to employ the same forward model for both EEG and MEG data. Based on these results, we conclude that the newly presented

The Discontinuous Galerkin Finite Element Method for Solving the MEG and the Combined MEG/EEG Forward Problem.

Science.gov (United States)

Piastra, Maria Carla; Nüßing, Andreas; Vorwerk, Johannes; Bornfleth, Harald; Oostenveld, Robert; Engwer, Christian; Wolters, Carsten H

2018-01-01

In Electro- (EEG) and Magnetoencephalography (MEG), one important requirement of source reconstruction is the forward model. The continuous Galerkin finite element method (CG-FEM) has become one of the dominant approaches for solving the forward problem over the last decades. Recently, a discontinuous Galerkin FEM (DG-FEM) EEG forward approach has been proposed as an alternative to CG-FEM (Engwer et al., 2017). It was shown that DG-FEM preserves the property of conservation of charge and that it can, in certain situations such as the so-called skull leakages , be superior to the standard CG-FEM approach. In this paper, we developed, implemented, and evaluated two DG-FEM approaches for the MEG forward problem, namely a conservative and a non-conservative one. The subtraction approach was used as source model. The validation and evaluation work was done in statistical investigations in multi-layer homogeneous sphere models, where an analytic solution exists, and in a six-compartment realistically shaped head volume conductor model. In agreement with the theory, the conservative DG-FEM approach was found to be superior to the non-conservative DG-FEM implementation. This approach also showed convergence with increasing resolution of the hexahedral meshes. While in the EEG case, in presence of skull leakages, DG-FEM outperformed CG-FEM, in MEG, DG-FEM achieved similar numerical errors as the CG-FEM approach, i.e., skull leakages do not play a role for the MEG modality. In particular, for the finest mesh resolution of 1 mm sources with a distance of 1.59 mm from the brain-CSF surface, DG-FEM yielded mean topographical errors (relative difference measure, RDM%) of 1.5% and mean magnitude errors (MAG%) of 0.1% for the magnetic field. However, if the goal is a combined source analysis of EEG and MEG data, then it is highly desirable to employ the same forward model for both EEG and MEG data. Based on these results, we conclude that the newly presented conservative DG

The Application of Discontinuous Galerkin Methods in Conjugate Heat Transfer Simulations of Gas Turbines

Directory of Open Access Journals (Sweden)

Zeng-Rong Hao

2014-11-01

Full Text Available The performance of modern heavy-duty gas turbines is greatly determined by the accurate numerical predictions of thermal loading on the hot-end components. The purpose of this paper is: (1 to present an approach applying a novel numerical technique—the discontinuous Galerkin (DG method—to conjugate heat transfer (CHT simulations, develop the engineering-oriented numerical platform, and validate the feasibility of the methodology and tool preliminarily; and (2 to utilize the constructed platform to investigate the aerothermodynamic features of a typical transonic turbine vane with convection cooling. Fluid dynamic and solid heat conductive equations are discretized into explicit DG formulations. A centroid-expanded Taylor basis is adopted for various types of elements. The Bassi-Rebay method is used in the computation of gradients. A coupled strategy based on a data exchange process via numerical flux on interface quadrature points is simply devised. Additionally, various turbulence Reynolds-Averaged-Navier-Stokes (RANS models and the local-variable-based transition model γ-Reθ are assimilated into the integral framework, combining sophisticated modelling with the innovative algorithm. Numerical tests exhibit good consistency between computational and analytical or experimental results, demonstrating that the presented approach and tool can handle well general CHT simulations. Application and analysis in the turbine vane, focusing on features around where there in cluster exist shock, separation and transition, illustrate the effects of Bradshaw’s shear stress limitation and separation-induced-transition modelling. The general overestimation of heat transfer intensity behind shock is conjectured to be associated with compressibility effects on transition modeling. This work presents an unconventional formulation in CHT problems and achieves its engineering applications in gas turbines.

Discontinuous Galerkin Time-Domain Analysis of Power-Ground Planes Taking Into Account Decoupling Capacitors

KAUST Repository

Li, Ping

2017-03-22

In this paper, a discontinuous Galerkin time-domain (DGTD) method is developed to analyze the power-ground planes taking into account the decoupling capacitors. In the presence of decoupling capacitors, the whole physical system can be split into two subsystems: 1) the field subsystem that is governed by Maxwell\\'s equations that will be solved by the DGTD method, and 2) the circuit subsystem including the capacitor and its parasitic inductor and resistor, which is going to be characterized by the modified nodal analysis algorithm constructed circuit equations. With the aim to couple the two subsystems together, a lumped port is defined over a coaxial surface between the via barrel and the ground plane. To reach the coupling from the field to the circuit subsystem, a lumped voltage source calculated by the integration of electric field along the radial direction is introduced. On the other hand, to facilitate the coupling from the circuit to field subsystem, a lumped port current source calculated from the circuit equation is introduced, which serves as an impressed current source for the field subsystem. With these two auxiliary terms, a hybrid field-circuit matrix equation is established, which enables the field and circuit subsystems are solved in a synchronous scheme. Furthermore, the arbitrarily shaped antipads are considered by enforcing the proper wave port excitation using the magnetic surface current source derived from the antipads supported electric eigenmodes. In this way, the S-parameters corresponding to different modes can be conveniently extracted. To further improve the efficiency of the proposed algorithm in handling multiscale meshes, the local time-stepping marching scheme is applied. The proposed algorithm is verified by several representative examples.

A (Dis)continuous finite element model for generalized 2D vorticity dynamics

NARCIS (Netherlands)

Bernsen, E.; Bokhove, Onno; van der Vegt, Jacobus J.W.

2005-01-01

A mixed continuous and discontinuous Galerkin finite element discretization is constructed for a generalized vorticity streamfunction formulation in two spatial dimensions. This formulation consists of a hyperbolic (potential) vorticity equation and a linear elliptic equation for a (transport)

DNS of Low-Pressure Turbine Cascade Flows with Elevated Inflow Turbulence Using a Discontinuous-Galerkin Spectral-Element Method

Science.gov (United States)

Garai, Anirban; Diosady, Laslo T.; Murman, Scott M.; Madavan, Nateri K.

2016-01-01

Recent progress towards developing a new computational capability for accurate and efficient high-fidelity direct numerical simulation (DNS) and large-eddy simulation (LES) of turbomachinery is described. This capability is based on an entropy- stable Discontinuous-Galerkin spectral-element approach that extends to arbitrarily high orders of spatial and temporal accuracy, and is implemented in a computationally efficient manner on a modern high performance computer architecture. An inflow turbulence generation procedure based on a linear forcing approach has been incorporated in this framework and DNS conducted to study the effect of inflow turbulence on the suction- side separation bubble in low-pressure turbine (LPT) cascades. The T106 series of airfoil cascades in both lightly (T106A) and highly loaded (T106C) configurations at exit isentropic Reynolds numbers of 60,000 and 80,000, respectively, are considered. The numerical simulations are performed using 8th-order accurate spatial and 4th-order accurate temporal discretization. The changes in separation bubble topology due to elevated inflow turbulence is captured by the present method and the physical mechanisms leading to the changes are explained. The present results are in good agreement with prior numerical simulations but some expected discrepancies with the experimental data for the T106C case are noted and discussed.

Development of an upwind sailing ergometer.

Science.gov (United States)

Callewaert, Margot; Geerts, Stefan; Lataire, Evert; Boone, Jan; Vantorre, Marc; Bourgois, Jan

2013-11-01

To develop a sailing ergometer that accurately simulates upwind sailing exercise. A sailing ergometer that measures roll moment accompanied by a biofeedback system that allows imposing a certain quasi-isometric upwind sailing protocol (ie, 18 bouts of 90-s hiking at constantly varying hiking intensity interspersed with 10 s to tack) was developed. Ten male high-level Laser sailors performed an incremental cycling test (ICT; ie, step protocol at 80 W + 40 W/3 min) and an upwind sailing test (UST). During both, heart rate (HR), oxygen uptake (VO(2)), ventilation (V(E)), respiratory-exchange ratio, and rating of perceived exertion were measured. During UST, also the difference between the required and produced hiking moment (HM) was calculated as error score (ES). HR, VO(2), and V(E) were calculated relative to their peak values determined during ICT. After UST, the subjects were questioned about their opinion on the resemblance between this UST and real-time upwind sailing. An average HM of 89.0% ± 2.2% HM(max) and an average ES of 4.1% ± 1.8% HM(max) were found. Mean HR, VO(2), and V(E) were, respectively, 80% ± 4% HR(peak), 39.5% ± 4.5% VO(2peak), and 30.3% ± 3.7% VE(peak). Both HM and cardiorespiratory values appear to be largely comparable to literature reports during on-water upwind sailing. Moreover, the subjects gave the upwind sailing ergometer a positive resemblance score. Results suggest that this ergometer accurately simulates on-water upwind sailing exercise. As such, this ergometer could be a great help in performance diagnostics and training follow-up.

A hybridized discontinuous Galerkin framework for high-order particle-mesh operator splitting of the incompressible Navier-Stokes equations

Science.gov (United States)

Maljaars, Jakob M.; Labeur, Robert Jan; Möller, Matthias

2018-04-01

A generic particle-mesh method using a hybridized discontinuous Galerkin (HDG) framework is presented and validated for the solution of the incompressible Navier-Stokes equations. Building upon particle-in-cell concepts, the method is formulated in terms of an operator splitting technique in which Lagrangian particles are used to discretize an advection operator, and an Eulerian mesh-based HDG method is employed for the constitutive modeling to account for the inter-particle interactions. Key to the method is the variational framework provided by the HDG method. This allows to formulate the projections between the Lagrangian particle space and the Eulerian finite element space in terms of local (i.e. cellwise) ℓ2-projections efficiently. Furthermore, exploiting the HDG framework for solving the constitutive equations results in velocity fields which excellently approach the incompressibility constraint in a local sense. By advecting the particles through these velocity fields, the particle distribution remains uniform over time, obviating the need for additional quality control. The presented methodology allows for a straightforward extension to arbitrary-order spatial accuracy on general meshes. A range of numerical examples shows that optimal convergence rates are obtained in space and, given the particular time stepping strategy, second-order accuracy is obtained in time. The model capabilities are further demonstrated by presenting results for the flow over a backward facing step and for the flow around a cylinder.

Regionally Implicit Discontinuous Galerkin Methods for Solving the Relativistic Vlasov-Maxwell System Submitted to Iowa State University

Science.gov (United States)

Guthrey, Pierson Tyler

The relativistic Vlasov-Maxwell system (RVM) models the behavior of collisionless plasma, where electrons and ions interact via the electromagnetic fields they generate. In the RVM system, electrons could accelerate to significant fractions of the speed of light. An idea that is actively being pursued by several research groups around the globe is to accelerate electrons to relativistic speeds by hitting a plasma with an intense laser beam. As the laser beam passes through the plasma it creates plasma wakes, much like a ship passing through water, which can trap electrons and push them to relativistic speeds. Such setups are known as laser wakefield accelerators, and have the potential to yield particle accelerators that are significantly smaller than those currently in use. Ultimately, the goal of such research is to harness the resulting electron beams to generate electromagnetic waves that can be used in medical imaging applications. High-order accurate numerical discretizations of kinetic Vlasov plasma models are very effective at yielding low-noise plasma simulations, but are computationally expensive to solve because of the high dimensionality. In addition to the general difficulties inherent to numerically simulating Vlasov models, the relativistic Vlasov-Maxwell system has unique challenges not present in the non-relativistic case. One such issue is that operator splitting of the phase gradient leads to potential instabilities, thus we require an alternative to operator splitting of the phase. The goal of the current work is to develop a new class of high-order accurate numerical methods for solving kinetic Vlasov models of plasma. The main discretization in configuration space is handled via a high-order finite element method called the discontinuous Galerkin method (DG). One difficulty is that standard explicit time-stepping methods for DG suffer from time-step restrictions that are significantly worse than what a simple Courant-Friedrichs-Lewy (CFL

A discontinuous Galerkin method with a bound preserving limiter for the advection of non-diffusive fields in solid Earth geodynamics

Science.gov (United States)

He, Ying; Puckett, Elbridge Gerry; Billen, Magali I.

2017-02-01

Mineral composition has a strong effect on the properties of rocks and is an essentially non-diffusive property in the context of large-scale mantle convection. Due to the non-diffusive nature and the origin of compositionally distinct regions in the Earth the boundaries between distinct regions can be nearly discontinuous. While there are different methods for tracking rock composition in numerical simulations of mantle convection, one must consider trade-offs between computational cost, accuracy or ease of implementation when choosing an appropriate method. Existing methods can be computationally expensive, cause over-/undershoots, smear sharp boundaries, or are not easily adapted to tracking multiple compositional fields. Here we present a Discontinuous Galerkin method with a bound preserving limiter (abbreviated as DG-BP) using a second order Runge-Kutta, strong stability-preserving time discretization method for the advection of non-diffusive fields. First, we show that the method is bound-preserving for a point-wise divergence free flow (e.g., a prescribed circular flow in a box). However, using standard adaptive mesh refinement (AMR) there is an over-shoot error (2%) because the cell average is not preserved during mesh coarsening. The effectiveness of the algorithm for convection-dominated flows is demonstrated using the falling box problem. We find that the DG-BP method maintains sharper compositional boundaries (3-5 elements) as compared to an artificial entropy-viscosity method (6-15 elements), although the over-/undershoot errors are similar. When used with AMR the DG-BP method results in fewer degrees of freedom due to smaller regions of mesh refinement in the neighborhood of the discontinuity. However, using Taylor-Hood elements and a uniform mesh there is an over-/undershoot error on the order of 0.0001%, but this error increases to 0.01-0.10% when using AMR. Therefore, for research problems in which a continuous field method is desired the DG

One-Sided Smoothness-Increasing Accuracy-Conserving Filtering for Enhanced Streamline Integration through Discontinuous Fields

NARCIS (Netherlands)

Walfisch, D.; Ryan, J.K.; Kirby, R.M.; Haimes, R.

2008-01-01

The discontinuous Galerkin (DG) method continues to maintain heightened levels of interest within the simulation community because of the discretization flexibility it provides. One of the fundamental properties of the DG methodology and arguably its most powerful property is the ability to combine

Mollified birth in natural-age-grid Galerkin methods for age-structured biological systems

International Nuclear Information System (INIS)

Ayati, Bruce P; Dupont, Todd F

2009-01-01

We present natural-age-grid Galerkin methods for a model of a biological population undergoing aging. We use a mollified birth term in the method and analysis. The error due to mollification is of arbitrary order, depending on the choice of mollifier. The methods in this paper generalize the methods presented in [1], where the approximation space in age was taken to be a discontinuous piecewise polynomial subspace of L 2 . We refer to these methods as 'natural-age-grid' Galerkin methods since transport in the age variable is computed through the smooth movement of the age grid at the natural dimensionless velocity of one. The time variable has been left continuous to emphasize this smooth motion, as well as the independence of the time and age discretizations. The methods are shown to be superconvergent in the age variable

A blended continuous–discontinuous finite element method for solving the multi-fluid plasma model

Energy Technology Data Exchange (ETDEWEB)

Sousa, E.M., E-mail: sousae@uw.edu; Shumlak, U., E-mail: shumlak@uw.edu

2016-12-01

The multi-fluid plasma model represents electrons, multiple ion species, and multiple neutral species as separate fluids that interact through short-range collisions and long-range electromagnetic fields. The model spans a large range of temporal and spatial scales, which renders the model stiff and presents numerical challenges. To address the large range of timescales, a blended continuous and discontinuous Galerkin method is proposed, where the massive ion and neutral species are modeled using an explicit discontinuous Galerkin method while the electrons and electromagnetic fields are modeled using an implicit continuous Galerkin method. This approach is able to capture large-gradient ion and neutral physics like shock formation, while resolving high-frequency electron dynamics in a computationally efficient manner. The details of the Blended Finite Element Method (BFEM) are presented. The numerical method is benchmarked for accuracy and tested using two-fluid one-dimensional soliton problem and electromagnetic shock problem. The results are compared to conventional finite volume and finite element methods, and demonstrate that the BFEM is particularly effective in resolving physics in stiff problems involving realistic physical parameters, including realistic electron mass and speed of light. The benefit is illustrated by computing a three-fluid plasma application that demonstrates species separation in multi-component plasmas.

Three-dimensional dynamic rupture simulation with a high-order discontinuous Galerkin method on unstructured tetrahedral meshes

KAUST Repository

Pelties, Christian

2012-02-18

Accurate and efficient numerical methods to simulate dynamic earthquake rupture and wave propagation in complex media and complex fault geometries are needed to address fundamental questions in earthquake dynamics, to integrate seismic and geodetic data into emerging approaches for dynamic source inversion, and to generate realistic physics-based earthquake scenarios for hazard assessment. Modeling of spontaneous earthquake rupture and seismic wave propagation by a high-order discontinuous Galerkin (DG) method combined with an arbitrarily high-order derivatives (ADER) time integration method was introduced in two dimensions by de la Puente et al. (2009). The ADER-DG method enables high accuracy in space and time and discretization by unstructured meshes. Here we extend this method to three-dimensional dynamic rupture problems. The high geometrical flexibility provided by the usage of tetrahedral elements and the lack of spurious mesh reflections in the ADER-DG method allows the refinement of the mesh close to the fault to model the rupture dynamics adequately while concentrating computational resources only where needed. Moreover, ADER-DG does not generate spurious high-frequency perturbations on the fault and hence does not require artificial Kelvin-Voigt damping. We verify our three-dimensional implementation by comparing results of the SCEC TPV3 test problem with two well-established numerical methods, finite differences, and spectral boundary integral. Furthermore, a convergence study is presented to demonstrate the systematic consistency of the method. To illustrate the capabilities of the high-order accurate ADER-DG scheme on unstructured meshes, we simulate an earthquake scenario, inspired by the 1992 Landers earthquake, that includes curved faults, fault branches, and surface topography. Copyright 2012 by the American Geophysical Union.

Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system

KAUST Repository

Bryson, Steve

2010-10-11

We introduce a new second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. We prove that the scheme both preserves "lake at rest" steady states and guarantees the positivity of the computed fluid depth. Moreover, it can be applied to models with discontinuous bottom topography and irregular channel widths. We demonstrate these features of the new scheme, as well as its high resolution and robustness in a number of numerical examples. © EDP Sciences, SMAI, 2010.

Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system

KAUST Repository

Bryson, Steve; Epshteyn, Yekaterina; Kurganov, Alexander; Petrova, Guergana

2010-01-01

We introduce a new second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. We prove that the scheme both preserves "lake at rest" steady states and guarantees the positivity of the computed fluid depth. Moreover, it can be applied to models with discontinuous bottom topography and irregular channel widths. We demonstrate these features of the new scheme, as well as its high resolution and robustness in a number of numerical examples. © EDP Sciences, SMAI, 2010.

Upwind impacts of ammonia from an intensive poultry unit

International Nuclear Information System (INIS)

Jones, L.; Nizam, M.S.; Reynolds, B.; Bareham, S.; Oxley, E.R.B.

2013-01-01

This study investigated potential ammonia impacts on a sand dune nature reserve 600 m upwind of an intensive poultry unit. Ammonia concentrations and total nitrogen deposition were measured over a calendar year. A series of ammonia and nitrogen exposure experiments using dune grassland species were conducted in controlled manipulations and in the field. Ammonia emissions from the intensive poultry unit were detected up to 2.8 km upwind, contributing to exceedance of critical levels of ammonia 800 m upwind and exceedance of critical loads of nitrogen 2.8 km upwind. Emissions contributed 30% of the total N load in parts of the upwind conservation site. In the nitrogen exposure experiments, plants showed elevated tissue nitrogen contents, and responded to ammonia concentrations and nitrogen deposition loads observed in the conservation site by increasing biomass. Estimated long-term impacts suggest an increase in the soil carbon pool of 9% over a 50-year timescale. -- Highlights: •Ammonia from a poultry unit can be detected 2.8 km upwind. •Ammonia caused exceedance of critical levels 800 m and critical loads 2.8 km upwind. •Dune grassland species utilised ammonia as a nutrient source. •Plant biomass increased at low levels of ammonia and total nitrogen deposition. •Soil C pools are predicted to increase by 9% over 50 years due to the excess ammonia. -- Ammonia from a poultry unit has upwind impacts, exceeding critical levels 800 m and critical loads 2.8 km upwind, and increasing biomass and tissue N of dune grassland species

A discontinous Galerkin finite element method with an efficient time integration scheme for accurate simulations

KAUST Repository

Liu, Meilin

2011-07-01

A discontinuous Galerkin finite element method (DG-FEM) with a highly-accurate time integration scheme is presented. The scheme achieves its high accuracy using numerically constructed predictor-corrector integration coefficients. Numerical results show that this new time integration scheme uses considerably larger time steps than the fourth-order Runge-Kutta method when combined with a DG-FEM using higher-order spatial discretization/basis functions for high accuracy. © 2011 IEEE.

Upwind algorithm for the parabolized Navier-Stokes equations

Science.gov (United States)

Lawrence, Scott L.; Tannehill, John C.; Chausee, Denny S.

1989-01-01

A new upwind algorithm based on Roe's scheme has been developed to solve the two-dimensional parabolized Navier-Stokes equations. This method does not require the addition of user-specified smoothing terms for the capture of discontinuities such as shock waves. Thus, the method is easy to use and can be applied without modification to a wide variety of supersonic flowfields. The advantages and disadvantages of this adaptation are discussed in relation to those of the conventional Beam-Warming (1978) scheme in terms of accuracy, stability, computer time and storage requirements, and programming effort. The new algorithm has been validated by applying it to three laminar test cases, including flat-plate boundary-layer flow, hypersonic flow past a 15-deg compression corner, and hypersonic flow into a converging inlet. The computed results compare well with experiment and show a dramatic improvement in the resolution of flowfield details when compared with results obtained using the conventional Beam-Warming algorithm.

A Discontinuous Galerkin Model for Fluorescence Loss in Photobleaching

DEFF Research Database (Denmark)

Hansen, Christian Valdemar; Schroll, Achim; Wüstner, Daniel

2018-01-01

Fluorescence loss in photobleaching (FLIP) is a modern microscopy method for visualization of transport processes in living cells. This paper presents the simulation of FLIP sequences based on a calibrated reaction–di usion system de ned on segmented cell images. By the use of a discontinuous...... of the nuclear membrane for GFP passage, directly from the FLIP image series. Thus, we present for the rst time, to our knowledge, a quantitative computational FLIP method for inferring several molecular transport parameters in parallel from FLIP image data acquired at commercial microscope systems....

An upwind algorithm for the parabolized Navier-Stokes equations

Science.gov (United States)

Lawrence, S. L.; Tannehill, J. C.; Chaussee, D. S.

1986-01-01

A new upwind algorithm based on Roe's scheme has been developed to solve the two-dimensional parabolized Navier-Stokes (PNS) equations. This method does not require the addition of user specified smoothing terms for the capture of discontinuities such as shock waves. Thus, the method is easy to use and can be applied without modification to a wide variety of supersonic flowfields. The advantages and disadvantages of this adaptation are discussed in relation to those of the conventional Beam-Warming scheme in terms of accuracy, stability, computer time and storage, and programming effort. The new algorithm has been validated by applying it to three laminar test cases including flat plate boundary-layer flow, hypersonic flow past a 15 deg compression corner, and hypersonic flow into a converging inlet. The computed results compare well with experiment and show a dramatic improvement in the resolution of flowfield details when compared with the results obtained using the conventional Beam-Warming algorithm.

An efficient Adaptive Mesh Refinement (AMR) algorithm for the Discontinuous Galerkin method: Applications for the computation of compressible two-phase flows

Science.gov (United States)

Papoutsakis, Andreas; Sazhin, Sergei S.; Begg, Steven; Danaila, Ionut; Luddens, Francky

2018-06-01

We present an Adaptive Mesh Refinement (AMR) method suitable for hybrid unstructured meshes that allows for local refinement and de-refinement of the computational grid during the evolution of the flow. The adaptive implementation of the Discontinuous Galerkin (DG) method introduced in this work (ForestDG) is based on a topological representation of the computational mesh by a hierarchical structure consisting of oct- quad- and binary trees. Adaptive mesh refinement (h-refinement) enables us to increase the spatial resolution of the computational mesh in the vicinity of the points of interest such as interfaces, geometrical features, or flow discontinuities. The local increase in the expansion order (p-refinement) at areas of high strain rates or vorticity magnitude results in an increase of the order of accuracy in the region of shear layers and vortices. A graph of unitarian-trees, representing hexahedral, prismatic and tetrahedral elements is used for the representation of the initial domain. The ancestral elements of the mesh can be split into self-similar elements allowing each tree to grow branches to an arbitrary level of refinement. The connectivity of the elements, their genealogy and their partitioning are described by linked lists of pointers. An explicit calculation of these relations, presented in this paper, facilitates the on-the-fly splitting, merging and repartitioning of the computational mesh by rearranging the links of each node of the tree with a minimal computational overhead. The modal basis used in the DG implementation facilitates the mapping of the fluxes across the non conformal faces. The AMR methodology is presented and assessed using a series of inviscid and viscous test cases. Also, the AMR methodology is used for the modelling of the interaction between droplets and the carrier phase in a two-phase flow. This approach is applied to the analysis of a spray injected into a chamber of quiescent air, using the Eulerian

Stable Galerkin versus equal-order Galerkin least-squares elements for the stokes flow problem

International Nuclear Information System (INIS)

Franca, L.P.; Frey, S.L.; Sampaio, R.

1989-11-01

Numerical experiments are performed for the stokes flow problem employing a stable Galerkin method and a Galerkin/Least-squares method with equal-order elements. Error estimates for the methods tested herein are reviewed. The numerical results presented attest the good stability properties of all methods examined herein. (A.C.A.S.) [pt

The Reverse Time Migration technique coupled with Interior Penalty Discontinuous Galerkin method.

Science.gov (United States)

Baldassari, C.; Barucq, H.; Calandra, H.; Denel, B.; Diaz, J.

2009-04-01

Seismic imaging is based on the seismic reflection method which produces an image of the subsurface from reflected waves recordings by using a tomography process and seismic migration is the industrial standard to improve the quality of the images. The migration process consists in replacing the recorded wavefields at their actual place by using various mathematical and numerical methods but each of them follows the same schedule, according to the pioneering idea of Claerbout: numerical propagation of the source function (propagation) and of the recorded wavefields (retropropagation) and next, construction of the image by applying an imaging condition. The retropropagation step can be realized accouting for the time reversibility of the wave equation and the resulting algorithm is currently called Reverse Time Migration (RTM). To be efficient, especially in three dimensional domain, the RTM requires the solution of the full wave equation by fast numerical methods. Finite element methods are considered as the best discretization method for solving the wave equation, even if they lead to the solution of huge systems with several millions of degrees of freedom, since they use meshes adapted to the domain topography and the boundary conditions are naturally taken into account in the variational formulation. Among the different finite element families, the spectral element one (SEM) is very interesting because it leads to a diagonal mass matrix which dramatically reduces the cost of the numerical computation. Moreover this method is very accurate since it allows the use of high order finite elements. However, SEM uses meshes of the domain made of quadrangles in 2D or hexaedra in 3D which are difficult to compute and not always suitable for complex topographies. Recently, Grote et al. applied the IPDG (Interior Penalty Discontinuous Galerkin) method to the wave equation. This approach is very interesting since it relies on meshes with triangles in 2D or tetrahedra in 3D

Method of moving frames to solve time-dependent Maxwell's equations on anisotropic curved surfaces: Applications to invisible cloak and ELF propagation

Science.gov (United States)

Chun, Sehun

2017-07-01

Applying the method of moving frames to Maxwell's equations yields two important advancements for scientific computing. The first is the use of upwind flux for anisotropic materials in Maxwell's equations, especially in the context of discontinuous Galerkin (DG) methods. Upwind flux has been available only to isotropic material, because of the difficulty of satisfying the Rankine-Hugoniot conditions in anisotropic media. The second is to solve numerically Maxwell's equations on curved surfaces without the metric tensor and composite meshes. For numerical validation, spectral convergences are displayed for both two-dimensional anisotropic media and isotropic spheres. In the first application, invisible two-dimensional metamaterial cloaks are simulated with a relatively coarse mesh by both the lossless Drude model and the piecewisely-parametered layered model. In the second application, extremely low frequency propagation on various surfaces such as spheres, irregular surfaces, and non-convex surfaces is demonstrated.

Extension of meshless Galerkin/Petrov-Galerkin approach without using Lagrange multipliers

International Nuclear Information System (INIS)

Kamitani, Atsushi; Takayama, Teruou; Itoh, Taku; Nakamura, Hiroaki

2011-01-01

By directly discretizing the weak form used in the finite element method, meshless methods have been derived. Neither the Lagrange multiplier method nor the penalty method is employed in the derivation of the methods. The resulting methods are divided into two groups, depending on whether the discretization is based on the Galerkin or the Petrov-Galerkin approach. Each group is further subdivided into two groups, according to the method for imposing the essential boundary condition. Hence, four types of the meshless methods have been formulated. The accuracy of these methods is illustrated for two-dimensional Poisson problems. (author)

galerkin's methods

African Journals Online (AJOL)

user

The assumed deflection shapes used in the approximate methods such as in the Galerkin's method were normally ... to direct compressive forces Nx, was derived by Navier. [3]. ..... tend to give higher frequency and stiffness, as well as.

Multilevel Preconditioners for Discontinuous Galerkin Approximations of Elliptic Problems with Jump Coefficients

Science.gov (United States)

2010-12-01

discontinuous coefficients on geometrically nonconforming substructures. Technical Report Serie A 634, Instituto de Matematica Pura e Aplicada, Brazil, 2009...Instituto de Matematica Pura e Aplicada, Brazil, 2010. submitted. [41] M. Dryja, M. V. Sarkis, and O. B. Widlund. Multilevel Schwarz methods for

Entropy Stable Spectral Collocation Schemes for the Navier-Stokes Equations: Discontinuous Interfaces

Science.gov (United States)

Carpenter, Mark H.; Fisher, Travis C.; Nielsen, Eric J.; Frankel, Steven H.

2013-01-01

Nonlinear entropy stability and a summation-by-parts framework are used to derive provably stable, polynomial-based spectral collocation methods of arbitrary order. The new methods are closely related to discontinuous Galerkin spectral collocation methods commonly known as DGFEM, but exhibit a more general entropy stability property. Although the new schemes are applicable to a broad class of linear and nonlinear conservation laws, emphasis herein is placed on the entropy stability of the compressible Navier-Stokes equations.

A Numerical Development in the Dynamical Equations of Solitons in Optical Fibers

Directory of Open Access Journals (Sweden)

Érica Regina Takano Natti

2006-02-01

Full Text Available It was evaluated the numerical resolution of a nonlinear differential equations system that describes the solitons propagation in dielectric optical fibers, through the method of finite elements, which is implemented based on Streamline Upwind Petrov-Galerkin (SUPG and Consistent Approximate Upwind (CAU formulations.

Magnetic field integral equation analysis of surface plasmon scattering by rectangular dielectric channel discontinuities.

Science.gov (United States)

Chremmos, Ioannis

2010-01-01

The scattering of a surface plasmon polariton (SPP) by a rectangular dielectric channel discontinuity is analyzed through a rigorous magnetic field integral equation method. The scattering phenomenon is formulated by means of the magnetic-type scalar integral equation, which is subsequently treated through an entire-domain Galerkin method of moments (MoM), based on a Fourier-series plane wave expansion of the magnetic field inside the discontinuity. The use of Green's function Fourier transform allows all integrations over the area and along the boundary of the discontinuity to be performed analytically, resulting in a MoM matrix with entries that are expressed as spectral integrals of closed-form expressions. Complex analysis techniques, such as Cauchy's residue theorem and the saddle-point method, are applied to obtain the amplitudes of the transmitted and reflected SPP modes and the radiated field pattern. Through numerical results, we examine the wavelength selectivity of transmission and reflection against the channel dimensions as well as the sensitivity to changes in the refractive index of the discontinuity, which is useful for sensing applications.

A Finite Element Model for convection-dominatel transport problems

International Nuclear Information System (INIS)

Carmo, E.G.D. do; Galeao, A.C.N.R.

1987-08-01

A new Protev-Galerkin Finite Element Model which automatically incorporates the search for the appropriate upwind direction is presented. It is also shown that modifying the Petrov-Galerkin weightin functions associated with elements adjascent to downwing boudaries effectively eliminates numerical oscillations normally obtained near boundary layers. (Author) [pt

Galerkin v. least-squares Petrov–Galerkin projection in nonlinear model reduction

International Nuclear Information System (INIS)

Carlberg, Kevin Thomas; Barone, Matthew F.; Antil, Harbir

2016-01-01

Least-squares Petrov–Galerkin (LSPG) model-reduction techniques such as the Gauss–Newton with Approximated Tensors (GNAT) method have shown promise, as they have generated stable, accurate solutions for large-scale turbulent, compressible flow problems where standard Galerkin techniques have failed. Furthermore, there has been limited comparative analysis of the two approaches. This is due in part to difficulties arising from the fact that Galerkin techniques perform optimal projection associated with residual minimization at the time-continuous level, while LSPG techniques do so at the time-discrete level. This work provides a detailed theoretical and computational comparison of the two techniques for two common classes of time integrators: linear multistep schemes and Runge–Kutta schemes. We present a number of new findings, including conditions under which the LSPG ROM has a time-continuous representation, conditions under which the two techniques are equivalent, and time-discrete error bounds for the two approaches. Perhaps most surprisingly, we demonstrate both theoretically and computationally that decreasing the time step does not necessarily decrease the error for the LSPG ROM; instead, the time step should be ‘matched’ to the spectral content of the reduced basis. In numerical experiments carried out on a turbulent compressible-flow problem with over one million unknowns, we show that increasing the time step to an intermediate value decreases both the error and the simulation time of the LSPG reduced-order model by an order of magnitude.

Hybrid upwind discretization of nonlinear two-phase flow with gravity

Science.gov (United States)

Lee, S. H.; Efendiev, Y.; Tchelepi, H. A.

2015-08-01

Multiphase flow in porous media is described by coupled nonlinear mass conservation laws. For immiscible Darcy flow of multiple fluid phases, whereby capillary effects are negligible, the transport equations in the presence of viscous and buoyancy forces are highly nonlinear and hyperbolic. Numerical simulation of multiphase flow processes in heterogeneous formations requires the development of discretization and solution schemes that are able to handle the complex nonlinear dynamics, especially of the saturation evolution, in a reliable and computationally efficient manner. In reservoir simulation practice, single-point upwinding of the flux across an interface between two control volumes (cells) is performed for each fluid phase, whereby the upstream direction is based on the gradient of the phase-potential (pressure plus gravity head). This upwinding scheme, which we refer to as Phase-Potential Upwinding (PPU), is combined with implicit (backward-Euler) time discretization to obtain a Fully Implicit Method (FIM). Even though FIM suffers from numerical dispersion effects, it is widely used in practice. This is because of its unconditional stability and because it yields conservative, monotone numerical solutions. However, FIM is not unconditionally convergent. The convergence difficulties are particularly pronounced when the different immiscible fluid phases switch between co-current and counter-current states as a function of time, or (Newton) iteration. Whether the multiphase flow across an interface (between two control-volumes) is co-current, or counter-current, depends on the local balance between the viscous and buoyancy forces, and how the balance evolves in time. The sensitivity of PPU to small changes in the (local) pressure distribution exacerbates the problem. The common strategy to deal with these difficulties is to cut the timestep and try again. Here, we propose a Hybrid-Upwinding (HU) scheme for the phase fluxes, then HU is combined with implicit

Numerical Investigations on the Aerodynamic Performance of Wind Turbine：Downwind Versus Upwind Configuration

Institute of Scientific and Technical Information of China (English)

Hu Zhou; Decheng Wan

2015-01-01

Although the upwind configuration is more popular in the field of wind energy, the downwind one is a promising type for the offshore wind energy due to its special advantages. Different configurations have different aerodynamic performance and it is important to predict the performance of both downwind and upwind configurations accurately for designing and developing more reliable wind turbines. In this paper, a numerical investigation on the aerodynamic performance of National Renewable Energy Laboratory (NREL) phase VI wind turbine in downwind and upwind configurations is presented. The open source toolbox OpenFOAM coupled with arbitrary mesh interface (AMI) method is applied to tackle rotating problems of wind turbines. Two 3D numerical models of NREL phase VI wind turbine with downwind and upwind configurations under four typical working conditions of incoming wind velocities are set up for the study of different unsteady characteristics of the downwind and upwind configurations, respectively. Numerical results of wake vortex structure, time histories of thrust, pressure distribution on the blade and limiting streamlines which can be used to identify points of separation in a 3D flow are presented. It can be concluded that thrust reduction due to blade-tower interaction is small for upwind wind turbines but relatively large for downwind wind turbines and attention should be paid to the vibration at a certain frequency induced by the cyclic reduction for both configurations. The results and conclusions are helpful to analyze the different aerodynamic performance of wind turbines between downwind and upwind configurations, providing useful references for practical design of wind turbine.

Conformal and covariant Z4 formulation of the Einstein equations: Strongly hyperbolic first-order reduction and solution with discontinuous Galerkin schemes

Science.gov (United States)

Dumbser, Michael; Guercilena, Federico; Köppel, Sven; Rezzolla, Luciano; Zanotti, Olindo

2018-04-01

We present a strongly hyperbolic first-order formulation of the Einstein equations based on the conformal and covariant Z4 system (CCZ4) with constraint-violation damping, which we refer to as FO-CCZ4. As CCZ4, this formulation combines the advantages of a conformal and traceless formulation, with the suppression of constraint violations given by the damping terms, but being first order in time and space, it is particularly suited for a discontinuous Galerkin (DG) implementation. The strongly hyperbolic first-order formulation has been obtained by making careful use of first and second-order ordering constraints. A proof of strong hyperbolicity is given for a selected choice of standard gauges via an analytical computation of the entire eigenstructure of the FO-CCZ4 system. The resulting governing partial differential equations system is written in nonconservative form and requires the evolution of 58 unknowns. A key feature of our formulation is that the first-order CCZ4 system decouples into a set of pure ordinary differential equations and a reduced hyperbolic system of partial differential equations that contains only linearly degenerate fields. We implement FO-CCZ4 in a high-order path-conservative arbitrary-high-order-method-using-derivatives (ADER)-DG scheme with adaptive mesh refinement and local time-stepping, supplemented with a third-order ADER-WENO subcell finite-volume limiter in order to deal with singularities arising with black holes. We validate the correctness of the formulation through a series of standard tests in vacuum, performed in one, two and three spatial dimensions, and also present preliminary results on the evolution of binary black-hole systems. To the best of our knowledge, these are the first successful three-dimensional simulations of moving punctures carried out with high-order DG schemes using a first-order formulation of the Einstein equations.

Arbitrary-Lagrangian-Eulerian Discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes

Science.gov (United States)

Boscheri, Walter; Dumbser, Michael

2017-10-01

We present a new family of high order accurate fully discrete one-step Discontinuous Galerkin (DG) finite element schemes on moving unstructured meshes for the solution of nonlinear hyperbolic PDE in multiple space dimensions, which may also include parabolic terms in order to model dissipative transport processes, like molecular viscosity or heat conduction. High order piecewise polynomials of degree N are adopted to represent the discrete solution at each time level and within each spatial control volume of the computational grid, while high order of accuracy in time is achieved by the ADER approach, making use of an element-local space-time Galerkin finite element predictor. A novel nodal solver algorithm based on the HLL flux is derived to compute the velocity for each nodal degree of freedom that describes the current mesh geometry. In our algorithm the spatial mesh configuration can be defined in two different ways: either by an isoparametric approach that generates curved control volumes, or by a piecewise linear decomposition of each spatial control volume into simplex sub-elements. Each technique generates a corresponding number of geometrical degrees of freedom needed to describe the current mesh configuration and which must be considered by the nodal solver for determining the grid velocity. The connection of the old mesh configuration at time tn with the new one at time t n + 1 provides the space-time control volumes on which the governing equations have to be integrated in order to obtain the time evolution of the discrete solution. Our numerical method belongs to the category of so-called direct Arbitrary-Lagrangian-Eulerian (ALE) schemes, where a space-time conservation formulation of the governing PDE system is considered and which already takes into account the new grid geometry (including a possible rezoning step) directly during the computation of the numerical fluxes. We emphasize that our method is a moving mesh method, as opposed to total

Numerical algorithms based on Galerkin methods for the modeling of reactive interfaces in photoelectrochemical (PEC) solar cells

Science.gov (United States)

Harmon, Michael; Gamba, Irene M.; Ren, Kui

2016-12-01

This work concerns the numerical solution of a coupled system of self-consistent reaction-drift-diffusion-Poisson equations that describes the macroscopic dynamics of charge transport in photoelectrochemical (PEC) solar cells with reactive semiconductor and electrolyte interfaces. We present three numerical algorithms, mainly based on a mixed finite element and a local discontinuous Galerkin method for spatial discretization, with carefully chosen numerical fluxes, and implicit-explicit time stepping techniques, for solving the time-dependent nonlinear systems of partial differential equations. We perform computational simulations under various model parameters to demonstrate the performance of the proposed numerical algorithms as well as the impact of these parameters on the solution to the model.

An Explicit Upwind Algorithm for Solving the Parabolized Navier-Stokes Equations

Science.gov (United States)

Korte, John J.

1991-01-01

An explicit, upwind algorithm was developed for the direct (noniterative) integration of the 3-D Parabolized Navier-Stokes (PNS) equations in a generalized coordinate system. The new algorithm uses upwind approximations of the numerical fluxes for the pressure and convection terms obtained by combining flux difference splittings (FDS) formed from the solution of an approximate Riemann (RP). The approximate RP is solved using an extension of the method developed by Roe for steady supersonic flow of an ideal gas. Roe's method is extended for use with the 3-D PNS equations expressed in generalized coordinates and to include Vigneron's technique of splitting the streamwise pressure gradient. The difficulty associated with applying Roe's scheme in the subsonic region is overcome. The second-order upwind differencing of the flux derivatives are obtained by adding FDS to either an original forward or backward differencing of the flux derivative. This approach is used to modify an explicit MacCormack differencing scheme into an upwind differencing scheme. The second order upwind flux approximations, applied with flux limiters, provide a method for numerically capturing shocks without the need for additional artificial damping terms which require adjustment by the user. In addition, a cubic equation is derived for determining Vegneron's pressure splitting coefficient using the updated streamwise flux vector. Decoding the streamwise flux vector with the updated value of Vigneron's pressure splitting improves the stability of the scheme. The new algorithm is applied to 2-D and 3-D supersonic and hypersonic laminar flow test cases. Results are presented for the experimental studies of Holden and of Tracy. In addition, a flow field solution is presented for a generic hypersonic aircraft at a Mach number of 24.5 and angle of attack of 1 degree. The computed results compare well to both experimental data and numerical results from other algorithms. Computational times required

Central upwind scheme for a compressible two-phase flow model.

Science.gov (United States)

Ahmed, Munshoor; Saleem, M Rehan; Zia, Saqib; Qamar, Shamsul

2015-01-01

In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS) and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme.

Central upwind scheme for a compressible two-phase flow model.

Directory of Open Access Journals (Sweden)

Munshoor Ahmed

Full Text Available In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme.

Off-fault plasticity in three-dimensional dynamic rupture simulations using a modal Discontinuous Galerkin method on unstructured meshes: Implementation, verification, and application

Science.gov (United States)

Wollherr, Stephanie; Gabriel, Alice-Agnes; Uphoff, Carsten

2018-05-01

The dynamics and potential size of earthquakes depend crucially on rupture transfers between adjacent fault segments. To accurately describe earthquake source dynamics, numerical models can account for realistic fault geometries and rheologies such as nonlinear inelastic processes off the slip interface. We present implementation, verification, and application of off-fault Drucker-Prager plasticity in the open source software SeisSol (www.seissol.org). SeisSol is based on an arbitrary high-order derivative modal Discontinuous Galerkin (ADER-DG) method using unstructured, tetrahedral meshes specifically suited for complex geometries. Two implementation approaches are detailed, modelling plastic failure either employing sub-elemental quadrature points or switching to nodal basis coefficients. At fine fault discretizations the nodal basis approach is up to 6 times more efficient in terms of computational costs while yielding comparable accuracy. Both methods are verified in community benchmark problems and by three dimensional numerical h- and p-refinement studies with heterogeneous initial stresses. We observe no spectral convergence for on-fault quantities with respect to a given reference solution, but rather discuss a limitation to low-order convergence for heterogeneous 3D dynamic rupture problems. For simulations including plasticity, a high fault resolution may be less crucial than commonly assumed, due to the regularization of peak slip rate and an increase of the minimum cohesive zone width. In large-scale dynamic rupture simulations based on the 1992 Landers earthquake, we observe high rupture complexity including reverse slip, direct branching, and dynamic triggering. The spatio-temporal distribution of rupture transfers are altered distinctively by plastic energy absorption, correlated with locations of geometrical fault complexity. Computational cost increases by 7% when accounting for off-fault plasticity in the demonstrating application. Our results

Time-Domain Full-Wave Modeling of Nonlinear Air Breakdown in High-Power Microwave Devices and Systems

Science.gov (United States)

2017-09-30

distribution is unlimited. 13. SUPPLEMENTARY NOTES 14. ABSTRACT This final report describes the effort to develop a discontinuous Galerkin time ...Approved for public release; distribution is unlimited. 1.0 SUMMARY In this report, a discontinuous Galerkin time -domain (DGTD) method is developed...public release; distribution is unlimited. [23] S. Yan, C.-P. Lin, R. R. Arslanbekov, V. I. Kolobov, and J.-M. Jin, “A discontinuous Galerkin time

UPWIND 1A2 Metrology. Final Report

DEFF Research Database (Denmark)

Eecen, P.J.; Wagenaar, J.W.; Stefanatos, N.

. Since this problem covers many areas of wind energy, the work package is defined as a crosscutting activity. The objectives of the metrology work package are to develop metrology tools in wind energy to significantly enhance the quality of measurement and testing techniques. The first deliverable...... is a valuable tool for the further assessment and interest has been shown from other work packages, such as Training. This report describes the activities that have been carried out in the Work Package 1A2 Metrology of the UpWind project. Activities from Risø are described in a separate report: T.F. Pedersen...... was to perform a state of the art assessment to identify all relevant measurands. The required accuracies and required sampling frequencies have been identified from the perspective of the users of the data (the other work packages in UpWind). This work led to the definition of the Metrology Database, which...

Non-Galerkin Coarse Grids for Algebraic Multigrid

Energy Technology Data Exchange (ETDEWEB)

Falgout, Robert D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Schroder, Jacob B. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2014-06-26

Algebraic multigrid (AMG) is a popular and effective solver for systems of linear equations that arise from discretized partial differential equations. And while AMG has been effectively implemented on large scale parallel machines, challenges remain, especially when moving to exascale. Particularly, stencil sizes (the number of nonzeros in a row) tend to increase further down in the coarse grid hierarchy, and this growth leads to more communication. Therefore, as problem size increases and the number of levels in the hierarchy grows, the overall efficiency of the parallel AMG method decreases, sometimes dramatically. This growth in stencil size is due to the standard Galerkin coarse grid operator, $P^T A P$, where $P$ is the prolongation (i.e., interpolation) operator. For example, the coarse grid stencil size for a simple three-dimensional (3D) seven-point finite differencing approximation to diffusion can increase into the thousands on present day machines, causing an associated increase in communication costs. We therefore consider algebraically truncating coarse grid stencils to obtain a non-Galerkin coarse grid. First, the sparsity pattern of the non-Galerkin coarse grid is determined by employing a heuristic minimal “safe” pattern together with strength-of-connection ideas. Second, the nonzero entries are determined by collapsing the stencils in the Galerkin operator using traditional AMG techniques. The result is a reduction in coarse grid stencil size, overall operator complexity, and parallel AMG solve phase times.

多孔介质两相流的守恒迎风有限元法%CONSERVATIVE UPWIND FINITE ELEMENT METHOD FOR TWO-PHASE FLOW IN POROUS MEDIA

Institute of Scientific and Technical Information of China (English)

马纳·萨德; 胡健伟

2001-01-01

Two-phase, immiscible in compressible flow in porous media governed by a system of non-linear partial differential equations arised from reservoir simulation is discussed. Galerkin method is applied for the pressure equation. For the convection-dominated saturation equation, a kind of partial upwind finite element scheme is constructed. The numerical solution got by this scheme satisfies the discrete mass conservation law and converges to the solution in norm L∞(0,T;L2(Ω)).%本文讨论油藏模拟中描述多孔介质两相不可压非混溶流动的偏微分方程组.压力方程用Galerkin方法,而对流占优的饱和度方程用一类部分迎风有限元法.数值解满足离散的质量守恒原理,并以L∞(0,Y;L2(Ω))范收敛于原解.

A study to reduce the numerical diffusion of upwind scheme in two dimensional convection phenomena analysis

International Nuclear Information System (INIS)

Lee, Goung Jin; Kim, Soong Pyung

1990-01-01

In solving the convection-diffusion phenomena, it is common to use central difference scheme or upwind scheme. The central difference scheme has second order accuracy, while the upwind scheme is only first order accurate. However, since the variation rising in the convection-diffusion problem is exponential, central difference scheme ceased to be a good method for anything but extremely small values of Δx. At large values of Δx, which is all one can afford in most practical problems, it is the upwind scheme that gives more reasonable results than the central scheme. But in the conventional upwind scheme, since the accuracy is only first order, false diffusion is somewhat large, and when the real diffusion is smaller than the numerical diffusion, solutions may be very errorneous. So in this paper, a method to reduce the numerical diffusion of upwind scheme is studied. Developed scheme uses same number of nodes as conventional upwind scheme, but it considers the direction of flow more sophistically. As a conclusion, the developed scheme shows very good results. It can reduce false diffusion greatly with the cost of small complexity. Also, algorithm of the developed scheme is presented at appendix. (Author)

High-order upwind schemes for the wave equation on overlapping grids: Maxwell's equations in second-order form

Science.gov (United States)

Angel, Jordan B.; Banks, Jeffrey W.; Henshaw, William D.

2018-01-01

High-order accurate upwind approximations for the wave equation in second-order form on overlapping grids are developed. Although upwind schemes are well established for first-order hyperbolic systems, it was only recently shown by Banks and Henshaw [1] how upwinding could be incorporated into the second-order form of the wave equation. This new upwind approach is extended here to solve the time-domain Maxwell's equations in second-order form; schemes of arbitrary order of accuracy are formulated for general curvilinear grids. Taylor time-stepping is used to develop single-step space-time schemes, and the upwind dissipation is incorporated by embedding the exact solution of a local Riemann problem into the discretization. Second-order and fourth-order accurate schemes are implemented for problems in two and three space dimensions, and overlapping grids are used to treat complex geometry and problems with multiple materials. Stability analysis of the upwind-scheme on overlapping grids is performed using normal mode theory. The stability analysis and computations confirm that the upwind scheme remains stable on overlapping grids, including the difficult case of thin boundary grids when the traditional non-dissipative scheme becomes unstable. The accuracy properties of the scheme are carefully evaluated on a series of classical scattering problems for both perfect conductors and dielectric materials in two and three space dimensions. The upwind scheme is shown to be robust and provide high-order accuracy.

Spatial eigensolution analysis of energy-stable flux reconstruction schemes and influence of the numerical flux on accuracy and robustness

Science.gov (United States)

Mengaldo, Gianmarco; De Grazia, Daniele; Moura, Rodrigo C.; Sherwin, Spencer J.

2018-04-01

This study focuses on the dispersion and diffusion characteristics of high-order energy-stable flux reconstruction (ESFR) schemes via the spatial eigensolution analysis framework proposed in [1]. The analysis is performed for five ESFR schemes, where the parameter 'c' dictating the properties of the specific scheme recovered is chosen such that it spans the entire class of ESFR methods, also referred to as VCJH schemes, proposed in [2]. In particular, we used five values of 'c', two that correspond to its lower and upper bounds and the others that identify three schemes that are linked to common high-order methods, namely the ESFR recovering two versions of discontinuous Galerkin methods and one recovering the spectral difference scheme. The performance of each scheme is assessed when using different numerical intercell fluxes (e.g. different levels of upwinding), ranging from "under-" to "over-upwinding". In contrast to the more common temporal analysis, the spatial eigensolution analysis framework adopted here allows one to grasp crucial insights into the diffusion and dispersion properties of FR schemes for problems involving non-periodic boundary conditions, typically found in open-flow problems, including turbulence, unsteady aerodynamics and aeroacoustics.

Combining discrete equations method and upwind downwind-controlled splitting for non-reacting and reacting two-fluid computations

International Nuclear Information System (INIS)

Tang, K.

2012-01-01

When numerically investigating multiphase phenomena during severe accidents in a reactor system, characteristic lengths of the multi-fluid zone (non-reactive and reactive) are found to be much smaller than the volume of the reactor containment, which makes the direct modeling of the configuration hardly achievable. Alternatively, we propose to consider the physical multiphase mixture zone as an infinitely thin interface. Then, the reactive Riemann solver is inserted into the Reactive Discrete Equations Method (RDEM) to compute high speed combustion waves represented by discontinuous interfaces. An anti-diffusive approach is also coupled with RDEM to accurately simulate reactive interfaces. Increased robustness and efficiency when computing both multiphase interfaces and reacting flows are achieved thanks to an original upwind downwind-controlled splitting method (UDCS). UDCS is capable of accurately solving interfaces on multi-dimensional unstructured meshes, including reacting fronts for both deflagration and detonation configurations. (author)

Galerkin methods for Boltzmann-Poisson transport with reflection conditions on rough boundaries

Science.gov (United States)

Morales Escalante, José A.; Gamba, Irene M.

2018-06-01

We consider in this paper the mathematical and numerical modeling of reflective boundary conditions (BC) associated to Boltzmann-Poisson systems, including diffusive reflection in addition to specularity, in the context of electron transport in semiconductor device modeling at nano scales, and their implementation in Discontinuous Galerkin (DG) schemes. We study these BC on the physical boundaries of the device and develop a numerical approximation to model an insulating boundary condition, or equivalently, a pointwise zero flux mathematical condition for the electron transport equation. Such condition balances the incident and reflective momentum flux at the microscopic level, pointwise at the boundary, in the case of a more general mixed reflection with momentum dependant specularity probability p (k →). We compare the computational prediction of physical observables given by the numerical implementation of these different reflection conditions in our DG scheme for BP models, and observe that the diffusive condition influences the kinetic moments over the whole domain in position space.

Isometric quadriceps strength determines sailing performance and neuromuscular fatigue during an upwind sailing emulation.

Science.gov (United States)

Bourgois, Jan G; Callewaert, Margot; Celie, Bert; De Clercq, Dirk; Boone, Jan

2016-01-01

This study investigates the physiological responses to upwind sailing on a laser emulation ergometer and analyses the components of the physical profile that determine the physiological responses related to sailing level. Ten male high-level laser sailors performed an upwind sailing test, incremental cycling test and quadriceps strength test. During the upwind sailing test, heart rate (HR), oxygen uptake, ventilation, respiratory exchange ratio, rating of perceived exertion (RPE) and lactate concentration were measured, combined with near-infrared spectroscopy (NIRS) and electromyography (EMG) registration of the M. Vastus lateralis. Repeated measures ANOVA showed for the cardio-respiratory, metabolic and muscles responses (mean power frequency [MPF], root mean square [RMS], deoxy[Hb+Mb]) during the upwind sailing test an initial significant increase followed by a stabilisation, despite a constant increase in RPE. Stepwise regression analysis showed that better sailing level was for 46.5% predicted by lower MPF decrease. Lower MPF decrease was for 57.8% predicted by a higher maximal isometric quadriceps strength. In conclusion, this study indicates that higher sailing level was mainly determined by a lower rate of neuromuscular fatigue during the upwind sailing test (as indicated by MPF decrease). Additionally, the level of neuromuscular fatigue was mainly determined by higher maximal isometric quadriceps strength stressing the importance of resistance training in the planning of training.

Hiking strap force decreases during sustained upwind sailing

DEFF Research Database (Denmark)

Buchardt, R; Bay, Jonathan; Bojsen-Møller, Jens

2017-01-01

The hypothesis, that sailing upwind in wind speeds above 12 knots causes fatigue, which manifests as a reduction in exerted hiking strap force and/or maximal isometric voluntary contraction force (MVC) of the knee extensors, was evaluated. Additionally, it was investigated if a relationship exists...... between maximal exerted hiking force (hMVC) and sailing performance. In part 1 of the study, 12 national level athletes sailed upwind for 2 × 10 min while hiking strap forces were continuously acquired. Before, in between and after sailing periods, the MVC of the knee extensors was measured. In part 2...... of the study, hMVC was measured dry land in a hiking bench and correlated with the overall results at a national championship. Hiking strap force decreased from the first to the last minute in both 10 min sailing periods (430 ± 131 vs. 285 ± 130 N, P 

Upwind scheme for acoustic disturbances generated by low-speed flows

DEFF Research Database (Denmark)

Ekaterinaris, J.A.

1997-01-01

, compressible how equations, A numerical method for the solution of the equations governing the acoustic field is presented. The primitive variable form of the governing equations is used for the numerical solution. Time integration is performed with a fourth-order, Runge-Kutta method, Discretization...... of the primitive variables space derivatives is obtained with a high-order, upwind-biased numerical scheme. Upwinding of these convective fluxes is performed according to the eigenvalue sign of the coefficient matrices. Nonreflecting boundary conditions are applied to properly convect outgoing waves away from...... the computational domain. Solutions are obtained for the acoustic field generated by a pair of corotating point vortices. Computed results are compared with the existing analytic solution for the sound field....

Low-diffusion rotated upwind schemes, multigrid and defect correction for steady, multi-dimensional Euler flows

NARCIS (Netherlands)

Koren, B.; Hackbusch, W.; Trottenberg, U.

1991-01-01

Two simple, multi-dimensional upwind discretizations for the steady Euler equations are derived, with the emphasis Iying on bath a good accuracy and a good solvability. The multi-dimensional upwinding consists of applying a one-dimensional Riemann solver with a locally rotated left and right state,

Central-Upwind Schemes for Two-Layer Shallow Water Equations

KAUST Repository

Kurganov, Alexander; Petrova, Guergana

2009-01-01

We derive a second-order semidiscrete central-upwind scheme for one- and two-dimensional systems of two-layer shallow water equations. We prove that the presented scheme is well-balanced in the sense that stationary steady-state solutions

A high-order particle-in-cell method for low density plasma flow and the simulation of gyrotron resonator devices

International Nuclear Information System (INIS)

Stock, Andreas

2013-01-01

Within this thesis a parallelized, transient, three-dimensional, high-order discontinuous Galerkin Particle-in-Cell solver is developed and used to simulate the resonant cavity of a gyrotron. The high-order discontinuous Galerkin approach - a Finite-Element type method - provides a fast and efficient algorithm to numerically solve Maxwell's equations used within this thesis. Besides its outstanding dissipation and dispersion properties, the discontinuous Galerkin approach easily allows for using unstructured grids, as required to simulate complex-shaped engineering devices. The discontinuous Galerkin approach approximates a wavelength with significantly less degrees of freedom compared to other methods, e.g. Finite Difference methods. Furthermore, the parallelization capabilities of the discontinuous Galerkin framework are excellent due to the very local dependencies between the elements. These properties are essential for the efficient numerical treatment of the Vlasov-Maxwell system with the Particle-in-Cell method. This system describes the self-consistent interaction of charged particles and the electromagnetic field. As central application within this thesis gyrotron resonators are simulated with the discontinuous Galerkin Particle-in-Cell method on high-performance-computers. The gyrotron is a high-power millimeter wave source, used for the electron cyclotron resonance heating of magnetically confined fusion plasma, e.g. in the Wendelstein 7-X experimental fusion-reactor. Compared to state-of-the-art simulation tools used for the design of gyrotron resonators the Particle-in-Cell method does not use any significant physically simplifications w.r.t. the modelling of the particle-field-interaction, the geometry and the wave-spectrum. Hence, it is the method of choice for validation of current simulation tools being restricted by these simplifications. So far, the Particle-in-Cell method was restricted to be used for demonstration calculations only, because

A high-order particle-in-cell method for low density plasma flow and the simulation of gyrotron resonator devices

Energy Technology Data Exchange (ETDEWEB)

Stock, Andreas

2013-04-26

Within this thesis a parallelized, transient, three-dimensional, high-order discontinuous Galerkin Particle-in-Cell solver is developed and used to simulate the resonant cavity of a gyrotron. The high-order discontinuous Galerkin approach - a Finite-Element type method - provides a fast and efficient algorithm to numerically solve Maxwell's equations used within this thesis. Besides its outstanding dissipation and dispersion properties, the discontinuous Galerkin approach easily allows for using unstructured grids, as required to simulate complex-shaped engineering devices. The discontinuous Galerkin approach approximates a wavelength with significantly less degrees of freedom compared to other methods, e.g. Finite Difference methods. Furthermore, the parallelization capabilities of the discontinuous Galerkin framework are excellent due to the very local dependencies between the elements. These properties are essential for the efficient numerical treatment of the Vlasov-Maxwell system with the Particle-in-Cell method. This system describes the self-consistent interaction of charged particles and the electromagnetic field. As central application within this thesis gyrotron resonators are simulated with the discontinuous Galerkin Particle-in-Cell method on high-performance-computers. The gyrotron is a high-power millimeter wave source, used for the electron cyclotron resonance heating of magnetically confined fusion plasma, e.g. in the Wendelstein 7-X experimental fusion-reactor. Compared to state-of-the-art simulation tools used for the design of gyrotron resonators the Particle-in-Cell method does not use any significant physically simplifications w.r.t. the modelling of the particle-field-interaction, the geometry and the wave-spectrum. Hence, it is the method of choice for validation of current simulation tools being restricted by these simplifications. So far, the Particle-in-Cell method was restricted to be used for demonstration calculations only, because

Application of volume-weighted skew-upwind differencing to thermal and fluid mixing in the cold leg and downcomer of a PWR

International Nuclear Information System (INIS)

Chen, F.F.; Miao, C.C.; Chen, B.C.J.; Domanus, H.M.; Lyczkowski, R.W.; Sha, W.T.

1983-01-01

Upwind differencing has been the most common numerical scheme used in computational fluid flow and heat transfer in past years. However, the numerical diffusion induced by the use of upwind differencing can be significant in problems involving thermal mixing. Thermal and fluid mixing in a pressurized water reactor during high pressurized coolant injection is a typical example where numerical diffusion is significant. An improved volume-weighted skew-upwind differencing is used here to reduce numerical diffusion without overshooting or undershooting which is the major defect of original skew-upwind differencing proposed by Raithby. The basic concept of volume-weighted skew-upwind differencing is shown. Computations were performed using COMMIX-1B, an extended version of the COMMIX-1A. The experiment analyzed here is test No. 1 of the SAI experiment

Model Adaptation in Parametric Space for POD-Galerkin Models

Science.gov (United States)

Gao, Haotian; Wei, Mingjun

2017-11-01

The development of low-order POD-Galerkin models is largely motivated by the expectation to use the model developed with a set of parameters at their native values to predict the dynamic behaviors of the same system under different parametric values, in other words, a successful model adaptation in parametric space. However, most of time, even small deviation of parameters from their original value may lead to large deviation or unstable results. It has been shown that adding more information (e.g. a steady state, mean value of a different unsteady state, or an entire different set of POD modes) may improve the prediction of flow with other parametric states. For a simple case of the flow passing a fixed cylinder, an orthogonal mean mode at a different Reynolds number may stabilize the POD-Galerkin model when Reynolds number is changed. For a more complicated case of the flow passing an oscillatory cylinder, a global POD-Galerkin model is first applied to handle the moving boundaries, then more information (e.g. more POD modes) is required to predicate the flow under different oscillatory frequencies. Supported by ARL.

A hybrid perturbation-Galerkin technique for partial differential equations

Science.gov (United States)

Geer, James F.; Anderson, Carl M.

1990-01-01

A two-step hybrid perturbation-Galerkin technique for improving the usefulness of perturbation solutions to partial differential equations which contain a parameter is presented and discussed. In the first step of the method, the leading terms in the asymptotic expansion(s) of the solution about one or more values of the perturbation parameter are obtained using standard perturbation methods. In the second step, the perturbation functions obtained in the first step are used as trial functions in a Bubnov-Galerkin approximation. This semi-analytical, semi-numerical hybrid technique appears to overcome some of the drawbacks of the perturbation and Galerkin methods when they are applied by themselves, while combining some of the good features of each. The technique is illustrated first by a simple example. It is then applied to the problem of determining the flow of a slightly compressible fluid past a circular cylinder and to the problem of determining the shape of a free surface due to a sink above the surface. Solutions obtained by the hybrid method are compared with other approximate solutions, and its possible application to certain problems associated with domain decomposition is discussed.

Entropy Stable Staggered Grid Discontinuous Spectral Collocation Methods of any Order for the Compressible Navier--Stokes Equations

KAUST Repository

Parsani, Matteo

2016-10-04

Staggered grid, entropy stable discontinuous spectral collocation operators of any order are developed for the compressible Euler and Navier--Stokes equations on unstructured hexahedral elements. This generalization of previous entropy stable spectral collocation work [M. H. Carpenter, T. C. Fisher, E. J. Nielsen, and S. H. Frankel, SIAM J. Sci. Comput., 36 (2014), pp. B835--B867, M. Parsani, M. H. Carpenter, and E. J. Nielsen, J. Comput. Phys., 292 (2015), pp. 88--113], extends the applicable set of points from tensor product, Legendre--Gauss--Lobatto (LGL), to a combination of tensor product Legendre--Gauss (LG) and LGL points. The new semidiscrete operators discretely conserve mass, momentum, energy, and satisfy a mathematical entropy inequality for the compressible Navier--Stokes equations in three spatial dimensions. They are valid for smooth as well as discontinuous flows. The staggered LG and conventional LGL point formulations are compared on several challenging test problems. The staggered LG operators are significantly more accurate, although more costly from a theoretical point of view. The LG and LGL operators exhibit similar robustness, as is demonstrated using test problems known to be problematic for operators that lack a nonlinear stability proof for the compressible Navier--Stokes equations (e.g., discontinuous Galerkin, spectral difference, or flux reconstruction operators).

Stochastic Galerkin methods for the steady-state Navier–Stokes equations

Energy Technology Data Exchange (ETDEWEB)

Sousedík, Bedřich, E-mail: sousedik@umbc.edu [Department of Mathematics and Statistics, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250 (United States); Elman, Howard C., E-mail: elman@cs.umd.edu [Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742 (United States)

2016-07-01

We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmark problems.

Nonlinear dynamic analysis using Petrov-Galerkin natural element method

International Nuclear Information System (INIS)

Lee, Hong Woo; Cho, Jin Rae

2004-01-01

According to our previous study, it is confirmed that the Petrov-Galerkin Natural Element Method (PG-NEM) completely resolves the numerical integration inaccuracy in the conventional Bubnov-Galerkin Natural Element Method (BG-NEM). This paper is an extension of PG-NEM to two-dimensional nonlinear dynamic problem. For the analysis, a constant average acceleration method and a linearized total Lagrangian formulation is introduced with the PG-NEM. At every time step, the grid points are updated and the shape functions are reproduced from the relocated nodal distribution. This process enables the PG-NEM to provide more accurate and robust approximations. The representative numerical experiments performed by the test Fortran program, and the numerical results confirmed that the PG-NEM effectively and accurately approximates the nonlinear dynamic problem

Analysis of central and upwind compact schemes

International Nuclear Information System (INIS)

Sengupta, T.K.; Ganeriwal, G.; De, S.

2003-01-01

Central and upwind compact schemes for spatial discretization have been analyzed with respect to accuracy in spectral space, numerical stability and dispersion relation preservation. A von Neumann matrix spectral analysis is developed here to analyze spatial discretization schemes for any explicit and implicit schemes to investigate the full domain simultaneously. This allows one to evaluate various boundary closures and their effects on the domain interior. The same method can be used for stability analysis performed for the semi-discrete initial boundary value problems (IBVP). This analysis tells one about the stability for every resolved length scale. Some well-known compact schemes that were found to be G-K-S and time stable are shown here to be unstable for selective length scales by this analysis. This is attributed to boundary closure and we suggest special boundary treatment to remove this shortcoming. To demonstrate the asymptotic stability of the resultant schemes, numerical solution of the wave equation is compared with analytical solution. Furthermore, some of these schemes are used to solve two-dimensional Navier-Stokes equation and a computational acoustic problem to check their ability to solve problems for long time. It is found that those schemes, that were found unstable for the wave equation, are unsuitable for solving incompressible Navier-Stokes equation. In contrast, the proposed compact schemes with improved boundary closure and an explicit higher-order upwind scheme produced correct results. The numerical solution for the acoustic problem is compared with the exact solution and the quality of the match shows that the used compact scheme has the requisite DRP property

Ultra-Scalable Algorithms for Large-Scale Uncertainty Quantification in Inverse Wave Propagation

Science.gov (United States)

2016-03-04

gradient), as well as linear systems with Hessian operators that arise in the trace estimation (along with incremental forward/adjoint wave equations ...with the Elemental library [54] to enable fast and scalable randomized linear algebra . We have also been working on domain decomposition...discontinuous Petrov Galerkin method, in Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations : 2012

Implicit upwind schemes for computational fluid dynamics. Solution by domain decomposition

International Nuclear Information System (INIS)

Clerc, S.

1998-01-01

In this work, the numerical simulation of fluid dynamics equations is addressed. Implicit upwind schemes of finite volume type are used for this purpose. The first part of the dissertation deals with the improvement of the computational precision in unfavourable situations. A non-conservative treatment of some source terms is studied in order to correct some shortcomings of the usual operator-splitting method. Besides, finite volume schemes based on Godunov's approach are unsuited to compute low Mach number flows. A modification of the up-winding by preconditioning is introduced to correct this defect. The second part deals with the solution of steady-state problems arising from an implicit discretization of the equations. A well-posed linearized boundary value problem is formulated. We prove the convergence of a domain decomposition algorithm of Schwartz type for this problem. This algorithm is implemented either directly, or in a Schur complement framework. Finally, another approach is proposed, which consists in decomposing the non-linear steady state problem. (author)

Space-time least-squares Petrov-Galerkin projection in nonlinear model reduction.

Energy Technology Data Exchange (ETDEWEB)

Choi, Youngsoo [Sandia National Laboratories (SNL-CA), Livermore, CA (United States). Extreme-scale Data Science and Analytics Dept.; Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Carlberg, Kevin Thomas [Sandia National Laboratories (SNL-CA), Livermore, CA (United States). Extreme-scale Data Science and Analytics Dept.

2017-09-01

Our work proposes a space-time least-squares Petrov-Galerkin (ST-LSPG) projection method for model reduction of nonlinear dynamical systems. In contrast to typical nonlinear model-reduction methods that first apply Petrov-Galerkin projection in the spatial dimension and subsequently apply time integration to numerically resolve the resulting low-dimensional dynamical system, the proposed method applies projection in space and time simultaneously. To accomplish this, the method first introduces a low-dimensional space-time trial subspace, which can be obtained by computing tensor decompositions of state-snapshot data. The method then computes discrete-optimal approximations in this space-time trial subspace by minimizing the residual arising after time discretization over all space and time in a weighted ℓ²-norm. This norm can be de ned to enable complexity reduction (i.e., hyper-reduction) in time, which leads to space-time collocation and space-time GNAT variants of the ST-LSPG method. Advantages of the approach relative to typical spatial-projection-based nonlinear model reduction methods such as Galerkin projection and least-squares Petrov-Galerkin projection include: (1) a reduction of both the spatial and temporal dimensions of the dynamical system, (2) the removal of spurious temporal modes (e.g., unstable growth) from the state space, and (3) error bounds that exhibit slower growth in time. Numerical examples performed on model problems in fluid dynamics demonstrate the ability of the method to generate orders-of-magnitude computational savings relative to spatial-projection-based reduced-order models without sacrificing accuracy.

Applications of mixed Petrov-Galerkin finite element methods to transient and steady state creep analysis

International Nuclear Information System (INIS)

Guerreiro, J.N.C.; Loula, A.F.D.

1988-12-01

The mixed Petrov-Galerkin finite element formulation is applied to transiente and steady state creep problems. Numerical analysis has shown additional stability of this method compared to classical Galerkin formulations. The accuracy of the new formulation is confirmed in some representative examples of two dimensional and axisymmetric problems. (author) [pt

A comparison of the effect of the first and second upwind schemes on the predictions of the modified RELAP5/MOD3

Energy Technology Data Exchange (ETDEWEB)

Analytis, G.Th. [Paul Scherrer Institute (PSI), Villigen (Switzerland)

1995-09-01

As is well-known, both TRAC-BF1 and TRAC-PF are using the first upwind scheme when finite-differencing the phasic momentum equations. In contrast, RELAP5 uses the second upwind which is less diffusive. In this work, we shall assess the differences between the two schemes with our modified version of RELAP5/MOD3 by analyzing some transients of interest. These will include the LOFT LP-LB-1 and LOBI small break LOCA (SB-LOCA) BL34 tests, and a commercial PWR 200% hypothetical large break LOCA (LB-LOCA). In particular, we shall show that for some of these transients, the employment of the first upwind scheme results in significantly different code predictions than the ones obtained when the second upwind scheme is used.

Camellia v1.0 Manual: Part I

Energy Technology Data Exchange (ETDEWEB)

Roberts, Nathan V. [Argonne National Lab. (ANL), Argonne, IL (United States). Argonne Leadership Computing Facility

2016-09-28

Camellia began as an effort to simplify implementation of efficient solvers for the discontinuous Petrov-Galerkin (DPG) finite element methodology of Demkowicz and Gopalakrishnan. Since then, the feature set has expanded, to allow implementation of traditional continuous Galerkin methods, as well as discontinuous Galerkin (DG) methods, hybridizable DG (HDG) methods, first-order-system least squares (FOSLS), and the primal DPG method. This manual serves as an introduction to using Camellia. We begin, in Section 1.1, by describing some of the core features of Camellia. In Section 1.2 we provide an outline of the manual as a whole.

Aplicación del método Petrov-galerkin como técnica para la estabilización de la solución en problemas unidimensionales de convección-difusión-reacción

Directory of Open Access Journals (Sweden)

Diego Alexander Garzón Alvarado

2009-01-01

Full Text Available El presente artículo estudia el método Streamline Upwind Petrov Galerkin como técnica de estabilización de la solución numérica de las ecuaciones diferenciales de advección-difusión-reacción; se analiza el método a la luz de la naturaleza no auto adjunta del operador diferencial convectivo y de las transformaciones necesarias para la estabilización de la solución por medio de la eliminación del efecto no autoadjunto inducido por el término convectivo. Se desarrollaron seis diversos ejemplos numéricos, los cuales incluyen problemas de coeficientes variables, altamente convectivos, fuertemente reactivos, sistemas de ecuaciones diferenciales y soluciones transitorias. Se encuentra un excelente desempeño de esta técnica de estabilización para todos los casos anteriormente mencionados, exceptuando los problemas con términos reactivos fuertes.

Galerkin method for solving diffusion equations

International Nuclear Information System (INIS)

Tsapelkin, E.S.

1975-01-01

A programme for the solution of the three-dimensional two-group multizone neutron diffusion problem in (x, y, z)-geometry is described. The programme XYZ-5 gives the currents of both groups, the effective neutron multiplication coefficient and several integral properties of the reactor. The solution was found with the Galerkin method using speciallly constructed and chosen coordinate functions. The programme is written in ALGOL-60 and consists of 5 parts. Its text is given

A novel finite element method for moving conductor eddy current problems

Energy Technology Data Exchange (ETDEWEB)

Liu, Z.; Eastham, A.R.; Dawson, G.E. (Queen' s Univ., Kingston, Ontario (Canada). Dept. of Electrical Engineering)

1993-11-01

A novel finite element method, as an alternative to upwinding, is proposed based on the elimination of the factors which could cause numerical oscillation and instability by properly choosing a set of unconventional weighting functions. The proposed method is first developed and verified for a one dimensional case and then extended to two dimensional problems. The calculation results for a 2D problem, along with the exact solutions and those obtained from Galerkin's and ''optimal'' upwinding methods, show that the proposed method is superior to the other two methods in terms of accuracy and freedom from oscillation.

A new finite element formulation for CFD:VIII. The Galerkin/least-squares method for advective-diffusive equations

International Nuclear Information System (INIS)

Hughes, T.J.R.; Hulbert, G.M.; Franca, L.P.

1988-10-01

Galerkin/least-squares finite element methods are presented for advective-diffusive equations. Galerkin/least-squares represents a conceptual simplification of SUPG, and is in fact applicable to a wide variety of other problem types. A convergence analysis and error estimates are presented. (author) [pt

2D numerical comparison of trailing edge flaps - UpWind WP1B3

DEFF Research Database (Denmark)

Buhl, Thomas; Andersen, Peter Bjørn; Barlas, T.K.

This report covers the investigations and comparisons of trailing edge flaps carried out by Delft and Risø. The work is a part of the W1B3 work package of the UpWind EU-project. This report covers only 2D test cases with simple control of the trailing edge flap with the objective of keeping CL...... constant. The 5MW UpWind reference turbine is used for the calculations. The section in 75% radius is investigated for three different cases; 1) a wind step from 10m/s to 11m/s, 2) a wind “gust” from 10 m/s to 14m/s in 1 second and followed by 10m/s, 3) finally a turbulent wind series is simulated...

A comparative study of upwind and MacCormack schemes for CAA benchmark problems

Science.gov (United States)

Viswanathan, K.; Sankar, L. N.

1995-01-01

In this study, upwind schemes and MacCormack schemes are evaluated as to their suitability for aeroacoustic applications. The governing equations are cast in a curvilinear coordinate system and discretized using finite volume concepts. A flux splitting procedure is used for the upwind schemes, where the signals crossing the cell faces are grouped into two categories: signals that bring information from outside into the cell, and signals that leave the cell. These signals may be computed in several ways, with the desired spatial and temporal accuracy achieved by choosing appropriate interpolating polynomials. The classical MacCormack schemes employed here are fourth order accurate in time and space. Results for categories 1, 4, and 6 of the workshop's benchmark problems are presented. Comparisons are also made with the exact solutions, where available. The main conclusions of this study are finally presented.

application of the galerkin-vlasov method to the flexural analysis

African Journals Online (AJOL)

user

In this research, the Galerkin-Vlasov variational method was used to present a general formulation of the Kirchhoff plate problem with simply supported edges and under distributed ..... analysed for elastic, dynamic and stability behaviour,.

Analysis of circular fibers with an arbitrary index profile by the Galerkin method.

Science.gov (United States)

Guo, Shangping; Wu, Feng; Ikram, Khalid; Albin, Sacharia

2004-01-01

We propose a full-vectorial Galerkin method for the analysis of circular symmetric fibers with arbitrary index profiles. A set of orthogonal Laguerre-Gauss functions is used to calculate the dispersion relation and mode fields of TE and TM modes. Examples are given for both standard step-index fibers and Bragg fibers. For standard step-index fiber with low or high index contrast, the Galerkin method agrees well with the analytical results. In the case of the TE mode of a Bragg fiber it agrees well with the asymptotic results.

On the Preconditioning of a Newton-Krylov Solver for a High-Order reconstructed Discontinuous Galerkin Discretization of All-Speed Compressible Flow with Phase Change for Application in Laser-Based Additive Manufacturing

Energy Technology Data Exchange (ETDEWEB)

Weston, Brian T. [Univ. of California, Davis, CA (United States)

2017-05-17

This dissertation focuses on the development of a fully-implicit, high-order compressible ow solver with phase change. The work is motivated by laser-induced phase change applications, particularly by the need to develop large-scale multi-physics simulations of the selective laser melting (SLM) process in metal additive manufacturing (3D printing). Simulations of the SLM process require precise tracking of multi-material solid-liquid-gas interfaces, due to laser-induced melting/ solidi cation and evaporation/condensation of metal powder in an ambient gas. These rapid density variations and phase change processes tightly couple the governing equations, requiring a fully compressible framework to robustly capture the rapid density variations of the ambient gas and the melting/evaporation of the metal powder. For non-isothermal phase change, the velocity is gradually suppressed through the mushy region by a variable viscosity and Darcy source term model. The governing equations are discretized up to 4th-order accuracy with our reconstructed Discontinuous Galerkin spatial discretization scheme and up to 5th-order accuracy with L-stable fully implicit time discretization schemes (BDF2 and ESDIRK3-5). The resulting set of non-linear equations is solved using a robust Newton-Krylov method, with the Jacobian-free version of the GMRES solver for linear iterations. Due to the sti nes associated with the acoustic waves and thermal and viscous/material strength e ects, preconditioning the GMRES solver is essential. A robust and scalable approximate block factorization preconditioner was developed, which utilizes the velocity-pressure (vP) and velocity-temperature (vT) Schur complement systems. This multigrid block reduction preconditioning technique converges for high CFL/Fourier numbers and exhibits excellent parallel and algorithmic scalability on classic benchmark problems in uid dynamics (lid-driven cavity ow and natural convection heat transfer) as well as for laser

Computing with high-resolution upwind schemes for hyperbolic equations

International Nuclear Information System (INIS)

Chakravarthy, S.R.; Osher, S.; California Univ., Los Angeles)

1985-01-01

Computational aspects of modern high-resolution upwind finite-difference schemes for hyperbolic systems of conservation laws are examined. An operational unification is demonstrated for constructing a wide class of flux-difference-split and flux-split schemes based on the design principles underlying total variation diminishing (TVD) schemes. Consideration is also given to TVD scheme design by preprocessing, the extension of preprocessing and postprocessing approaches to general control volumes, the removal of expansion shocks and glitches, relaxation methods for implicit TVD schemes, and a new family of high-accuracy TVD schemes. 21 references

POD-Galerkin Model for Incompressible Single-Phase Flow in Porous Media

KAUST Repository

Wang, Yi; Yu, Bo; Sun, Shuyu

2017-01-01

Fast prediction modeling via proper orthogonal decomposition method combined with Galerkin projection is applied to incompressible single-phase fluid flow in porous media. Cases for different configurations of porous media, boundary conditions

Petrov-Galerkin mixed formulations for bidimensional elasticity

International Nuclear Information System (INIS)

Toledo, E.M.; Loula, A.F.D.; Guerreiro, J.N.C.

1989-10-01

A new formulation for two-dimensional elasticity in stress and displacements is presented. Consistently adding to the Galerkin classical formulation residuals forms of constitutive and equilibrium equations, the original saddle point is transformed into a minimization problem without any restrictions. We also propose a stress post processing technique using both equilibrium and constitutive equations. Numerical analysis error estimates and numerical results are presented confirming the predicted rates of convergence. (A.C.A.S.) [pt

Supercomputer implementation of finite element algorithms for high speed compressible flows. Progress report, period ending 30 June 1986

International Nuclear Information System (INIS)

Thornton, E.A.; Ramakrishnan, R.

1986-06-01

Prediction of compressible flow phenomena using the finite element method is of recent origin and considerable interest. Two shock capturing finite element formulations for high speed compressible flows are described. A Taylor-Galerkin formulation uses a Taylor series expansion in time coupled with a Galerkin weighted residual statement. The Taylor-Galerkin algorithms use explicit artificial dissipation, and the performance of three dissipation models are compared. A Petrov-Galerkin algorithm has as its basis the concepts of streamline upwinding. Vectorization strategies are developed to implement the finite element formulations on the NASA Langley VPS-32. The vectorization scheme results in finite element programs that use vectors of length of the order of the number of nodes or elements. The use of the vectorization procedure speeds up processing rates by over two orders of magnitude. The Taylor-Galerkin and Petrov-Galerkin algorithms are evaluated for 2D inviscid flows on criteria such as solution accuracy, shock resolution, computational speed and storage requirements. The convergence rates for both algorithms are enhanced by local time-stepping schemes. Extension of the vectorization procedure for predicting 2D viscous and 3D inviscid flows are demonstrated. Conclusions are drawn regarding the applicability of the finite element procedures for realistic problems that require hundreds of thousands of nodes

A high-order Petrov-Galerkin method for the Boltzmann transport equation

International Nuclear Information System (INIS)

Pain, C.C.; Candy, A.S.; Piggott, M.D.; Buchan, A.; Eaton, M.D.; Goddard, A.J.H.; Oliveira, C.R.E. de

2005-01-01

We describe a new Petrov-Galerkin method using high-order terms to introduce dissipation in a residual-free formulation. The method is developed following both a Taylor series analysis and a variational principle, and the result has much in common with traditional Petrov-Galerkin, Self Adjoint Angular Flux (SAAF) and Even Parity forms of the Boltzmann transport equation. In addition, we consider the subtleties in constructing appropriate boundary conditions. In sub-grid scale (SGS) modelling of fluids the advantages of high-order dissipation are well known. Fourth-order terms, for example, are commonly used as a turbulence model with uniform dissipation. They have been shown to have superior properties to SGS models based upon second-order dissipation or viscosity. Even higher-order forms of dissipation (e.g. 16.-order) can offer further advantages, but are only easily realised by spectral methods because of the solution continuity requirements that these higher-order operators demand. Higher-order operators are more effective, bringing a higher degree of representation to the solution locally. Second-order operators, for example, tend to relax the solution to a linear variation locally, whereas a high-order operator will tend to relax the solution to a second-order polynomial locally. The form of the dissipation is also important. For example, the dissipation may only be applied (as it is in this work) in the streamline direction. While for many problems, for example Large Eddy Simulation (LES), simply adding a second or fourth-order dissipation term is a perfectly satisfactory SGS model, it is well known that a consistent residual-free formulation is required for radiation transport problems. This motivated the consideration of a new Petrov-Galerkin method that is residual-free, but also benefits from the advantageous features that SGS modelling introduces. We close with a demonstration of the advantages of this new discretization method over standard Petrov-Galerkin

Galerkin approximations of nonlinear optimal control problems in Hilbert spaces

Directory of Open Access Journals (Sweden)

Mickael D. Chekroun

2017-07-01

Full Text Available Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. Approximation theorems are available in the literature. The originality of our approach relies on the identification of a set of natural assumptions that allows us to deal with a broad class of nonlinear evolution equations and cost functionals for which we derive convergence of the value functions associated with the optimal control problem of the Galerkin approximations. This convergence result holds for a broad class of nonlinear control strategies as well. In particular, we show that the framework applies to the optimal control of semilinear heat equations posed on a general compact manifold without boundary. The framework is then shown to apply to geoengineering and mitigation of greenhouse gas emissions formulated here in terms of optimal control of energy balance climate models posed on the sphere $\\mathbb{S}^2$.

Discontinuous Galerkin Dynamical Core in HOMME

Energy Technology Data Exchange (ETDEWEB)

Nair, R. D. [Univ. of Colorado, Boulder, CO (United States); Tufo, Henry [Univ. of Colorado, Boulder, CO (United States)

2012-08-14

Atmospheric numerical modeling has been going through radical changes over the past decade. One major reason for this trend is due to the recent paradigm change in scientific computing , triggered by the arrival of petascale computing resources with core counts in the tens of thousands to hundreds of thousands range. Modern atmospheric modelers must adapt grid systems and numerical algorithms to facilitate an unprecedented levels of scalability on these modern highly parallel computer architectures. The numerical algorithms which can address these challenges should have the local properties such as high on-processor floating-point operation count to bytes moved and minimum parallel communication overhead.

A Galerkin approximation for linear elastic shallow shells

Science.gov (United States)

Figueiredo, I. N.; Trabucho, L.

1992-03-01

This work is a generalization to shallow shell models of previous results for plates by B. Miara (1989). Using the same basis functions as in the plate case, we construct a Galerkin approximation of the three-dimensional linearized elasticity problem, and establish some error estimates as a function of the thickness, the curvature, the geometry of the shell, the forces and the Lamé costants.

A drift-diffusion-reaction model for excitonic photovoltaic bilayers: Photovoltaic bilayers: Asymptotic analysis and a 2D hdg finite element scheme

KAUST Repository

Brinkman, Daniel

2013-05-01

We present and discuss a mathematical model for the operation of bilayer organic photovoltaic devices. Our model couples drift-diffusion-recombination equations for the charge carriers (specifically, electrons and holes) with a reaction-diffusion equation for the excitons/polaron pairs and Poisson\\'s equation for the self-consistent electrostatic potential. The material difference (i.e. the HOMO/LUMO gap) of the two organic substrates forming the bilayer device is included as a work-function potential. Firstly, we perform an asymptotic analysis of the scaled one-dimensional stationary state system: (i) with focus on the dynamics on the interface and (ii) with the goal of simplifying the bulk dynamics away from the interface. Secondly, we present a two-dimensional hybrid discontinuous Galerkin finite element numerical scheme which is very well suited to resolve: (i) the material changes, (ii) the resulting strong variation over the interface, and (iii) the necessary upwinding in the discretization of drift-diffusion equations. Finally, we compare the numerical results with the approximating asymptotics. © 2013 World Scientific Publishing Company.

2D numerical comparison of trailing edge flaps - UpWind WP1B3

Energy Technology Data Exchange (ETDEWEB)

Buhl, T.; Andersen, Peter B. (Risoe National Lab., DTU (DK)); Barlas, T.K. (DUWIND, Delft Technical Univ. (NL))

2007-11-15

This report covers the investigations and comparisons of trailing edge flaps carried out by Delft and Risoe. The work is a part of the W1B3 work package of the UpWind EU-project. This report covers only 2D test cases with simple control of the trailing edge flap with the objective of keeping CL constant. The 5MW UpWind reference turbine is used for the calculations. The section in 75% radius is investigated for three different cases; (1) a wind step from 10m/s to 11m/s, (2) a wind 'gust' from 10 m/s to 14m/s in 1 second and followed by 10m/s, (3) finally a turbulent wind series is simulated, and the performance of the flaps is investigated. The two different codes from Delft and Risoe are compared in the mentioned cases. (au)

Multi-dimensional upwinding-based implicit LES for the vorticity transport equations

Science.gov (United States)

Foti, Daniel; Duraisamy, Karthik

2017-11-01

Complex turbulent flows such as rotorcraft and wind turbine wakes are characterized by the presence of strong coherent structures that can be compactly described by vorticity variables. The vorticity-velocity formulation of the incompressible Navier-Stokes equations is employed to increase numerical efficiency. Compared to the traditional velocity-pressure formulation, high order numerical methods and sub-grid scale models for the vorticity transport equation (VTE) have not been fully investigated. Consistent treatment of the convection and stretching terms also needs to be addressed. Our belief is that, by carefully designing sharp gradient-capturing numerical schemes, coherent structures can be more efficiently captured using the vorticity-velocity formulation. In this work, a multidimensional upwind approach for the VTE is developed using the generalized Riemann problem-based scheme devised by Parish et al. (Computers & Fluids, 2016). The algorithm obtains high resolution by augmenting the upwind fluxes with transverse and normal direction corrections. The approach is investigated with several canonical vortex-dominated flows including isolated and interacting vortices and turbulent flows. The capability of the technique to represent sub-grid scale effects is also assessed. Navy contract titled ``Turbulence Modelling Across Disparate Length Scales for Naval Computational Fluid Dynamics Applications,'' through Continuum Dynamics, Inc.

Numerical solution of special ultra-relativistic Euler equations using central upwind scheme

Science.gov (United States)

Ghaffar, Tayabia; Yousaf, Muhammad; Qamar, Shamsul

2018-06-01

This article is concerned with the numerical approximation of one and two-dimensional special ultra-relativistic Euler equations. The governing equations are coupled first-order nonlinear hyperbolic partial differential equations. These equations describe perfect fluid flow in terms of the particle density, the four-velocity and the pressure. A high-resolution shock-capturing central upwind scheme is employed to solve the model equations. To avoid excessive numerical diffusion, the considered scheme avails the specific information of local propagation speeds. By using Runge-Kutta time stepping method and MUSCL-type initial reconstruction, we have obtained 2nd order accuracy of the proposed scheme. After discussing the model equations and the numerical technique, several 1D and 2D test problems are investigated. For all the numerical test cases, our proposed scheme demonstrates very good agreement with the results obtained by well-established algorithms, even in the case of highly relativistic 2D test problems. For validation and comparison, the staggered central scheme and the kinetic flux-vector splitting (KFVS) method are also implemented to the same model. The robustness and efficiency of central upwind scheme is demonstrated by the numerical results.

Generalized multiscale finite element methods. nonlinear elliptic equations

KAUST Repository

Efendiev, Yalchin R.; Galvis, Juan; Li, Guanglian; Presho, Michael

2013-01-01

In this paper we use the Generalized Multiscale Finite Element Method (GMsFEM) framework, introduced in [26], in order to solve nonlinear elliptic equations with high-contrast coefficients. The proposed solution method involves linearizing the equation so that coarse-grid quantities of previous solution iterates can be regarded as auxiliary parameters within the problem formulation. With this convention, we systematically construct respective coarse solution spaces that lend themselves to either continuous Galerkin (CG) or discontinuous Galerkin (DG) global formulations. Here, we use Symmetric Interior Penalty Discontinuous Galerkin approach. Both methods yield a predictable error decline that depends on the respective coarse space dimension, and we illustrate the effectiveness of the CG and DG formulations by offering a variety of numerical examples. © 2014 Global-Science Press.

Optimized waveform relaxation domain decomposition method for discrete finite volume non stationary convection diffusion equation

International Nuclear Information System (INIS)

Berthe, P.M.

2013-01-01

In the context of nuclear waste repositories, we consider the numerical discretization of the non stationary convection diffusion equation. Discontinuous physical parameters and heterogeneous space and time scales lead us to use different space and time discretizations in different parts of the domain. In this work, we choose the discrete duality finite volume (DDFV) scheme and the discontinuous Galerkin scheme in time, coupled by an optimized Schwarz waveform relaxation (OSWR) domain decomposition method, because this allows the use of non-conforming space-time meshes. The main difficulty lies in finding an upwind discretization of the convective flux which remains local to a sub-domain and such that the multi domain scheme is equivalent to the mono domain one. These difficulties are first dealt with in the one-dimensional context, where different discretizations are studied. The chosen scheme introduces a hybrid unknown on the cell interfaces. The idea of up winding with respect to this hybrid unknown is extended to the DDFV scheme in the two-dimensional setting. The well-posedness of the scheme and of an equivalent multi domain scheme is shown. The latter is solved by an OSWR algorithm, the convergence of which is proved. The optimized parameters in the Robin transmission conditions are obtained by studying the continuous or discrete convergence rates. Several test-cases, one of which inspired by nuclear waste repositories, illustrate these results. (author) [fr

A stochastic Galerkin method for the Euler equations with Roe variable transformation

KAUST Repository

Pettersson, Per; Iaccarino, Gianluca; Nordströ m, Jan

2014-01-01

The Euler equations subject to uncertainty in the initial and boundary conditions are investigated via the stochastic Galerkin approach. We present a new fully intrusive method based on a variable transformation of the continuous equations. Roe variables are employed to get quadratic dependence in the flux function and a well-defined Roe average matrix that can be determined without matrix inversion.In previous formulations based on generalized polynomial chaos expansion of the physical variables, the need to introduce stochastic expansions of inverse quantities, or square roots of stochastic quantities of interest, adds to the number of possible different ways to approximate the original stochastic problem. We present a method where the square roots occur in the choice of variables, resulting in an unambiguous problem formulation.The Roe formulation saves computational cost compared to the formulation based on expansion of conservative variables. Moreover, the Roe formulation is more robust and can handle cases of supersonic flow, for which the conservative variable formulation fails to produce a bounded solution. For certain stochastic basis functions, the proposed method can be made more effective and well-conditioned. This leads to increased robustness for both choices of variables. We use a multi-wavelet basis that can be chosen to include a large number of resolution levels to handle more extreme cases (e.g. strong discontinuities) in a robust way. For smooth cases, the order of the polynomial representation can be increased for increased accuracy. © 2013 Elsevier Inc.

Feed back Petrov-Galerkin methods for convection dominated problems

International Nuclear Information System (INIS)

Carmo, E.G.D. do; Galeao, A.C.

1988-09-01

The Petrov-Galerkin method is adaptively applied to convection dominated problems. To this end a feedback function is created which increases the control of derivatives in the direction of he gradient of the approximate solution. This leads to a method with good stability properties close to boundary layers and high accuracy in those regions where regular solutions do occur. (author) [pt

Reduction of Air Pollution Levels Downwind of a Road with an Upwind Noise Barrier

Science.gov (United States)

We propose a dispersion model to characterize the impact of an upwind solid noise barrier next to a highway on air pollution concentrations downwind of the road. The model is based on data from wind tunnel experiments conducted by Heist et al. (2009). The model assumes that the...

Topology optimization using the improved element-free Galerkin method for elasticity*

International Nuclear Information System (INIS)

Wu Yi; Ma Yong-Qi; Feng Wei; Cheng Yu-Min

2017-01-01

The improved element-free Galerkin (IEFG) method of elasticity is used to solve the topology optimization problems. In this method, the improved moving least-squares approximation is used to form the shape function. In a topology optimization process, the entire structure volume is considered as the constraint. From the solid isotropic microstructures with penalization, we select relative node density as a design variable. Then we choose the minimization of compliance to be an objective function, and compute its sensitivity with the adjoint method. The IEFG method in this paper can overcome the disadvantages of the singular matrices that sometimes appear in conventional element-free Galerkin (EFG) method. The central processing unit (CPU) time of each example is given to show that the IEFG method is more efficient than the EFG method under the same precision, and the advantage that the IEFG method does not form singular matrices is also shown. (paper)

Applicability of the Galerkin method to the approximate solution of the multigroup diffusion equation

International Nuclear Information System (INIS)

Obradovic, D.

1970-04-01

In the study of the nuclear reactors space-time behaviour the modal analysis is very often used though some basic mathematical problems connected with application of this methods are still unsolved. In this paper the modal analysis is identified as a set of the methods in the mathematical literature known as the Galerkin methods (or projection methods, or sometimes direct methods). Using the results of the mathematical investigations of these methods the applicability of the Galerkin type methods to the calculations of the eigenvalue and eigenvectors of the stationary and non-stationary diffusion operator, as well as for the solutions of the corresponding functional equations, is established (author)

Flow and wakes in large wind farms: Final report for UpWind WP8

DEFF Research Database (Denmark)

Barthelmie, Rebecca Jane; Frandsen, Sten Tronæs; Rathmann, Ole

This report summarises the research undertaken through the European Commission funded project UpWind Wp8:Flow. The objective of the work was to develop understanding of flow in large wind farms and to evaluate models of power losses due to wind turbine wakes focusing on complex terrain and offshore...

Numerical solution of the unsteady diffusion-convection-reaction equation based on improved spectral Galerkin method

Science.gov (United States)

Zhong, Jiaqi; Zeng, Cheng; Yuan, Yupeng; Zhang, Yuzhe; Zhang, Ye

2018-04-01

The aim of this paper is to present an explicit numerical algorithm based on improved spectral Galerkin method for solving the unsteady diffusion-convection-reaction equation. The principal characteristics of this approach give the explicit eigenvalues and eigenvectors based on the time-space separation method and boundary condition analysis. With the help of Fourier series and Galerkin truncation, we can obtain the finite-dimensional ordinary differential equations which facilitate the system analysis and controller design. By comparing with the finite element method, the numerical solutions are demonstrated via two examples. It is shown that the proposed method is effective.

An element-free Galerkin (EFG) method for generalized Fisher equations (GFE)

International Nuclear Information System (INIS)

Shi Ting-Yu; Ge Hong-Xia; Cheng Rong-Jun

2013-01-01

A generalized Fisher equation (GFE) relates the time derivative of the average of the intrinsic rate of growth to its variance. The exact mathematical result of the GFE has been widely used in population dynamics and genetics, where it originated. Many researchers have studied the numerical solutions of the GFE, up to now. In this paper, we introduce an element-free Galerkin (EFG) method based on the moving least-square approximation to approximate positive solutions of the GFE from population dynamics. Compared with other numerical methods, the EFG method for the GFE needs only scattered nodes instead of meshing the domain of the problem. The Galerkin weak form is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. In comparison with the traditional method, numerical solutions show that the new method has higher accuracy and better convergence. Several numerical examples are presented to demonstrate the effectiveness of the method

User's Manual for the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA)

Science.gov (United States)

Gnoffo, Peter A.; Cheatwood, F. McNeil

1996-01-01

This user's manual provides detailed instructions for the installation and the application of version 4.1 of the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA). Also provides simulation of flow field in thermochemical nonequilibrium around vehicles traveling at hypersonic velocities through the atmosphere. Earlier versions of LAURA were predominantly research codes, and they had minimal (or no) documentation. This manual describes UNIX-based utilities for customizing the code for special applications that also minimize system resource requirements. The algorithm is reviewed, and the various program options are related to specific equations and variables in the theoretical development.

Organising medication discontinuation

DEFF Research Database (Denmark)

Nixon, Michael; Kousgaard, Marius Brostrøm

2016-01-01

medication? Methods: Twenty four GPs were interviewed using a maximum variation sample strategy. Participant observations were done in three general practices, for one day each, totalling approximately 30 consultations. Results: The results show that different discontinuation cues (related to the type...... a medication, in agreement with the patients, from a professional perspective. Three research questions were examined in this study: when does medication discontinuation occur in general practice, how is discontinuing medication handled in the GP’s practice and how do GPs make decisions about discontinuing...

Central-Upwind Schemes for Two-Layer Shallow Water Equations

KAUST Repository

Kurganov, Alexander

2009-01-01

We derive a second-order semidiscrete central-upwind scheme for one- and two-dimensional systems of two-layer shallow water equations. We prove that the presented scheme is well-balanced in the sense that stationary steady-state solutions are exactly preserved by the scheme and positivity preserving; that is, the depth of each fluid layer is guaranteed to be nonnegative. We also propose a new technique for the treatment of the nonconservative products describing the momentum exchange between the layers. The performance of the proposed method is illustrated on a number of numerical examples, in which we successfully capture (quasi) steady-state solutions and propagating interfaces. © 2009 Society for Industrial and Applied Mathematics.

Early discontinuation

DEFF Research Database (Denmark)

Hansen, Dorte Gilså; Felde, Lina; Gichangi, Anthony

2007-01-01

prevalence and rate of early discontinuation of different drugs consisting of, in this study, lipid-lowering drugs, antihypertensive drugs, antidepressants, antidiabetics and drugs against osteoporosis. Material and methods This was a register study based on prescription data covering a 4-year period...... and consisting of 470,000 citizens. For each practice and group of drug, a 1-year prevalence for 2002 and the rate of early discontinuation among new users in 2002-2003 were estimated. Early discontinuation was defined as no prescriptions during the second half-year following the first prescription....... There was a positive association between the prevalence of prescribing for the specific drugs studied (antidepressants, antidiabetics, drugs against osteoporosis and lipid-lowering drugs) and early discontinuation (r = 0.29 -0.44), but not for anti-hypertensive drugs. The analysis of the association between prevalence...

Augmented Lagrangian for shallow viscoplastic flow with topography

Science.gov (United States)

Ionescu, Ioan R.

2013-06-01

In this paper we have developed a robust numerical algorithm for the visco-plastic Saint-Venant model with topography. For the time discretization an implicit (backward) Euler scheme was used. To solve the resulting nonlinear equations, a four steps iterative algorithm was proposed. To handle the non-differentiability of the plastic terms an iterative decomposition-coordination formulation coupled with the augmented Lagrangian method was adopted. The proposed algorithm is consistent, i.e. if the convergence is achieved then the iterative solution satisfies the nonlinear system at each time iteration. The equations for the velocity field are discretized using the finite element method, while a discontinuous Galerkin method, with an upwind choice of the flux, is adopted for solving the hyperbolic equations that describe the evolution of the thickness. The algorithm permits to solve alternatively, at each iteration, the equations for the velocity field and for the thickness. The iterative decomposition coordination formulation coupled with the augmented Lagrangian method works very well and no instabilities are present. The proposed algorithm has a very good convergence rate, with the exception of large Reynolds numbers (Re≫1000), not involved in the applications concerned by the shallow viscoplastic model. The discontinuous Galerkin technique assure the mass conservation of the shallow system. The model has the exact C-property for a plane bottom and an asymptotic C-property for a general topography. Some boundary value problems were selected to analyze the robustness of the numerical algorithm and the predictive capabilities of the mechanical model. The comparison with an exact rigid flow solution illustrates the accuracy of the numerical scheme in handling the non-differentiability of the plastic terms. The influence of the mesh and of the time step are investigated for the flow of a Bingham fluid in a talweg. The role of the material cohesion in stopping a

The discrete maximum principle for Galerkin solutions of elliptic problems

Czech Academy of Sciences Publication Activity Database

Vejchodský, Tomáš

2012-01-01

Roč. 10, č. 1 (2012), s. 25-43 ISSN 1895-1074 R&D Projects: GA AV ČR IAA100760702 Institutional research plan: CEZ:AV0Z10190503 Keywords : discrete maximum principle * monotone methods * Galerkin solution Subject RIV: BA - General Mathematics Impact factor: 0.405, year: 2012 http://www.springerlink.com/content/x73624wm23x4wj26

A study of upwind schemes on the laminar hypersonic heating predictions for the reusable space vehicle

Science.gov (United States)

Qu, Feng; Sun, Di; Zuo, Guang

2018-06-01

With the rapid development of the Computational Fluid Dynamics (CFD), Accurate computing hypersonic heating is in a high demand for the design of the new generation reusable space vehicle to conduct deep space exploration. In the past years, most researchers try to solve this problem by concentrating on the choice of the upwind schemes or the definition of the cell Reynolds number. However, the cell Reynolds number dependencies and limiter dependencies of the upwind schemes, which are of great importance to their performances in hypersonic heating computations, are concerned by few people. In this paper, we conduct a systematic study on these properties respectively. Results in our test cases show that SLAU (Simple Low-dissipation AUSM-family) is with a much higher level of accuracy and robustness in hypersonic heating predictions. Also, it performs much better in terms of the limiter dependency and the cell Reynolds number dependency.

Stochastic Least-Squares Petrov--Galerkin Method for Parameterized Linear Systems

Energy Technology Data Exchange (ETDEWEB)

Lee, Kookjin [Univ. of Maryland, College Park, MD (United States). Dept. of Computer Science; Carlberg, Kevin [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Elman, Howard C. [Univ. of Maryland, College Park, MD (United States). Dept. of Computer Science and Inst. for Advanced Computer Studies

2018-03-29

Here, we consider the numerical solution of parameterized linear systems where the system matrix, the solution, and the right-hand side are parameterized by a set of uncertain input parameters. We explore spectral methods in which the solutions are approximated in a chosen finite-dimensional subspace. It has been shown that the stochastic Galerkin projection technique fails to minimize any measure of the solution error. As a remedy for this, we propose a novel stochatic least-squares Petrov--Galerkin (LSPG) method. The proposed method is optimal in the sense that it produces the solution that minimizes a weighted $\\ell^2$-norm of the residual over all solutions in a given finite-dimensional subspace. Moreover, the method can be adapted to minimize the solution error in different weighted $\\ell^2$-norms by simply applying a weighting function within the least-squares formulation. In addition, a goal-oriented seminorm induced by an output quantity of interest can be minimized by defining a weighting function as a linear functional of the solution. We establish optimality and error bounds for the proposed method, and extensive numerical experiments show that the weighted LSPG method outperforms other spectral methods in minimizing corresponding target weighted norms.

Development of One Dimensional Hyperbolic Coupled Solver for Two-Phase Flows

International Nuclear Information System (INIS)

Kim, Eoi Jin; Kim, Jong Tae; Jeong, Jae June

2008-08-01

The purpose of this study is a code development for one dimensional two-phase two-fluid flows. In this study, the computations of two-phase flow were performed by using the Roe scheme which is one of the upwind schemes. The upwind scheme is widely used in the computational fluid dynamics because it can capture discontinuities clearly such as a shock. And this scheme is applicable to multi-phase flows by the extension methods which were developed by Toumi, Stadtke, etc. In this study, the extended Roe upwind scheme by Toumi for two-phase flow was implemented in the one-dimensional code. The scheme was applied to a shock tube problem and a water faucet problem. This numerical method seems efficient for non oscillating solutions of two phase flow problems, and also capable for capturing discontinuities

Development of One Dimensional Hyperbolic Coupled Solver for Two-Phase Flows

Energy Technology Data Exchange (ETDEWEB)

Kim, Eoi Jin; Kim, Jong Tae; Jeong, Jae June

2008-08-15

The purpose of this study is a code development for one dimensional two-phase two-fluid flows. In this study, the computations of two-phase flow were performed by using the Roe scheme which is one of the upwind schemes. The upwind scheme is widely used in the computational fluid dynamics because it can capture discontinuities clearly such as a shock. And this scheme is applicable to multi-phase flows by the extension methods which were developed by Toumi, Stadtke, etc. In this study, the extended Roe upwind scheme by Toumi for two-phase flow was implemented in the one-dimensional code. The scheme was applied to a shock tube problem and a water faucet problem. This numerical method seems efficient for non oscillating solutions of two phase flow problems, and also capable for capturing discontinuities.

The dimension split element-free Galerkin method for three-dimensional potential problems

Science.gov (United States)

Meng, Z. J.; Cheng, H.; Ma, L. D.; Cheng, Y. M.

2018-02-01

This paper presents the dimension split element-free Galerkin (DSEFG) method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-dimensional potential problem can be transformed into a series of two-dimensional problems. For these two-dimensional problems, the improved moving least-squares (IMLS) approximation is applied to construct the shape function, which uses an orthogonal function system with a weight function as the basis functions. The Galerkin weak form is applied to obtain a discretized system equation, and the penalty method is employed to impose the essential boundary condition. The finite difference method is selected in the splitting direction. For the purposes of demonstration, some selected numerical examples are solved using the DSEFG method. The convergence study and error analysis of the DSEFG method are presented. The numerical examples show that the DSEFG method has greater computational precision and computational efficiency than the IEFG method.

Convergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficients

KAUST Repository

Beck, Joakim; Nobile, Fabio; Tamellini, Lorenzo; Tempone, Raul

2014-01-01

In this work we consider quasi-optimal versions of the Stochastic Galerkin method for solving linear elliptic PDEs with stochastic coefficients. In particular, we consider the case of a finite number N of random inputs and an analytic dependence of the solution of the PDE with respect to the parameters in a polydisc of the complex plane CN. We show that a quasi-optimal approximation is given by a Galerkin projection on a weighted (anisotropic) total degree space and prove a (sub)exponential convergence rate. As a specific application we consider a thermal conduction problem with non-overlapping inclusions of random conductivity. Numerical results show the sharpness of our estimates. © 2013 Elsevier Ltd. All rights reserved.

Convergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficients

KAUST Repository

Beck, Joakim

2014-03-01

In this work we consider quasi-optimal versions of the Stochastic Galerkin method for solving linear elliptic PDEs with stochastic coefficients. In particular, we consider the case of a finite number N of random inputs and an analytic dependence of the solution of the PDE with respect to the parameters in a polydisc of the complex plane CN. We show that a quasi-optimal approximation is given by a Galerkin projection on a weighted (anisotropic) total degree space and prove a (sub)exponential convergence rate. As a specific application we consider a thermal conduction problem with non-overlapping inclusions of random conductivity. Numerical results show the sharpness of our estimates. © 2013 Elsevier Ltd. All rights reserved.

Error Analysis of Galerkin's Method for Semilinear Equations

Directory of Open Access Journals (Sweden)

Tadashi Kawanago

2012-01-01

Full Text Available We establish a general existence result for Galerkin's approximate solutions of abstract semilinear equations and conduct an error analysis. Our results may be regarded as some extension of a precedent work (Schultz 1969. The derivation of our results is, however, different from the discussion in his paper and is essentially based on the convergence theorem of Newton’s method and some techniques for deriving it. Some of our results may be applicable for investigating the quality of numerical verification methods for solutions of ordinary and partial differential equations.

Modeling Storm Surges Using Discontinuous Galerkin Methods

Science.gov (United States)

2016-06-01

layer non-reflecting boundary condition (NRBC) on the right wall of the model. A NRBC is when an artificial boundary , B, is created, which truncates the... applications ,” Journal of Computational Physics, 2004. [30] P. L. Butzer and R. Weis, “On the lax equivalence theorem equipped with orders,” Journal of...closer to the shoreline. In our simulation, we also learned of the effects spurious waves can have on the results. Due to boundary conditions, a

Stochastic spectral Galerkin and collocation methods for PDEs with random coefficients: A numerical comparison

KAUST Repository

Bä ck, Joakim; Nobile, Fabio; Tamellini, Lorenzo; Tempone, Raul

2010-01-01

Much attention has recently been devoted to the development of Stochastic Galerkin (SG) and Stochastic Collocation (SC) methods for uncertainty quantification. An open and relevant research topic is the comparison of these two methods

Organising medication discontinuation: a qualitative study exploring the views of general practitioners toward discontinuing statins.

Science.gov (United States)

Nixon, Michael; Kousgaard, Marius Brostrøm

2016-07-07

Discontinuing medications is a complex decision making process and an important medical practice. It is a tool in reducing polypharmacy, reducing health system expenditure and improving patient quality of life. Few studies have looked at how general practitioners (GPs) discontinue a medication, in agreement with the patients, from a professional perspective. Three research questions were examined in this study: when does medication discontinuation occur in general practice, how is discontinuing medication handled in the GP's practice and how do GPs make decisions about discontinuing medication? Twenty four GPs were interviewed using a maximum variation sample strategy. Participant observations were done in three general practices, for one day each, totalling approximately 30 consultations. The results show that different discontinuation cues (related to the type of consultation, medical records and the patient) create situations of dissonance that can lead to the GP considering the option of discontinuation. We also show that there is a lot of ambiguity in situations of discontinuing and that some GPs trialled discontinuing as means of generating more information that could be used to deal with the ambiguity. We conclude that the practice of discontinuation should be conceptualised as a continually evaluative process and one that requires sustained reflection through a culture of systematically scheduled check-ups, routinely eliciting the patient's experience of taking drugs and trialling discontinuation. Some policy recommendations are offered including supporting GPs with lists or handbooks that directly address discontinuation and by developing more person centred clinical guidelines that discuss discontinuation more explicitly.

Convergence Analysis of Generalized Jacobi-Galerkin Methods for Second Kind Volterra Integral Equations with Weakly Singular Kernels

Directory of Open Access Journals (Sweden)

Haotao Cai

2017-01-01

Full Text Available We develop a generalized Jacobi-Galerkin method for second kind Volterra integral equations with weakly singular kernels. In this method, we first introduce some known singular nonpolynomial functions in the approximation space of the conventional Jacobi-Galerkin method. Secondly, we use the Gauss-Jacobi quadrature rules to approximate the integral term in the resulting equation so as to obtain high-order accuracy for the approximation. Then, we establish that the approximate equation has a unique solution and the approximate solution arrives at an optimal convergence order. One numerical example is presented to demonstrate the effectiveness of the proposed method.

Numerical and experimental validation of a particle Galerkin method for metal grinding simulation

Science.gov (United States)

Wu, C. T.; Bui, Tinh Quoc; Wu, Youcai; Luo, Tzui-Liang; Wang, Morris; Liao, Chien-Chih; Chen, Pei-Yin; Lai, Yu-Sheng

2018-03-01

In this paper, a numerical approach with an experimental validation is introduced for modelling high-speed metal grinding processes in 6061-T6 aluminum alloys. The derivation of the present numerical method starts with an establishment of a stabilized particle Galerkin approximation. A non-residual penalty term from strain smoothing is introduced as a means of stabilizing the particle Galerkin method. Additionally, second-order strain gradients are introduced to the penalized functional for the regularization of damage-induced strain localization problem. To handle the severe deformation in metal grinding simulation, an adaptive anisotropic Lagrangian kernel is employed. Finally, the formulation incorporates a bond-based failure criterion to bypass the prospective spurious damage growth issues in material failure and cutting debris simulation. A three-dimensional metal grinding problem is analyzed and compared with the experimental results to demonstrate the effectiveness and accuracy of the proposed numerical approach.

Error analysis of some Galerkin - least squares methods for the elasticity equations

International Nuclear Information System (INIS)

Franca, L.P.; Stenberg, R.

1989-05-01

We consider the recent technique of stabilizing mixed finite element methods by augmenting the Galerkin formulation with least squares terms calculated separately on each element. The error analysis is performed in a unified manner yielding improved results for some methods introduced earlier. In addition, a new formulation is introduced and analyzed [pt

Upwind MacCormack Euler solver with non-equilibrium chemistry

Science.gov (United States)

Sherer, Scott E.; Scott, James N.

1993-01-01

A computer code, designated UMPIRE, is currently under development to solve the Euler equations in two dimensions with non-equilibrium chemistry. UMPIRE employs an explicit MacCormack algorithm with dissipation introduced via Roe's flux-difference split upwind method. The code also has the capability to employ a point-implicit methodology for flows where stiffness is introduced through the chemical source term. A technique consisting of diagonal sweeps across the computational domain from each corner is presented, which is used to reduce storage and execution requirements. Results depicting one dimensional shock tube flow for both calorically perfect gas and thermally perfect, dissociating nitrogen are presented to verify current capabilities of the program. Also, computational results from a chemical reactor vessel with no fluid dynamic effects are presented to check the chemistry capability and to verify the point implicit strategy.

Bubble-Enriched Least-Squares Finite Element Method for Transient Advective Transport

Directory of Open Access Journals (Sweden)

Rajeev Kumar

2008-01-01

Full Text Available The least-squares finite element method (LSFEM has received increasing attention in recent years due to advantages over the Galerkin finite element method (GFEM. The method leads to a minimization problem in the L2-norm and thus results in a symmetric and positive definite matrix, even for first-order differential equations. In addition, the method contains an implicit streamline upwinding mechanism that prevents the appearance of oscillations that are characteristic of the Galerkin method. Thus, the least-squares approach does not require explicit stabilization and the associated stabilization parameters required by the Galerkin method. A new approach, the bubble enriched least-squares finite element method (BELSFEM, is presented and compared with the classical LSFEM. The BELSFEM requires a space-time element formulation and employs bubble functions in space and time to increase the accuracy of the finite element solution without degrading computational performance. We apply the BELSFEM and classical least-squares finite element methods to benchmark problems for 1D and 2D linear transport. The accuracy and performance are compared.

Galerkin v. discrete-optimal projection in nonlinear model reduction

Energy Technology Data Exchange (ETDEWEB)

Carlberg, Kevin Thomas [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Barone, Matthew Franklin [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Antil, Harbir [George Mason Univ., Fairfax, VA (United States)

2015-04-01

Discrete-optimal model-reduction techniques such as the Gauss{Newton with Approximated Tensors (GNAT) method have shown promise, as they have generated stable, accurate solutions for large-scale turbulent, compressible ow problems where standard Galerkin techniques have failed. However, there has been limited comparative analysis of the two approaches. This is due in part to difficulties arising from the fact that Galerkin techniques perform projection at the time-continuous level, while discrete-optimal techniques do so at the time-discrete level. This work provides a detailed theoretical and experimental comparison of the two techniques for two common classes of time integrators: linear multistep schemes and Runge{Kutta schemes. We present a number of new ndings, including conditions under which the discrete-optimal ROM has a time-continuous representation, conditions under which the two techniques are equivalent, and time-discrete error bounds for the two approaches. Perhaps most surprisingly, we demonstrate both theoretically and experimentally that decreasing the time step does not necessarily decrease the error for the discrete-optimal ROM; instead, the time step should be `matched' to the spectral content of the reduced basis. In numerical experiments carried out on a turbulent compressible- ow problem with over one million unknowns, we show that increasing the time step to an intermediate value decreases both the error and the simulation time of the discrete-optimal reduced-order model by an order of magnitude.

The Stochastic Galerkin Method for Darcy Flow Problem with Log-Normal Random

Czech Academy of Sciences Publication Activity Database

Beres, Michal; Domesová, Simona

2017-01-01

Roč. 15, č. 2 (2017), s. 267-279 ISSN 1336-1376 R&D Projects: GA MŠk LQ1602 Institutional support: RVO:68145535 Keywords : Darcy flow * Gaussian random field * Karhunen-Loeve decomposition * polynomial chaos * Stochastic Galerkin method Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics http://advances.utc.sk/index.php/AEEE/article/view/2280

System dynamics with interaction discontinuity

CERN Document Server

Luo, Albert C J

2015-01-01

This book describes system dynamics with discontinuity caused by system interactions and presents the theory of flow singularity and switchability at the boundary in discontinuous dynamical systems. Based on such a theory, the authors address dynamics and motion mechanism of engineering discontinuous systems due to interaction. Stability and bifurcations of fixed points in nonlinear discrete dynamical systems are presented, and mapping dynamics are developed for analytical predictions of periodic motions in engineering discontinuous dynamical systems. Ultimately, the book provides an alternative way to discuss the periodic and chaotic behaviors in discontinuous dynamical systems.

Symmetric-Galerkin BEM simulation of fracture with frictional contact

CSIR Research Space (South Africa)

Phan, AV

2003-06-14

Full Text Available FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2003; 57:835?851 (DOI: 10.1002/nme.707) Symmetric-Galerkin BEM simulation of fracture with frictional contact A.-V. Phan1;asteriskmath;?, J. A. L. Napier2, L. J. Gray3 and T. Kaplan3 1Department... Methods in Engineering 1975; 9:495?507. 35. Barsoum RS. On the use of isoparametric FFnite elements in linear fracture mechanics. International Journal for Numerical Methods in Engineering 1976; 10:25?37. 36. Gray LJ, Phan A-V, Paulino GH, Kaplan T...

Effective implementation of wavelet Galerkin method

Science.gov (United States)

Finěk, Václav; Šimunková, Martina

2012-11-01

It was proved by W. Dahmen et al. that an adaptive wavelet scheme is asymptotically optimal for a wide class of elliptic equations. This scheme approximates the solution u by a linear combination of N wavelets and a benchmark for its performance is the best N-term approximation, which is obtained by retaining the N largest wavelet coefficients of the unknown solution. Moreover, the number of arithmetic operations needed to compute the approximate solution is proportional to N. The most time consuming part of this scheme is the approximate matrix-vector multiplication. In this contribution, we will introduce our implementation of wavelet Galerkin method for Poisson equation -Δu = f on hypercube with homogeneous Dirichlet boundary conditions. In our implementation, we identified nonzero elements of stiffness matrix corresponding to the above problem and we perform matrix-vector multiplication only with these nonzero elements.

Application of a mixed Galerkin/least-squares method to axisymetric shell problems subjected to arbitrary loading

International Nuclear Information System (INIS)

Loula, A.F.D.; Toledo, E.M.; Franca, L.P.; Garcia, E.L.M.

1989-08-01

A variationaly consistent finite element formulation for constrained problems free from shear or membrane locking is applied to axisymetric shells subjected to arbitrary loading. The governing equations are writen according to Love's classical theory for a problem of bending of axisymetric thin and moderately thick shells accounting for shear deformation. The mixed variational formulation, in terms of stresses and displacements here presented consists of classical Galerkin method plus mesh-dependent least-square type terms employed with equal-order finite element polynomials. The additional terms enhance stability and accuracy of the original Galerkin method, as already proven theoretically and confirmed trough numerical experiments. Numerical results of some examples are presented to demonstrate the good stability and accuracy of the formulation. (author) [pt

On the stability of rotational discontinuities

International Nuclear Information System (INIS)

Richter, P.; Scholer, M.

1989-01-01

The stability of symmetric rotational discontinuities in which the magnetic field rotates by 180 degree is investigated by means of a one-dimensional self-consistent hybrid code. Rotational discontinuities with an angle Θ > 45 degree between the discontinuity normal direction and the upstream magnetic field are found to be relatively stable. The discontinuity normal is in the x direction and the initial magnetic field has finite y component only in the transition region. In the case of the ion (left-handed) sense of rotation of the tangential magnetic field, the transition region does not broaden with time. In the case of the electron (right-handed) sense of rotation, a damped wavetrain builds up in the B y component downstream of the rotational discontinuity and the discontinuity broadens with time. Rotational discontinuities with smaller angles, Θ, are unstable. Examples for a rotational discontinuity with Θ = 30 degree and the electron sense of rotation as well as a rotational discontinuity with Θ = 15 degree and the ion sense of rotation show that these discontinuities into waves. These waves travel approximately with Alfven velocity in the upstream direction and are therefore phase standing in the simulation system. The magnetic hodograms of these disintegrated discontinuities are S-shaped. The upstream portion of the hodogram is always right-handed; the downstream portion is always left-handed

Energy-preserving H1-Galerkin schemes for shallow water wave equations with peakon solutions

International Nuclear Information System (INIS)

Miyatake, Yuto; Matsuo, Takayasu

2012-01-01

New energy-preserving Galerkin schemes for the Camassa–Holm and the Degasperis–Procesi equations which model shallow water waves are presented. The schemes can be implemented only with cheap H 1 elements, which is expected to be sufficient to catch the characteristic peakon solutions. The keys of the derivation are the Hamiltonian structures of the equations and an L 2 -projection technique newly employed in the present Letter to mimic the Hamiltonian structures in a discrete setting, so that the desired energy-preserving property rightly follows. Numerical examples confirm the effectiveness of the schemes. -- Highlights: ► Numerical integration of the Camassa–Holm and Degasperis–Procesi equation. ► New energy-preserving Galerkin schemes for these equations are proposed. ► They can be implemented only with P1 elements. ► They well capture the characteristic peakon solutions over long time. ► The keys are the Hamiltonian structures and L 2 -projection technique.

A simplified model of the Martian atmosphere - Part 2: a POD-Galerkin analysis

Directory of Open Access Journals (Sweden)

S. G. Whitehouse

2005-01-01

Full Text Available In Part I of this study Whitehouse et al. (2005 performed a diagnostic analysis of a simplied model of the Martian atmosphere, in which topography was absent and in which heating was modelled as Newtonian relaxation towards a zonally symmetric equilibrium temperature field. There we derived a reduced-order approximation to the vertical and the horizonal structure of the baroclinically unstable Martian atmosphere, retaining only the barotropic mode and the leading order baroclinic modes. Our objectives in Part II of the study are to incorporate these approximations into a Proper Orthogonal Decomposition-Galerkin expansion of the spherical quasi-geostrophic model in order to derive hierarchies of nonlinear ordinary differential equations for the time-varying coefficients of the spatial structures. Two different vertical truncations are considered, as well as three different norms and 3 different Galerkin truncations. We investigate each in turn, using tools from bifurcation theory, to determine which of the systems most closely resembles the data for which the original diagnostics were performed.

Gauss-Galerkin quadrature rules for quadratic and cubic spline spaces and their application to isogeometric analysis

KAUST Repository

Barton, Michael; Calo, Victor M.

2016-01-01

We introduce Gaussian quadrature rules for spline spaces that are frequently used in Galerkin discretizations to build mass and stiffness matrices. By definition, these spaces are of even degrees. The optimal quadrature rules we recently derived

Generalized multiscale finite element method for elasticity equations

KAUST Repository

Chung, Eric T.

2014-10-05

In this paper, we discuss the application of generalized multiscale finite element method (GMsFEM) to elasticity equation in heterogeneous media. We consider steady state elasticity equations though some of our applications are motivated by elastic wave propagation in subsurface where the subsurface properties can be highly heterogeneous and have high contrast. We present the construction of main ingredients for GMsFEM such as the snapshot space and offline spaces. The latter is constructed using local spectral decomposition in the snapshot space. The spectral decomposition is based on the analysis which is provided in the paper. We consider both continuous Galerkin and discontinuous Galerkin coupling of basis functions. Both approaches have their cons and pros. Continuous Galerkin methods allow avoiding penalty parameters though they involve partition of unity functions which can alter the properties of multiscale basis functions. On the other hand, discontinuous Galerkin techniques allow gluing multiscale basis functions without any modifications. Because basis functions are constructed independently from each other, this approach provides an advantage. We discuss the use of oversampling techniques that use snapshots in larger regions to construct the offline space. We provide numerical results to show that one can accurately approximate the solution using reduced number of degrees of freedom.

Flow and wakes in large wind farms. Final report for UpWind WP8

Energy Technology Data Exchange (ETDEWEB)

Barthelmie, R.J.; Frandsen, S.T.; Rathmann, O. (Risoe DTU (Denmark)); Hansen, K. (Technical Univ. of Denmark (DTU), Kgs. Lyngby (Denmark)); Politis, E.; Prospathopoulos, J. (CRES (Greece)); Schepers, J.G. (ECN, Petten (Netherlands)); Rados, K. (NTUA, Athens (Greece)); Cabezon, D. (CENER, Sarriguren (Spain)); Schlez, W.; Neubert, A.; Heath, M. (Garrad Hassan and Partners (Germany) (United Kingdom))

2011-02-15

This report summarises the research undertaken through the European Commission funded project UpWind Wp8:Flow. The objective of the work was to develop understanding of flow in large wind farms and to evaluate models of power losses due to wind turbine wakes focusing on complex terrain and offshore. A crosscutting activity was to improve and compare the performance of computational fluid dynamics models with wind farm models. The report contains 6 deliverable reports and guideline to wind farm wake analysis as appendices. (Author)

A space-time mixed galerkin marching-on-in-time scheme for the time-domain combined field integral equation

KAUST Repository

Beghein, Yves

2013-03-01

The time domain combined field integral equation (TD-CFIE), which is constructed from a weighted sum of the time domain electric and magnetic field integral equations (TD-EFIE and TD-MFIE) for analyzing transient scattering from closed perfect electrically conducting bodies, is free from spurious resonances. The standard marching-on-in-time technique for discretizing the TD-CFIE uses Galerkin and collocation schemes in space and time, respectively. Unfortunately, the standard scheme is theoretically not well understood: stability and convergence have been proven for only one class of space-time Galerkin discretizations. Moreover, existing discretization schemes are nonconforming, i.e., the TD-MFIE contribution is tested with divergence conforming functions instead of curl conforming functions. We therefore introduce a novel space-time mixed Galerkin discretization for the TD-CFIE. A family of temporal basis and testing functions with arbitrary order is introduced. It is explained how the corresponding interactions can be computed efficiently by existing collocation-in-time codes. The spatial mixed discretization is made fully conforming and consistent by leveraging both Rao-Wilton-Glisson and Buffa-Christiansen basis functions and by applying the appropriate bi-orthogonalization procedures. The combination of both techniques is essential when high accuracy over a broad frequency band is required. © 2012 IEEE.

An improved wavelet-Galerkin method for dynamic response reconstruction and parameter identification of shear-type frames

Science.gov (United States)

Bu, Haifeng; Wang, Dansheng; Zhou, Pin; Zhu, Hongping

2018-04-01

An improved wavelet-Galerkin (IWG) method based on the Daubechies wavelet is proposed for reconstructing the dynamic responses of shear structures. The proposed method flexibly manages wavelet resolution level according to excitation, thereby avoiding the weakness of the wavelet-Galerkin multiresolution analysis (WGMA) method in terms of resolution and the requirement of external excitation. IWG is implemented by this work in certain case studies, involving single- and n-degree-of-freedom frame structures subjected to a determined discrete excitation. Results demonstrate that IWG performs better than WGMA in terms of accuracy and computation efficiency. Furthermore, a new method for parameter identification based on IWG and an optimization algorithm are also developed for shear frame structures, and a simultaneous identification of structural parameters and excitation is implemented. Numerical results demonstrate that the proposed identification method is effective for shear frame structures.

Comparison of two Galerkin quadrature methods

International Nuclear Information System (INIS)

Morel, J. E.; Warsa, J. S.; Franke, B. C.; Prinja, A. K.

2013-01-01

We compare two methods for generating Galerkin quadrature for problems with highly forward-peaked scattering. In Method 1, the standard Sn method is used to generate the moment-to-discrete matrix and the discrete-to-moment is generated by inverting the moment-to-discrete matrix. In Method 2, which we introduce here, the standard Sn method is used to generate the discrete-to-moment matrix and the moment-to-discrete matrix is generated by inverting the discrete-to-moment matrix. Method 1 has the advantage that it preserves both N eigenvalues and N eigenvectors (in a pointwise sense) of the scattering operator with an N-point quadrature. Method 2 has the advantage that it generates consistent angular moment equations from the corresponding S N equations while preserving N eigenvalues of the scattering operator with an N-point quadrature. Our computational results indicate that these two methods are quite comparable for the test problem considered. (authors)

A weak Galerkin least-squares finite element method for div-curl systems

Science.gov (United States)

Li, Jichun; Ye, Xiu; Zhang, Shangyou

2018-06-01

In this paper, we introduce a weak Galerkin least-squares method for solving div-curl problem. This finite element method leads to a symmetric positive definite system and has the flexibility to work with general meshes such as hybrid mesh, polytopal mesh and mesh with hanging nodes. Error estimates of the finite element solution are derived. The numerical examples demonstrate the robustness and flexibility of the proposed method.

Galerkin algorithm for multidimensional plasma simulation codes. Informal report

International Nuclear Information System (INIS)

Godfrey, B.B.

1979-03-01

A Galerkin finite element differencing scheme has been developed for a computer simulation of plasmas. The new difference equations identically satisfy an equation of continuity. Thus, the usual current correction procedure, involving inversion of Poisson's equation, is unnecessary. The algorithm is free of many numerical Cherenkov instabilities. This differencing scheme has been implemented in CCUBE, an already existing relativistic, electromagnetic, two-dimensional PIC code in arbitrary separable, orthogonal coordinates. The separability constraint is eliminated by the new algorithm. The new version of CCUBE exhibits good stability and accuracy with reduced computer memory and time requirements. Details of the algorithm and its implementation are presented

General Practitioners’ Decisions about Discontinuation of Medication

DEFF Research Database (Denmark)

Nixon, Michael Simon; Vendelø, Morten Thanning

2016-01-01

insights about decision making when discontinuing medication. It also offers one of the first examinations of how the institutional context embedding GPs influences their decisions about discontinuation. For policymakers interested in the discontinuation of medication, the findings suggest that de......Purpose – The purpose of this paper is to investigate how general practitioners’ (GPs) decisions about discontinuation of medication are influenced by their institutional context. Design/methodology/approach – In total, 24 GPs were interviewed, three practices were observed and documents were...... a weak frame for discontinuation. Three reasons for this are identified: the guidelines provide dominating triggers for prescribing, they provide weak priming for discontinuation as an option, and they underscore a cognitive constraint against discontinuation. Originality/value – The analysis offers new...

An h-p Taylor-Galerkin finite element method for compressible Euler equations

Science.gov (United States)

Demkowicz, L.; Oden, J. T.; Rachowicz, W.; Hardy, O.

1991-01-01

An extension of the familiar Taylor-Galerkin method to arbitrary h-p spatial approximations is proposed. Boundary conditions are analyzed, and a linear stability result for arbitrary meshes is given, showing the unconditional stability for the parameter of implicitness alpha not less than 0.5. The wedge and blunt body problems are solved with both linear, quadratic, and cubic elements and h-adaptivity, showing the feasibility of higher orders of approximation for problems with shocks.

Factors affecting IUCD discontinuation in Nepal

DEFF Research Database (Denmark)

Thapa, Subash; Paudel, Ishwari Sharma; Bhattarai, Sailesh

2015-01-01

Information related to contraception discontinuation, especially in the context of Nepal is very limited. A nested case-control study was carried out to determine the factors affecting discontinuation of intrauterine contraceptive devices (IUCDs). A total of 115 cases (IUCD discontinuers) and 115...

On High-Order Upwind Methods for Advection

Science.gov (United States)

Huynh, Hung T.

2017-01-01

Scheme III (piecewise linear) and V (piecewise parabolic) of Van Leer are shown to yield identical solutions provided the initial conditions are chosen in an appropriate manner. This result is counter intuitive since it is generally believed that piecewise linear and piecewise parabolic methods cannot produce the same solutions due to their different degrees of approximation. The result also shows a key connection between the approaches of discontinuous and continuous representations.

Galerkin FEM for Fractional Order Parabolic Equations with Initial Data in H − s , 0 ≤ s ≤ 1

KAUST Repository

Jin, Bangti; Lazarov, Raytcho; Pasciak, Joseph; Zhou, Zhi

2013-01-01

We investigate semi-discrete numerical schemes based on the standard Galerkin and lumped mass Galerkin finite element methods for an initial-boundary value problem for homogeneous fractional diffusion problems with non-smooth initial data. We assume that Ω ⊂ ℝd , d = 1,2,3 is a convex polygonal (polyhedral) domain. We theoretically justify optimal order error estimates in L2- and H1-norms for initial data in H-s (Ω), 0 ≤ s ≤ 1. We confirm our theoretical findings with a number of numerical tests that include initial data v being a Dirac δ-function supported on a (d-1)-dimensional manifold. © 2013 Springer-Verlag.

27 CFR 555.128 - Discontinuance of business.

Science.gov (United States)

2010-04-01

... 27 Alcohol, Tobacco Products and Firearms 3 2010-04-01 2010-04-01 false Discontinuance of business... Discontinuance of business. Where an explosive materials business or operations is discontinued and succeeded by... such facts and shall be delivered to the successor. Where discontinuance of the business or operations...

Modelling and computing the peaks of carbon emission with balanced growth

International Nuclear Information System (INIS)

Chang, Shuhua; Wang, Xinyu; Wang, Zheng

2016-01-01

Highlights: • We use a more practical utility function to quantify the society’s welfare. • A so-called discontinuous Galerkin method is proposed to solve the ordinary differential equation satisfied by the consumption. • The theoretical results of the discontinuous Galerkin method are obtained. • We establish a Markov model to forecast the energy mix and the industrial structure. - Abstract: In this paper, we assume that under the balanced and optimal economic growth path, the economic growth rate is equal to the consumption growth rate, from which we can obtain the ordinary differential equation governing the consumption level by solving an optimal control problem. Then, a novel numerical method, namely a so-called discontinuous Galerkin method, is applied to solve the ordinary differential equation. The error estimation and the superconvergence estimation of this method are also performed. The model’s mechanism, which makes our assumption coherent, is that once the energy intensity is given, the economic growth is determined, followed by the GDP, the energy demand and the emissions. By applying this model to China, we obtain the conclusion that under the balanced and optimal economic growth path the CO_2 emission will reach its peak in 2030 in China, which is consistent with the U.S.-China Joint Announcement on Climate Change and with other previous scientific results.

27 CFR 478.57 - Discontinuance of business.

Science.gov (United States)

2010-04-01

... 27 Alcohol, Tobacco Products and Firearms 3 2010-04-01 2010-04-01 false Discontinuance of business... Licenses § 478.57 Discontinuance of business. (a) Where a firearm or ammunition business is either discontinued or succeeded by a new owner, the owner of the business discontinued or succeeded shall within 30...

Peaks, plateaus, numerical instabilities, and achievable accuracy in Galerkin and norm minimizing procedures for solving Ax=b

Energy Technology Data Exchange (ETDEWEB)

Cullum, J. [IBM T.J. Watson Research Center, Yorktown Heights, NY (United States)

1994-12-31

Plots of the residual norms generated by Galerkin procedures for solving Ax = b often exhibit strings of irregular peaks. At seemingly erratic stages in the iterations, peaks appear in the residual norm plot, intervals of iterations over which the norms initially increase and then decrease. Plots of the residual norms generated by related norm minimizing procedures often exhibit long plateaus, sequences of iterations over which reductions in the size of the residual norm are unacceptably small. In an earlier paper the author discussed and derived relationships between such peaks and plateaus within corresponding Galerkin/Norm Minimizing pairs of such methods. In this paper, through a set of numerical experiments, the author examines connections between peaks, plateaus, numerical instabilities, and the achievable accuracy for such pairs of iterative methods. Three pairs of methods, GMRES/Arnoldi, QMR/BCG, and two bidiagonalization methods are studied.

DGTD Analysis of Electromagnetic Scattering from Penetrable Conductive Objects with IBC

KAUST Repository

Li, Ping; Shi, Yifei; Jiang, Li; Bagci, Hakan

2015-01-01

To avoid straightforward volumetric discretization, a discontinuous Galerkin time-domain (DGTD) method integrated with the impedance boundary condition (IBC) is presented in this paper to analyze the scattering from objects with finite conductivity

Management applications of discontinuity theory

Science.gov (United States)

Angeler, David G.; Allen, Craig R.; Barichievy, Chris; Eason, Tarsha; Garmestani, Ahjond S.; Graham, Nicholas A.J.; Granholm, Dean; Gunderson, Lance H.; Knutson, Melinda; Nash, Kirsty L.; Nelson, R. John; Nystrom, Magnus; Spanbauer, Trisha; Stow, Craig A.; Sundstrom, Shana M.

2015-01-01

Human impacts on the environment are multifaceted and can occur across distinct spatiotemporal scales. Ecological responses to environmental change are therefore difficult to predict, and entail large degrees of uncertainty. Such uncertainty requires robust tools for management to sustain ecosystem goods and services and maintain resilient ecosystems.We propose an approach based on discontinuity theory that accounts for patterns and processes at distinct spatial and temporal scales, an inherent property of ecological systems. Discontinuity theory has not been applied in natural resource management and could therefore improve ecosystem management because it explicitly accounts for ecological complexity.Synthesis and applications. We highlight the application of discontinuity approaches for meeting management goals. Specifically, discontinuity approaches have significant potential to measure and thus understand the resilience of ecosystems, to objectively identify critical scales of space and time in ecological systems at which human impact might be most severe, to provide warning indicators of regime change, to help predict and understand biological invasions and extinctions and to focus monitoring efforts. Discontinuity theory can complement current approaches, providing a broader paradigm for ecological management and conservation.

Proceedings of the upwind downwind cities air and health conference

International Nuclear Information System (INIS)

2006-01-01

The upwind downwind conference examined the health impacts of poor air quality and how land use decisions impact air quality as well as the roles of industry, community groups, academia and government in improving air quality. Conference attendees included planners, public health officials, policy makers, environmental managers, non-government organizations, academics, industry, community groups and politicians. The conference covered several topics including partnerships between public health and planning with respect to improving air quality in urban environments; the use of science in decision-making and development of new projects, policies and regulations; airshed agreements in North America, in addition to Ontario's new air quality regulations; and examples of citizen groups, non-government organizations, industry, academia and local, provincial and federal governments partnering to improve air quality. A total of 16 presentations were presented at the conference, of which 2 have been catalogued separately for inclusion in this database. The conference also featured several keynote speakers and panel discussions. tabs., figs

Discussion of the numerical stability of an improved upwinding scheme

International Nuclear Information System (INIS)

Hassan, Y.A.; Kim, J.H.

1986-01-01

The prediction of multidimensional heat transfer and fluid flow problems requires the solution of Navier-Stokes equations. Although the use of upwind approximation for the convection terms removes the potential of nonphysical spatial oscillations, such a procedure is burdened with excessive numerical diffusion. Recently published work by Smith and Hutton presented results for some 20 different candidate methods to estimate the convection terms. The overall conclusion was that none of the methods was totally successful. The more accurate methods exhibited nonphysical spatial oscillations. More recently, a procedure was proposed that alleviates the problem of false diffusion. The purpose of this paper is to present several challenging cases, with various flow orientation, to show that the proposed procedure always circumvents the negative coefficients in the discretization equation such that the influence coefficients cannot become negative. The Smith and Hutton test case has been examined to illustrate the merit of this technique. The results are competitive with a large majority of those examined by Smith and Hutton

Vertebral Fractures After Discontinuation of Denosumab

DEFF Research Database (Denmark)

Cummings, Steven R; Ferrari, Serge; Eastell, Richard

2018-01-01

. We analyzed the risk of new or worsening vertebral fractures, especially multiple vertebral fractures, in participants who discontinued denosumab during the FREEDOM study or its Extension. Participants received ≥2 doses of denosumab or placebo Q6M, discontinued treatment, and stayed in the study ≥7...... months after the last dose. Of 1001 participants who discontinued denosumab during FREEDOM or Extension, the vertebral fracture rate increased from 1.2 per 100 participant-years during the on-treatment period to 7.1, similar to participants who received and then discontinued placebo (n = 470; 8.5 per 100....... Therefore, patients who discontinue denosumab should rapidly transition to an alternative antiresorptive treatment. Clinicaltrails.gov: NCT00089791 (FREEDOM) and NCT00523341 (Extension). © 2017 American Society for Bone and Mineral Research....

Approximate solution of the transport equation by methods of Galerkin type

International Nuclear Information System (INIS)

Pitkaranta, J.

1977-01-01

Questions of the existence, uniqueness, and convergence of approximate solutions of transport equations by methods of the Galerkin type (where trial and weighting functions are the same) are discussed. The results presented do not exclude the infinite-dimensional case. Two strategies can be followed in the variational approximation of the transport operator: one proceeds from the original form of the transport equation, while the other is based on the partially symmetrized equation. Both principles are discussed in this paper. The transport equation is assumed in a discretized multigroup form

And still, a new beginning: the Galerkin least-squares gradient method

International Nuclear Information System (INIS)

Franca, L.P.; Carmo, E.G.D. do

1988-08-01

A finite element method is proposed to solve a scalar singular diffusion problem. The method is constructed by adding to the standard Galerkin a mesh-dependent term obtained by taking the gradient of the Euler-lagrange equation and multiplying it by its least-squares. For the one-dimensional homogeneous problem the method is designed to develop nodal exact solution. An error estimate shows that the method converges optimaly for any value of the singular parameter. Numerical results demonstrate the good stability and accuracy properties of the method. (author) [pt

A multiscale method for compressible liquid-vapor flow with surface tension*

Directory of Open Access Journals (Sweden)

Jaegle Felix

2013-01-01

Full Text Available Discontinuous Galerkin methods have become a powerful tool for approximating the solution of compressible flow problems. Their direct use for two-phase flow problems with phase transformation is not straightforward because this type of flows requires a detailed tracking of the phase front. We consider the fronts in this contribution as sharp interfaces and propose a novel multiscale approach. It combines an efficient high-order Discontinuous Galerkin solver for the computation in the bulk phases on the macro-scale with the use of a generalized Riemann solver on the micro-scale. The Riemann solver takes into account the effects of moderate surface tension via the curvature of the sharp interface as well as phase transformation. First numerical experiments in three space dimensions underline the overall performance of the method.

Modeling of flow and reactive transport in IPARS

KAUST Repository

Wheeler, Mary Fanett

2012-03-11

In this work, we describe a number of efficient and locally conservative methods for subsurface flow and reactive transport that have been or are currently being implemented in the IPARS (Integrated Parallel and Accurate Reservoir Simulator). For flow problems, we consider discontinuous Galerkin (DG) methods and mortar mixed finite element methods. For transport problems, we employ discontinuous Galerkin methods and Godunov-mixed methods. For efficient treatment of reactive transport simulations, we present a number of state-of-the-art dynamic mesh adaptation strategies and implementations. Operator splitting approaches and iterative coupling techniques are also discussed. Finally, numerical examples are provided to illustrate the capability of IPARS to treat general biogeochemistry as well as the effectivity of mesh adaptations with DG for transport. © 2012 Bentham Science Publishers. All rights reserved.

Individualized drug dosing using RBF-Galerkin method: Case of anemia management in chronic kidney disease.

Science.gov (United States)

Mirinejad, Hossein; Gaweda, Adam E; Brier, Michael E; Zurada, Jacek M; Inanc, Tamer

2017-09-01

Anemia is a common comorbidity in patients with chronic kidney disease (CKD) and is frequently associated with decreased physical component of quality of life, as well as adverse cardiovascular events. Current treatment methods for renal anemia are mostly population-based approaches treating individual patients with a one-size-fits-all model. However, FDA recommendations stipulate individualized anemia treatment with precise control of the hemoglobin concentration and minimal drug utilization. In accordance with these recommendations, this work presents an individualized drug dosing approach to anemia management by leveraging the theory of optimal control. A Multiple Receding Horizon Control (MRHC) approach based on the RBF-Galerkin optimization method is proposed for individualized anemia management in CKD patients. Recently developed by the authors, the RBF-Galerkin method uses the radial basis function approximation along with the Galerkin error projection to solve constrained optimal control problems numerically. The proposed approach is applied to generate optimal dosing recommendations for individual patients. Performance of the proposed approach (MRHC) is compared in silico to that of a population-based anemia management protocol and an individualized multiple model predictive control method for two case scenarios: hemoglobin measurement with and without observational errors. In silico comparison indicates that hemoglobin concentration with MRHC method has less variation among the methods, especially in presence of measurement errors. In addition, the average achieved hemoglobin level from the MRHC is significantly closer to the target hemoglobin than that of the other two methods, according to the analysis of variance (ANOVA) statistical test. Furthermore, drug dosages recommended by the MRHC are more stable and accurate and reach the steady-state value notably faster than those generated by the other two methods. The proposed method is highly efficient for

A space-time mixed galerkin marching-on-in-time scheme for the time-domain combined field integral equation

KAUST Repository

Beghein, Yves; Cools, Kristof; Bagci, Hakan; De Zutter, Danië l

2013-01-01

electrically conducting bodies, is free from spurious resonances. The standard marching-on-in-time technique for discretizing the TD-CFIE uses Galerkin and collocation schemes in space and time, respectively. Unfortunately, the standard scheme is theoretically

Transient Analysis of Dispersive Power-Ground Plate Pairs With Arbitrarily Shaped Antipads by the DGTD Method With Wave Port Excitation

KAUST Repository

Li, Ping; Jiang, Li Jun; Bagci, Hakan

2016-01-01

A discontinuous Galerkin time-domain (DGTD) method analyzing signal/power integrity on multilayered power-ground parallel plate pairs is proposed. The excitation is realized by introducing wave ports on the antipads where electric/magnetic current

Special discontinuities in nonlinearly elastic media

Science.gov (United States)

Chugainova, A. P.

2017-06-01

Solutions of a nonlinear hyperbolic system of equations describing weakly nonlinear quasitransverse waves in a weakly anisotropic elastic medium are studied. The influence of small-scale processes of dissipation and dispersion is investigated. The small-scale processes determine the structure of discontinuities (shocks) and a set of discontinuities with a stationary structure. Among the discontinuities with a stationary structure, there are special ones that, in addition to relations following from conservation laws, satisfy additional relations required for the existence of their structure. In the phase plane, the structure of such discontinuities is represented by an integral curve joining two saddles. Special discontinuities lead to nonunique self-similar solutions of the Riemann problem. Asymptotics of non-self-similar problems for equations with dissipation and dispersion are found numerically. These asymptotics correspond to self-similar solutions of the problems.

Ultrasonic assessment of shrinkage type discontinuities

International Nuclear Information System (INIS)

Hubber, John

2010-01-01

This investigation into ultrasonic internal discontinuities is intended to demonstrate typical examples of internal 'shrinkage' type discontinuities and its connection with the casting suitability, integrity and reliability in service. This type of discontinuity can be misinterpreted by ultrasonic technicians and can lead to the rejection of castings unnecessarily, due to the mis-characterization of fine shrinkage - discrete porosity. The samples for this investigation were taken from thirty ton heavy section ductile iron mill flange castings, manufactured by Graham Campbell Ferrum International. The sampled area was of discontinuities that were recorded for sizing on an area due to loss of back wall echo, but had acceptable reflectivity. A comparative sample was taken adjacent to the area of discrete porosity. The discontinuities found by this investigation are of a 'spongy' type, gaseous in appearance and are surrounded by acoustically sound material. All discontinuities discussed in this paper are centrally located in the through thickness of the casting. The porous nature of this type of discontinuity consisting of approximately 80-90% metal has its own residual strength, as indicated by the proof stress results which reveal a residual strength of up to 50-60% of that of the unaffected area of the casting. The affected areas are elliptical in shape and vary in density and through thickness throughout.

Stabilities of MHD rotational discontinuities

International Nuclear Information System (INIS)

Wang, S.

1984-11-01

In this paper, the stabilities of MHD rotational discontinuities are analyzed. The results show that the rotational discontinuities in an incompressible magnetofluid are not always stable with respect to infinitesimal perturbation. The instability condition in a special case is obtained. (author)

Dual and primal mixed Petrov-Galerkin finite element methods in heat transfer problems

International Nuclear Information System (INIS)

Loula, A.F.D.; Toledo, E.M.

1988-12-01

New mixed finite element formulations for the steady state heat transfer problem are presented with no limitation in the choice of conforming finite element spaces. Adding least square residual forms of the governing equations of the classical Galerkin formulation the original saddle point problem is transformed into a minimization problem. Stability analysis, error estimates and numerical results are presented, confirming the error estimates and the good performance of this new formulation. (author) [pt

The Galerkin Finite Element Method for A Multi-term Time-Fractional Diffusion equation

OpenAIRE

Jin, Bangti; Lazarov, Raytcho; Liu, Yikan; Zhou, Zhi

2014-01-01

We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite element method using continuous piecewise linear functions. Nearly optimal error estimates for both cases of initial data and inhomogeneous term are derived, which cover both smooth and nonsmooth data. Further we develop a fully discrete scheme based on a finite...

An Equal-Order DG Method for the Incompressible Navier-Stokes Equations

KAUST Repository

Cockburn, Bernardo; Kanschat, Guido; Schö tzau, Dominik

2008-01-01

We introduce and analyze a discontinuous Galerkin method for the incompressible Navier-Stokes equations that is based on finite element spaces of the same polynomial order for the approximation of the velocity and the pressure. Stability

An asymptotic-preserving stochastic Galerkin method for the radiative heat transfer equations with random inputs and diffusive scalings

Energy Technology Data Exchange (ETDEWEB)

Jin, Shi, E-mail: sjin@wisc.edu [Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706 (United States); Institute of Natural Sciences, Department of Mathematics, MOE-LSEC and SHL-MAC, Shanghai Jiao Tong University, Shanghai 200240 (China); Lu, Hanqing, E-mail: hanqing@math.wisc.edu [Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706 (United States)

2017-04-01

In this paper, we develop an Asymptotic-Preserving (AP) stochastic Galerkin scheme for the radiative heat transfer equations with random inputs and diffusive scalings. In this problem the random inputs arise due to uncertainties in cross section, initial data or boundary data. We use the generalized polynomial chaos based stochastic Galerkin (gPC-SG) method, which is combined with the micro–macro decomposition based deterministic AP framework in order to handle efficiently the diffusive regime. For linearized problem we prove the regularity of the solution in the random space and consequently the spectral accuracy of the gPC-SG method. We also prove the uniform (in the mean free path) linear stability for the space-time discretizations. Several numerical tests are presented to show the efficiency and accuracy of proposed scheme, especially in the diffusive regime.

A zonal Galerkin-free POD model for incompressible flows

Science.gov (United States)

Bergmann, Michel; Ferrero, Andrea; Iollo, Angelo; Lombardi, Edoardo; Scardigli, Angela; Telib, Haysam

2018-01-01

A domain decomposition method which couples a high and a low-fidelity model is proposed to reduce the computational cost of a flow simulation. This approach requires to solve the high-fidelity model in a small portion of the computational domain while the external field is described by a Galerkin-free Proper Orthogonal Decomposition (POD) model. We propose an error indicator to determine the extent of the interior domain and to perform an optimal coupling between the two models. This zonal approach can be used to study multi-body configurations or to perform detailed local analyses in the framework of shape optimisation problems. The efficiency of the method to perform predictive low-cost simulations is investigated for an unsteady flow and for an aerodynamic shape optimisation problem.

Optimization of Darrieus turbines with an upwind and downwind momentum model

Science.gov (United States)

Loth, J. L.; McCoy, H.

1983-08-01

This paper presents a theoretical aerodynamic performance optimization for two dimensional vertical axis wind turbines. A momentum type wake model is introduced with separate cosine type interference coefficients for the up and downwind half of the rotor. The cosine type loading permits the rotor blades to become unloaded near the junction of the upwind and downwind rotor halves. Both the optimum and the off design magnitude of the interference coefficients are obtained by equating the drag on each of the rotor halves to that on each of two cosine loaded actuator discs in series. The values for the optimum rotor efficiency, solidity and corresponding interference coefficients have been obtained in a closed form analytic solution by maximizing the power extracted from the downwind rotor half as well as from the entire rotor. A numerical solution was required when viscous effects were incorporated in the rotor optimization.

Weak form of Stokes-Dirac structures and geometric discretization of port-Hamiltonian systems

Science.gov (United States)

Kotyczka, Paul; Maschke, Bernhard; Lefèvre, Laurent

2018-05-01

We present the mixed Galerkin discretization of distributed parameter port-Hamiltonian systems. On the prototypical example of hyperbolic systems of two conservation laws in arbitrary spatial dimension, we derive the main contributions: (i) A weak formulation of the underlying geometric (Stokes-Dirac) structure with a segmented boundary according to the causality of the boundary ports. (ii) The geometric approximation of the Stokes-Dirac structure by a finite-dimensional Dirac structure is realized using a mixed Galerkin approach and power-preserving linear maps, which define minimal discrete power variables. (iii) With a consistent approximation of the Hamiltonian, we obtain finite-dimensional port-Hamiltonian state space models. By the degrees of freedom in the power-preserving maps, the resulting family of structure-preserving schemes allows for trade-offs between centered approximations and upwinding. We illustrate the method on the example of Whitney finite elements on a 2D simplicial triangulation and compare the eigenvalue approximation in 1D with a related approach.

Coupling multipoint flux mixed finite element methodswith continuous Galerkin methods for poroelasticity

KAUST Repository

Wheeler, Mary

2013-11-16

We study the numerical approximation on irregular domains with general grids of the system of poroelasticity, which describes fluid flow in deformable porous media. The flow equation is discretized by a multipoint flux mixed finite element method and the displacements are approximated by a continuous Galerkin finite element method. First-order convergence in space and time is established in appropriate norms for the pressure, velocity, and displacement. Numerical results are presented that illustrate the behavior of the method. © Springer Science+Business Media Dordrecht 2013.

An Element Free Galerkin method for an elastoplastic coupled to damage analysis

Directory of Open Access Journals (Sweden)

Sendi Zohra

2016-01-01

Full Text Available In this work, a Meshless approach for nonlinear solid mechanics is developed based on the Element Free Galerkin method. Furthermore, Meshless is combined with an elastoplastic model coupled to ductile damage. The efficiency of the proposed methodology is evaluated through various numerical examples. Besides these, two-dimensional tensile tests under several boundary conditions were studied and solved by a Dynamic-Explicit resolution scheme. Finally, the results obtained from the numerical simulations are analyzed and critically compared with Finite Element Method results.

Transient Thermal Analysis of 3-D Integrated Circuits Packages by the DGTD Method

KAUST Repository

Li, Ping; Dong, Yilin; Tang, Min; Mao, Junfa; Jiang, Li Jun; Bagci, Hakan

2017-01-01

Since accurate thermal analysis plays a critical role in the thermal design and management of the 3-D system-level integration, in this paper, a discontinuous Galerkin time-domain (DGTD) algorithm is proposed to achieve this purpose

Corner-transport-upwind lattice Boltzmann model for bubble cavitation

Science.gov (United States)

Sofonea, V.; Biciuşcǎ, T.; Busuioc, S.; Ambruş, Victor E.; Gonnella, G.; Lamura, A.

2018-02-01

Aiming to study the bubble cavitation problem in quiescent and sheared liquids, a third-order isothermal lattice Boltzmann model that describes a two-dimensional (2D) fluid obeying the van der Waals equation of state, is introduced. The evolution equations for the distribution functions in this off-lattice model with 16 velocities are solved using the corner-transport-upwind (CTU) numerical scheme on large square lattices (up to 6144 ×6144 nodes). The numerical viscosity and the regularization of the model are discussed for first- and second-order CTU schemes finding that the latter choice allows to obtain a very accurate phase diagram of a nonideal fluid. In a quiescent liquid, the present model allows us to recover the solution of the 2D Rayleigh-Plesset equation for a growing vapor bubble. In a sheared liquid, we investigated the evolution of the total bubble area, the bubble deformation, and the bubble tilt angle, for various values of the shear rate. A linear relation between the dimensionless deformation coefficient D and the capillary number Ca is found at small Ca but with a different factor than in equilibrium liquids. A nonlinear regime is observed for Ca≳0.2 .

Prediction of velocity and attitude of a yacht sailing upwind by computational fluid dynamics

Directory of Open Access Journals (Sweden)

Heebum Lee

2016-01-01

Full Text Available One of the most important factors in sailing yacht design is accurate velocity prediction. Velocity prediction programs (VPP's are widely used to predict velocity of sailing yachts. VPP's, which are primarily based on experimental data and experience of long years, however suffer limitations when applied in realistic conditions. Thus, in the present study, a high fidelity velocity prediction method using computational fluid dynamics (CFD was proposed. Using the developed method, velocity and attitude of a 30 feet sloop yacht, which was developed by Korea Research Institute of Ship and Ocean (KRISO and termed KORDY30, were predicted in upwind sailing condition.

Management applications of discontinuity theory | Science ...

Science.gov (United States)

1.Human impacts on the environment are multifaceted and can occur across distinct spatiotemporal scales. Ecological responses to environmental change are therefore difficult to predict, and entail large degrees of uncertainty. Such uncertainty requires robust tools for management to sustain ecosystem goods and services and maintain resilient ecosystems. 2.We propose an approach based on discontinuity theory that accounts for patterns and processes at distinct spatial and temporal scales, an inherent property of ecological systems. Discontinuity theory has not been applied in natural resource management and could therefore improve ecosystem management because it explicitly accounts for ecological complexity. 3.Synthesis and applications. We highlight the application of discontinuity approaches for meeting management goals. Specifically, discontinuity approaches have significant potential to measure and thus understand the resilience of ecosystems, to objectively identify critical scales of space and time in ecological systems at which human impact might be most severe, to provide warning indicators of regime change, to help predict and understand biological invasions and extinctions and to focus monitoring efforts. Discontinuity theory can complement current approaches, providing a broader paradigm for ecological management and conservation This manuscript provides insight on using discontinuity approaches to aid in managing complex ecological systems. In part

Discrete maximum principle for the P1 - P0 weak Galerkin finite element approximations

Science.gov (United States)

Wang, Junping; Ye, Xiu; Zhai, Qilong; Zhang, Ran

2018-06-01

This paper presents two discrete maximum principles (DMP) for the numerical solution of second order elliptic equations arising from the weak Galerkin finite element method. The results are established by assuming an h-acute angle condition for the underlying finite element triangulations. The mathematical theory is based on the well-known De Giorgi technique adapted in the finite element context. Some numerical results are reported to validate the theory of DMP.

Identifying the factors underlying discontinuation of triptans.

Science.gov (United States)

Wells, Rebecca E; Markowitz, Shira Y; Baron, Eric P; Hentz, Joseph G; Kalidas, Kavita; Mathew, Paul G; Halker, Rashmi; Dodick, David W; Schwedt, Todd J

2014-02-01

To identify factors associated with triptan discontinuation among migraine patients. It is unclear why many migraine patients who are prescribed triptans discontinue this treatment. This study investigated correlates of triptan discontinuation with a focus on potentially modifiable factors to improve compliance. This multicenter cross-sectional survey (n = 276) was performed at US tertiary care headache clinics. Headache fellows who were members of the American Headache Society Headache Fellows Research Consortium recruited episodic and chronic migraine patients who were current triptan users (use within prior 3 months and for ≥1 year) or past triptan users (no use within 6 months; prior use within 2 years). Univariate analyses were first completed to compare current triptan users to past users for: migraine characteristics, other migraine treatments, triptan education, triptan efficacy, triptan side effects, type of prescribing provider, Migraine Disability Assessment (MIDAS) scores and Beck Depression Inventory (BDI) scores. Then, a multivariable logistic regression model was selected from all possible combinations of predictor variables to determine the factors that best correlated with triptan discontinuation. Compared with those still using triptans (n = 207), those who had discontinued use (n = 69) had higher rates of medication overuse (30 vs. 18%, P = .04) and were more likely to have ever used opioids for migraine treatment (57 vs. 38%, P = .006) as well as higher MIDAS (mean 63 vs. 37, P = .001) and BDI scores (mean 10.4 vs. 7.4, P = .009). Compared with discontinued users, current triptan users were more likely to have had their triptan prescribed by a specialist (neurologist, headache specialist, or pain specialist) (74 vs. 54%, P = .002) and were more likely to report headache resolution (53 vs. 14%, P  24 (2.6, [1.5, 4.6]), BDI >4 (2.5, [1.4, 4.5]), and a history of ever using opioids for migraine therapy (2.2, [1

Time-discrete higher order ALE formulations: a priori error analysis

KAUST Repository

Bonito, Andrea; Kyza, Irene; Nochetto, Ricardo H.

2013-01-01

We derive optimal a priori error estimates for discontinuous Galerkin (dG) time discrete schemes of any order applied to an advection-diffusion model defined on moving domains and written in the Arbitrary Lagrangian Eulerian (ALE) framework. Our

27 CFR 478.127 - Discontinuance of business.

Science.gov (United States)

2010-04-01

... business was located: Provided, however, Where State law or local ordinance requires the delivery of... 27 Alcohol, Tobacco Products and Firearms 3 2010-04-01 2010-04-01 false Discontinuance of business... Records § 478.127 Discontinuance of business. Where a licensed business is discontinued and succeeded by a...

Application of an upwind Navier-Stokes code to two-dimensional transonic airfoil flow

International Nuclear Information System (INIS)

Rumsey, C.L.; Thomas, J.L.; Anderson, W.K.; Taylor, S.L.

1987-01-01

An upwind-biased implicit approximate factorization Navier-Stokes algorithm is applied to a variety of steady transonic airfoil cases, using the NACA 0012, RAE 2822, and Jones supercritical airfoils. The thin-layer form of the compressible Navier-Stokes equations is used. Both the CYBER 205 and CRAY 2 supercomputers are utilized, with average computational speeds of about 18 and 16 microsec/gridpoint/iteration, respectively. Lift curves, drag polars, and variations in drag coefficient with Mach number are determined for the NACA 0012 and Jones supercritical airfoils. Also, several cases are computed for comparison with experiment. The effect of grid density and grid extent on a typical turbulent airfoil solution is shown. An algebraic eddy-viscosity turbulence model is used for all of the computations. 10 references

A fractional spline collocation-Galerkin method for the time-fractional diffusion equation

Directory of Open Access Journals (Sweden)

Pezza L.

2018-03-01

Full Text Available The aim of this paper is to numerically solve a diffusion differential problem having time derivative of fractional order. To this end we propose a collocation-Galerkin method that uses the fractional splines as approximating functions. The main advantage is in that the derivatives of integer and fractional order of the fractional splines can be expressed in a closed form that involves just the generalized finite difference operator. This allows us to construct an accurate and efficient numerical method. Several numerical tests showing the effectiveness of the proposed method are presented.

Discontinuity formulas for multiparticle amplitudes

International Nuclear Information System (INIS)

Stapp, H.P.

1976-03-01

It is shown how discontinuity formulas for multiparticle scattering amplitudes are derived from unitarity and analyticity. The assumed analyticity property is the normal analytic structure, which was shown to be equivalent to the space-time macrocausality condition. The discontinuity formulas to be derived are the basis of multi-particle fixed-t dispersion relations

Work package 1B.2 under the European Commission: Integrated wind turbine design (UPWIND): Specification of long-term load measurement technique

Energy Technology Data Exchange (ETDEWEB)

Schmidt Paulsen, U.; Cutululis, N.; Soerensen, Poul

2007-02-15

The present report is the 12 month intermediate report of the UPWIND WP1B2 transmission and conversion. It describes the developed measurement technique for long-term load measurement technique, presents the hardware details, type of sensors and location, data storage and data analysis technique to verify design load assumptions. (au)

Testing discontinuities in nonparametric regression

KAUST Repository

Dai, Wenlin

2017-01-19

In nonparametric regression, it is often needed to detect whether there are jump discontinuities in the mean function. In this paper, we revisit the difference-based method in [13 H.-G. Müller and U. Stadtmüller, Discontinuous versus smooth regression, Ann. Stat. 27 (1999), pp. 299–337. doi: 10.1214/aos/1018031100

Testing discontinuities in nonparametric regression

KAUST Repository

Dai, Wenlin; Zhou, Yuejin; Tong, Tiejun

2017-01-01

In nonparametric regression, it is often needed to detect whether there are jump discontinuities in the mean function. In this paper, we revisit the difference-based method in [13 H.-G. Müller and U. Stadtmüller, Discontinuous versus smooth regression, Ann. Stat. 27 (1999), pp. 299–337. doi: 10.1214/aos/1018031100

Regge calculus from discontinuous metrics

International Nuclear Information System (INIS)

Khatsymovsky, V.M.

2003-01-01

Regge calculus is considered as a particular case of the more general system where the linklengths of any two neighbouring 4-tetrahedra do not necessarily coincide on their common face. This system is treated as that one described by metric discontinuous on the faces. In the superspace of all discontinuous metrics the Regge calculus metrics form some hypersurface defined by continuity conditions. Quantum theory of the discontinuous metric system is assumed to be fixed somehow in the form of quantum measure on (the space of functionals on) the superspace. The problem of reducing this measure to the Regge hypersurface is addressed. The quantum Regge calculus measure is defined from a discontinuous metric measure by inserting the δ-function-like phase factor. The requirement that continuity conditions be imposed in a 'face-independent' way fixes this factor uniquely. The term 'face-independent' means that this factor depends only on the (hyper)plane spanned by the face, not on it's form and size. This requirement seems to be natural from the viewpoint of existence of the well-defined continuum limit maximally free of lattice artefacts

Time-integration methods for finite element discretisations of the second-order Maxwell equation

NARCIS (Netherlands)

Sarmany, D.; Bochev, Mikhail A.; van der Vegt, Jacobus J.W.

This article deals with time integration for the second-order Maxwell equations with possibly non-zero conductivity in the context of the discontinuous Galerkin finite element method DG-FEM) and the $H(\\mathrm{curl})$-conforming FEM. For the spatial discretisation, hierarchic

ON THE APPLICATION OF THE METHOD OF B.G. GALERKIN TO LINEAR PROBLEMS ARISING FROM DYNAMICAL SYSTEMS WITH DISTRIBUTED PARAMETERS

Energy Technology Data Exchange (ETDEWEB)

Gurevich, S. G.

1955-07-01

Galerkin's method is applied to the solution of a linear partial differential equation of arbitrary order under specified initial and boundary conditions. An example is carried through in complete detail to illustrate the method. (auth)

Excursions in fluvial (dis)continuity

Science.gov (United States)

Grant, Gordon E.; O'Connor, James E.; Safran, Elizabeth

2017-01-01

Lurking below the twin concepts of connectivity and disconnectivity are their first, and in some ways, richer cousins: continuity and discontinuity. In this paper we explore how continuity and discontinuity represent fundamental and complementary perspectives in fluvial geomorphology, and how these perspectives inform and underlie our conceptions of connectivity in landscapes and rivers. We examine the historical roots of continuum and discontinuum thinking, and how much of our understanding of geomorphology rests on contrasting views of continuity and discontinuity. By continuum thinking we refer to a conception of geomorphic processes as well as geomorphic features that are expressed along continuous gradients without abrupt changes, transitions, or thresholds. Balance of forces, graded streams, and hydraulic geometry are all examples of this perspective. The continuum view has played a prominent role in diverse disciplinary fields, including ecology, paleontology, and evolutionary biology, in large part because it allows us to treat complex phenomena as orderly progressions and invoke or assume equilibrium processes that introduce order and prediction into our sciences.In contrast the discontinuous view is a distinct though complementary conceptual framework that incorporates non-uniform, non-progressive, and non-equilibrium thinking into understanding geomorphic processes and landscapes. We distinguish and discuss examples of three different ways in which discontinuous thinking can be expressed: 1) discontinuous spatial arrangements or singular events; 2) specific process domains generally associated with thresholds, either intrinsic or extrinsic; and 3) physical dynamics or changes in state, again often threshold-linked. In moving beyond the continuous perspective, a fertile set of ideas comes into focus: thresholds, non-equilibrium states, heterogeneity, catastrophe. The range of phenomena that is thereby opened up to scientific exploration similarly expands

Green's function approach to neutron flux discontinuities

International Nuclear Information System (INIS)

Saad, E.A.; El-Wakil, S.A.

1980-01-01

The present work is devoted to the presentation of analytical method for the calculation of elastically and inelastically slowed down neutrons in an infinite non-absorbing medium. On the basis of the central limit theory (CLT) and the integral transform technique the slowing down equation including inelastic scattering, in terms of the Green function of elastic scattering, is solved. The Green function is decomposed according to the number of collisions. Placzec discontinuity associated with elastic scattering in addition to two discontinuities due to inelastic scattering are investigated. Numerical calculations for Fe 56 show that the elastic discontinuity produces about 41.8% change in the collision density whilst the ratio of the inelastic collision density discontinuity at qsub(o)sup(+) to the Placzec discontinuity at usub(o) + 1n 1/oc gives 55.7 percent change. (author)

POD-Galerkin Model for Incompressible Single-Phase Flow in Porous Media

KAUST Repository

Wang, Yi

2017-01-25

Fast prediction modeling via proper orthogonal decomposition method combined with Galerkin projection is applied to incompressible single-phase fluid flow in porous media. Cases for different configurations of porous media, boundary conditions and problem scales are designed to examine the fidelity and robustness of the model. High precision (relative deviation 1.0 x 10(-4)% similar to 2.3 x 10(-1)%) and large acceleration (speed-up 880 similar to 98454 times) of POD model are found in these cases. Moreover, the computational time of POD model is quite insensitive to the complexity of problems. These results indicate POD model is especially suitable for large-scale complex problems in engineering.

Neural networks with discontinuous/impact activations

CERN Document Server

Akhmet, Marat

2014-01-01

This book presents as its main subject new models in mathematical neuroscience. A wide range of neural networks models with discontinuities are discussed, including impulsive differential equations, differential equations with piecewise constant arguments, and models of mixed type. These models involve discontinuities, which are natural because huge velocities and short distances are usually observed in devices modeling the networks. A discussion of the models, appropriate for the proposed applications, is also provided. This book also: Explores questions related to the biological underpinning for models of neural networks\\ Considers neural networks modeling using differential equations with impulsive and piecewise constant argument discontinuities Provides all necessary mathematical basics for application to the theory of neural networks Neural Networks with Discontinuous/Impact Activations is an ideal book for researchers and professionals in the field of engineering mathematics that have an interest in app...

Delirium Associated With Fluoxetine Discontinuation: A Case Report.

Science.gov (United States)

Fan, Kuang-Yuan; Liu, Hsing-Cheng

Withdrawal symptoms on selective serotonin reuptake inhibitor (SSRI) discontinuation have raised clinical attention increasingly. However, delirium is rarely reported in the SSRI discontinuation syndrome. We report a case of delirium developing after fluoxetine discontinuation in a 65-year-old female patient with major depressive disorder. She experienced psychotic depression with limited response to treatment of fluoxetine 40 mg/d and quetiapine 100 mg/d for 3 months. After admission, we tapered fluoxetine gradually in 5 days because of its limited effect. However, delirious pictures developed 2 days after we stopped fluoxetine. Three days later, we added back fluoxetine 10 mg/d. Her delirious features gradually improved, and the clinical presentation turned into previous psychotic depression state. We gradually increased the medication to fluoxetine 60 mg/d and olanzapine 20 mg/d in the following 3 weeks. Her psychotic symptoms decreased, and there has been no delirious picture noted thereafter. Delirium associated with fluoxetine discontinuation is a much rarer complication in SSRI discontinuation syndrome. The symptoms of SSRI discontinuation syndrome may be attributable to a rapid decrease in serotonin availability. In general, the shorter the half-life of any medication, the greater the likelihood patients will experience discontinuation symptoms. Genetic vulnerability might be a potential factor to explain that SSRI discontinuation syndrome also occurred rapidly in people taking long-half-life fluoxetine. The genetic polymorphisms of both pharmacokinetic and pharmacodynamic pathways might be potentially associated with SSRI discontinuation syndrome.

A pressure-based semi-implicit space-time discontinuous Galerkin method on staggered unstructured meshes for the solution of the compressible Navier-Stokes equations at all Mach numbers

Science.gov (United States)

Tavelli, Maurizio; Dumbser, Michael

2017-07-01

We propose a new arbitrary high order accurate semi-implicit space-time discontinuous Galerkin (DG) method for the solution of the two and three dimensional compressible Euler and Navier-Stokes equations on staggered unstructured curved meshes. The method is pressure-based and semi-implicit and is able to deal with all Mach number flows. The new DG scheme extends the seminal ideas outlined in [1], where a second order semi-implicit finite volume method for the solution of the compressible Navier-Stokes equations with a general equation of state was introduced on staggered Cartesian grids. Regarding the high order extension we follow [2], where a staggered space-time DG scheme for the incompressible Navier-Stokes equations was presented. In our scheme, the discrete pressure is defined on the primal grid, while the discrete velocity field and the density are defined on a face-based staggered dual grid. Then, the mass conservation equation, as well as the nonlinear convective terms in the momentum equation and the transport of kinetic energy in the energy equation are discretized explicitly, while the pressure terms appearing in the momentum and energy equation are discretized implicitly. Formal substitution of the discrete momentum equation into the total energy conservation equation yields a linear system for only one unknown, namely the scalar pressure. Here the equation of state is assumed linear with respect to the pressure. The enthalpy and the kinetic energy are taken explicitly and are then updated using a simple Picard procedure. Thanks to the use of a staggered grid, the final pressure system is a very sparse block five-point system for three dimensional problems and it is a block four-point system in the two dimensional case. Furthermore, for high order in space and piecewise constant polynomials in time, the system is observed to be symmetric and positive definite. This allows to use fast linear solvers such as the conjugate gradient (CG) method. In

A Galerkin least squares approach to viscoelastic flow.

Energy Technology Data Exchange (ETDEWEB)

Rao, Rekha R. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Schunk, Peter Randall [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2015-10-01

A Galerkin/least-squares stabilization technique is applied to a discrete Elastic Viscous Stress Splitting formulation of for viscoelastic flow. From this, a possible viscoelastic stabilization method is proposed. This method is tested with the flow of an Oldroyd-B fluid past a rigid cylinder, where it is found to produce inaccurate drag coefficients. Furthermore, it fails for relatively low Weissenberg number indicating it is not suited for use as a general algorithm. In addition, a decoupled approach is used as a way separating the constitutive equation from the rest of the system. A Pressure Poisson equation is used when the velocity and pressure are sought to be decoupled, but this fails to produce a solution when inflow/outflow boundaries are considered. However, a coupled pressure-velocity equation with a decoupled constitutive equation is successful for the flow past a rigid cylinder and seems to be suitable as a general-use algorithm.

Time-Discrete Higher-Order ALE Formulations: Stability

KAUST Repository

Bonito, Andrea; Kyza, Irene; Nochetto, Ricardo H.

2013-01-01

on the stability of the PDE but may influence that of a discrete scheme. We examine this critical issue for higher-order time stepping without space discretization. We propose time-discrete discontinuous Galerkin (dG) numerical schemes of any order for a time

Shock capturing techniques for hphp-adaptive finite elements

Czech Academy of Sciences Publication Activity Database

Hierro, A.; Kůs, Pavel; Badia, S.

2016-01-01

Roč. 309, 1 September (2016), s. 532-553 ISSN 0045-7825 Institutional support: RVO:67985840 Keywords : hphp-adaptivity * discontinuous Galerkin * shock capturing Subject RIV: BA - General Mathematics Impact factor: 3.949, year: 2016 http://www.sciencedirect.com/science/article/pii/S0045782516305862

Control in the coefficients with variational crimes

DEFF Research Database (Denmark)

Evgrafov, Anton; Marhadi, Kun Saptohartyadi

2012-01-01

We study convergence of discontinuous Galerkin-type discretizations of the problems of control in the coefficients of uniformly elliptic partial differential equations (PDEs). As a model problem we use that of the optimal design of thin (Kirchhoff) plates, where the governing equations...

General practitioners' decisions about discontinuation of medication: an explorative study.

Science.gov (United States)

Nixon, Michael Simon; Vendelø, Morten Thanning

2016-06-20

Purpose - The purpose of this paper is to investigate how general practitioners' (GPs) decisions about discontinuation of medication are influenced by their institutional context. Design/methodology/approach - In total, 24 GPs were interviewed, three practices were observed and documents were collected. The Gioia methodology was used to analyse data, drawing on a theoretical framework that integrate the sensemaking perspective and institutional theory. Findings - Most GPs, who actively consider discontinuation, are reluctant to discontinue medication, because the safest course of action for GPs is to continue prescriptions, rather than discontinue them. The authors conclude that this is in part due to the ambiguity about the appropriateness of discontinuing medication, experienced by the GPs, and in part because the clinical guidelines do not encourage discontinuation of medication, as they offer GPs a weak frame for discontinuation. Three reasons for this are identified: the guidelines provide dominating triggers for prescribing, they provide weak priming for discontinuation as an option, and they underscore a cognitive constraint against discontinuation. Originality/value - The analysis offers new insights about decision making when discontinuing medication. It also offers one of the first examinations of how the institutional context embedding GPs influences their decisions about discontinuation. For policymakers interested in the discontinuation of medication, the findings suggest that de-stigmatising discontinuation on an institutional level may be beneficial, allowing GPs to better justify discontinuation in light of the ambiguity they experience.

Implementation of the flow-modulated skew-upwind difference scheme in the COMMIX-1C code: A first assessment

International Nuclear Information System (INIS)

Bottoni, M.; Chien, T.H.; Dommanus, H.M.; Sha, W.T.; Shen, Y.; Laster, R.

1991-01-01

This paper explains in detail the implementation of the Flow-Modulated Skew-Upwind Difference (FMSUD) scheme in the momentum equation of the COMMIX-1C computer program, where the scheme has been used so far only in the energy equation. Because the three scalar components of the momentum equation are solved in different meshes, staggered with respect to the mesh used for the energy equation and displaced in the respective coordinate direction, implementation of the FMSUD scheme in the momentum equations is by far more demanding than the implementation of a single scalar equation in centered cells. For this reason, a new approach has been devised to treat the problem, from the mathematical viewpoint, in the maximum generality and for all flow conditions, taking into account automatically the direction of the velocity vector and thus choosing automatically the weighting factors to be associated to different cells in the skew-upwind discretization. The new mathematical approach is straightforward for the treatment of inner cells of the fluid-dynamic definition domain, but particular care must be paid to its implementation for boundary cells where the appropriate boundary conditions must be applied. The paper explains the test cases in which the implementation of the FMSUD method has been applied and discusses the quality of the numerical results against the correct solution, when the latter is known. 14 refs., 2 figs., 1 tab

Generalized multiscale finite element method. Symmetric interior penalty coupling

KAUST Repository

Efendiev, Yalchin R.; Galvis, Juan; Lazarov, Raytcho D.; Moon, M.; Sarkis, Marcus V.

2013-01-01

Motivated by applications to numerical simulations of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the framework of the discontinuous Galerkin finite element method. We propose two different finite element spaces on the coarse mesh. The first space is based on a local eigenvalue problem that uses an interior weighted L2-norm and a boundary weighted L2-norm for computing the "mass" matrix. The second choice is based on generation of a snapshot space and subsequent selection of a subspace of a reduced dimension. The approximation with these multiscale spaces is based on the discontinuous Galerkin finite element method framework. We investigate the stability and derive error estimates for the methods and further experimentally study their performance on a representative number of numerical examples. © 2013 Elsevier Inc.

Generalized multiscale finite element method. Symmetric interior penalty coupling

KAUST Repository

Efendiev, Yalchin R.

2013-12-01

Motivated by applications to numerical simulations of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the framework of the discontinuous Galerkin finite element method. We propose two different finite element spaces on the coarse mesh. The first space is based on a local eigenvalue problem that uses an interior weighted L2-norm and a boundary weighted L2-norm for computing the "mass" matrix. The second choice is based on generation of a snapshot space and subsequent selection of a subspace of a reduced dimension. The approximation with these multiscale spaces is based on the discontinuous Galerkin finite element method framework. We investigate the stability and derive error estimates for the methods and further experimentally study their performance on a representative number of numerical examples. © 2013 Elsevier Inc.

The structure of rotational discontinuities

International Nuclear Information System (INIS)

Neugebauer, M.

1989-01-01

This study examines the structures of a set of rotational discontinuities detected in the solar wind by the ISEE-3 spacecraft. It is found that the complexity of the structure increases as the angle θ between the propagation vector k and the magnetic field decreases. For rotational discontinuities that propagate at a large angle to the field with an ion (left-hand) sense of rotation, the magnetic hodograms tend to be flattened, in agreement with prior numerical simulations. When θ is large, angular overshoots are often observed at one or both ends of the discontinuity. When the propagation is nearly parallel to the field (i.e., when θ is small), many different types of structure are seen, ranging from straight lines, the S-shaped curves, to complex, disorganized shapes

Discontinuation Decision in Assisted Reproductive Techniques

Directory of Open Access Journals (Sweden)

Ashraf Moini

2009-01-01

Full Text Available Background: In vitro fertilization (IVF and intra cytoplasmic sperm injection (ICSI are recognizedas established and increasingly successful forms of treatment for infertility, yet significant numbersof couples discontinue treatment without achieving a live birth. This study aims to identify majorfactors that influence the decision to discontinue IVF/ICSI treatments.Materials and Methods: We studied the data of 338 couples who discontinued their infertilitytreatments after three cycles; based on medical records and phone contact. The main measure wasthe reason for stopping their treatments.Results: Economical problems were cited by 212 couples (62.7%, as their mean income wassignificantly less than other couples (p<0.0001. Lack of success was reported as a reason by229 (67.8%, from whom 165 (72% also had economical problems. Achieving independent-ART pregnancy was the reason for discontinuation in 20 (5.9% couples. Psychological stress,depression and anxiety were reported as other cessation factors by 169 (50%, 148 (43.8% and 182(53.8% couples, respectively.Conclusion: This survey suggests that the most common reasons for assisted reproductivetechnique (ART discontinuation after three cycles are: prior unsuccessful cycles, economicaland psychological problems. Therefore, the substantial proportion of couples could benefit frompsychological intervention, increasing awareness of ART outcomes and health funding to copemore adequately with failed treatments.

An Alternate Approach to Optimal L 2 -Error Analysis of Semidiscrete Galerkin Methods for Linear Parabolic Problems with Nonsmooth Initial Data

KAUST Repository

Goswami, Deepjyoti; Pani, Amiya K.

2011-01-01

In this article, we propose and analyze an alternate proof of a priori error estimates for semidiscrete Galerkin approximations to a general second order linear parabolic initial and boundary value problem with rough initial data. Our analysis

Factors predicting successful discontinuation of continuous renal replacement therapy.

Science.gov (United States)

Katayama, S; Uchino, S; Uji, M; Ohnuma, T; Namba, Y; Kawarazaki, H; Toki, N; Takeda, K; Yasuda, H; Izawa, J; Tokuhira, N; Nagata, I

2016-07-01

This multicentre, retrospective observational study was conducted from January 2010 to December 2010 to determine the optimal time for discontinuing continuous renal replacement therapy (CRRT) by evaluating factors predictive of successful discontinuation in patients with acute kidney injury. Analysis was performed for patients after CRRT was discontinued because of renal function recovery. Patients were divided into two groups according to the success or failure of CRRT discontinuation. In multivariate logistic regression analysis, urine output at discontinuation, creatinine level and CRRT duration were found to be significant variables (area under the receiver operating characteristic curve for urine output, 0.814). In conclusion, we found that higher urine output, lower creatinine and shorter CRRT duration were significant factors to predict successful discontinuation of CRRT.

Trapped particles at a magnetic discontinuity

Science.gov (United States)

Stern, D. P.

1972-01-01

At a tangential discontinuity between two constant magnetic fields a layer of trapped particles can exist, this work examines the conditions under which the current carried by such particles tends to maintain the discontinuity. Three cases are examined. If the discontinuity separates aligned vacuum fields, the only requirement is that they be antiparallel. With arbitrary relative orientations, the field must have equal intensities on both sides. Finally, with a guiding center plasma on both sides, the condition reduces to a relation which is also derivable from hydromagnetic theory. Arguments are presented for the occurrence of such trapped modes in the magnetopause and for the non-existence of specular particle reflection.

Application of Central Upwind Scheme for Solving Special Relativistic Hydrodynamic Equations

Science.gov (United States)

Yousaf, Muhammad; Ghaffar, Tayabia; Qamar, Shamsul

2015-01-01

The accurate modeling of various features in high energy astrophysical scenarios requires the solution of the Einstein equations together with those of special relativistic hydrodynamics (SRHD). Such models are more complicated than the non-relativistic ones due to the nonlinear relations between the conserved and state variables. A high-resolution shock-capturing central upwind scheme is implemented to solve the given set of equations. The proposed technique uses the precise information of local propagation speeds to avoid the excessive numerical diffusion. The second order accuracy of the scheme is obtained with the use of MUSCL-type initial reconstruction and Runge-Kutta time stepping method. After a discussion of the equations solved and of the techniques employed, a series of one and two-dimensional test problems are carried out. To validate the method and assess its accuracy, the staggered central and the kinetic flux-vector splitting schemes are also applied to the same model. The scheme is robust and efficient. Its results are comparable to those obtained from the sophisticated algorithms, even in the case of highly relativistic two-dimensional test problems. PMID:26070067

Discontinuity effects in dynamically loaded tilting pad journal bearings

DEFF Research Database (Denmark)

Thomsen, Kim; Klit, Peder; Vølund, Anders

2011-01-01

This paper describes two discontinuity effects that can occur when modelling radial tilting pad bearings subjected to high dynamic loads. The first effect to be treated is a pressure build-up discontinuity effect. The second effect is a contact-related discontinuity that disappears when a contact...... force is included in the theoretical model. Methods for avoiding the pressure build-up discontinuity effect are proposed....

Galerkin CFD solvers for use in a multi-disciplinary suite for modeling advanced flight vehicles

Science.gov (United States)

Moffitt, Nicholas J.

This work extends existing Galerkin CFD solvers for use in a multi-disciplinary suite. The suite is proposed as a means of modeling advanced flight vehicles, which exhibit strong coupling between aerodynamics, structural dynamics, controls, rigid body motion, propulsion, and heat transfer. Such applications include aeroelastics, aeroacoustics, stability and control, and other highly coupled applications. The suite uses NASA STARS for modeling structural dynamics and heat transfer. Aerodynamics, propulsion, and rigid body dynamics are modeled in one of the five CFD solvers below. Euler2D and Euler3D are Galerkin CFD solvers created at OSU by Cowan (2003). These solvers are capable of modeling compressible inviscid aerodynamics with modal elastics and rigid body motion. This work reorganized these solvers to improve efficiency during editing and at run time. Simple and efficient propulsion models were added, including rocket, turbojet, and scramjet engines. Viscous terms were added to the previous solvers to create NS2D and NS3D. The viscous contributions were demonstrated in the inertial and non-inertial frames. Variable viscosity (Sutherland's equation) and heat transfer boundary conditions were added to both solvers but not verified in this work. Two turbulence models were implemented in NS2D and NS3D: Spalart-Allmarus (SA) model of Deck, et al. (2002) and Menter's SST model (1994). A rotation correction term (Shur, et al., 2000) was added to the production of turbulence. Local time stepping and artificial dissipation were adapted to each model. CFDsol is a Taylor-Galerkin solver with an SA turbulence model. This work improved the time accuracy, far field stability, viscous terms, Sutherland?s equation, and SA model with NS3D as a guideline and added the propulsion models from Euler3D to CFDsol. Simple geometries were demonstrated to utilize current meshing and processing capabilities. Air-breathing hypersonic flight vehicles (AHFVs) represent the ultimate

Multigrid for the Galerkin least squares method in linear elasticity: The pure displacement problem

Energy Technology Data Exchange (ETDEWEB)

Yoo, Jaechil [Univ. of Wisconsin, Madison, WI (United States)

1996-12-31

Franca and Stenberg developed several Galerkin least squares methods for the solution of the problem of linear elasticity. That work concerned itself only with the error estimates of the method. It did not address the related problem of finding effective methods for the solution of the associated linear systems. In this work, we prove the convergence of a multigrid (W-cycle) method. This multigrid is robust in that the convergence is uniform as the parameter, v, goes to 1/2 Computational experiments are included.

Discontinuities during UV writing of waveguides

DEFF Research Database (Denmark)

Svalgaard, Mikael; Harpøth, Anders; Andersen, Marc

2005-01-01

UV writing of waveguides can be hampered by discontinuities where the index change process suddenly shuts down. We show that thermal effects may account for this behaviour.......UV writing of waveguides can be hampered by discontinuities where the index change process suddenly shuts down. We show that thermal effects may account for this behaviour....

Motion of Charged Particles near Magnetic Field Discontinuities

International Nuclear Information System (INIS)

Dodin, I.Y.; Fisch, N.J.

2000-01-01

The motion of charged particles in slowly changing magnetic fields exhibits adiabatic invariance even in the presence of abrupt magnetic discontinuities. Particles near discontinuities in magnetic fields, what we call ''boundary particles'', are constrained to remain near an arbitrarily fractured boundary even as the particle drifts along the discontinuity. A new adiabatic invariant applies to the motion of these particles

Sensitivity analysis of the Galerkin finite element method neutron diffusion solver to the shape of the elements

Energy Technology Data Exchange (ETDEWEB)

Hosseini, Seyed Abolfaz [Dept. of Energy Engineering, Sharif University of Technology, Tehran (Iran, Islamic Republic of)

2017-02-15

The purpose of the present study is the presentation of the appropriate element and shape function in the solution of the neutron diffusion equation in two-dimensional (2D) geometries. To this end, the multigroup neutron diffusion equation is solved using the Galerkin finite element method in both rectangular and hexagonal reactor cores. The spatial discretization of the equation is performed using unstructured triangular and quadrilateral finite elements. Calculations are performed using both linear and quadratic approximations of shape function in the Galerkin finite element method, based on which results are compared. Using the power iteration method, the neutron flux distributions with the corresponding eigenvalue are obtained. The results are then validated against the valid results for IAEA-2D and BIBLIS-2D benchmark problems. To investigate the dependency of the results to the type and number of the elements, and shape function order, a sensitivity analysis of the calculations to the mentioned parameters is performed. It is shown that the triangular elements and second order of the shape function in each element give the best results in comparison to the other states.

Simulation of incompressible flows with heat and mass transfer using parallel finite element method

Directory of Open Access Journals (Sweden)

Jalal Abedi

2003-02-01

Full Text Available The stabilized finite element formulations based on the SUPG (Stream-line-Upwind/Petrov-Galerkin and PSPG (Pressure-Stabilization/Petrov-Galerkin methods are developed and applied to solve buoyancy-driven incompressible flows with heat and mass transfer. The SUPG stabilization term allows us to solve flow problems at high speeds (advection dominant flows and the PSPG term eliminates instabilities associated with the use of equal order interpolation functions for both pressure and velocity. The finite element formulations are implemented in parallel using MPI. In parallel computations, the finite element mesh is partitioned into contiguous subdomains using METIS, which are then assigned to individual processors. To ensure a balanced load, the number of elements assigned to each processor is approximately equal. To solve nonlinear systems in large-scale applications, we developed a matrix-free GMRES iterative solver. Here we totally eliminate a need to form any matrices, even at the element levels. To measure the accuracy of the method, we solve 2D and 3D example of natural convection flows at moderate to high Rayleigh numbers.

Adaptive numerical modeling of dynamic crack propagation

International Nuclear Information System (INIS)

Adouani, H.; Tie, B.; Berdin, C.; Aubry, D.

2006-01-01

We propose an adaptive numerical strategy that aims at developing reliable and efficient numerical tools to model dynamic crack propagation and crack arrest. We use the cohesive zone theory as behavior of interface-type elements to model crack. Since the crack path is generally unknown beforehand, adaptive meshing is proposed to model the dynamic crack propagation. The dynamic study requires the development of specific solvers for time integration. As both geometry and finite element mesh of the studied structure evolve in time during transient analysis, the stability behavior of dynamic solver becomes a major concern. For this purpose, we use the space-time discontinuous Galerkin finite element method, well-known to provide a natural framework to manage meshes that evolve in time. As an important result, we prove that the space-time discontinuous Galerkin solver is unconditionally stable, when the dynamic crack propagation is modeled by the cohesive zone theory, which is highly non-linear. (authors)

Signal integrity analysis on discontinuous microstrip line

International Nuclear Information System (INIS)

Qiao, Qingyang; Dai, Yawen; Chen, Zipeng

2013-01-01

In high speed PCB design, microstirp lines were used to control the impedance, however, the discontinuous microstrip line can cause signal integrity problems. In this paper, we use the transmission line theory to study the characteristics of microstrip lines. Research results indicate that the discontinuity such as truncation, gap and size change result in the problems such as radiation, reflection, delay and ground bounce. We change the discontinuities to distributed parameter circuits, analysed the steady-state response and transient response and the phase delay. The transient response cause radiation and voltage jump.

Validating the Galerkin least-squares finite element methods in predicting mixing flows in stirred tank reactors

International Nuclear Information System (INIS)

Johnson, K.; Bittorf, K.J.

2002-01-01

A novel approach for computer aided modeling and optimizing mixing process has been developed using Galerkin least-squares finite element technology. Computer aided mixing modeling and analysis involves Lagrangian and Eulerian analysis for relative fluid stretching, and energy dissipation concepts for laminar and turbulent flows. High quality, conservative, accurate, fluid velocity, and continuity solutions are required for determining mixing quality. The ORCA Computational Fluid Dynamics (CFD) package, based on a finite element formulation, solves the incompressible Reynolds Averaged Navier Stokes (RANS) equations. Although finite element technology has been well used in areas of heat transfer, solid mechanics, and aerodynamics for years, it has only recently been applied to the area of fluid mixing. ORCA, developed using the Galerkin Least-Squares (GLS) finite element technology, provides another formulation for numerically solving the RANS based and LES based fluid mechanics equations. The ORCA CFD package is validated against two case studies. The first, a free round jet, demonstrates that the CFD code predicts the theoretical velocity decay rate, linear expansion rate, and similarity profile. From proper prediction of fundamental free jet characteristics, confidence can be derived when predicting flows in a stirred tank, as a stirred tank reactor can be considered a series of free jets and wall jets. (author)

Adaptive stochastic Galerkin FEM with hierarchical tensor representations

KAUST Repository

Eigel, Martin

2016-01-08

PDE with stochastic data usually lead to very high-dimensional algebraic problems which easily become unfeasible for numerical computations because of the dense coupling structure of the discretised stochastic operator. Recently, an adaptive stochastic Galerkin FEM based on a residual a posteriori error estimator was presented and the convergence of the adaptive algorithm was shown. While this approach leads to a drastic reduction of the complexity of the problem due to the iterative discovery of the sparsity of the solution, the problem size and structure is still rather limited. To allow for larger and more general problems, we exploit the tensor structure of the parametric problem by representing operator and solution iterates in the tensor train (TT) format. The (successive) compression carried out with these representations can be seen as a generalisation of some other model reduction techniques, e.g. the reduced basis method. We show that this approach facilitates the efficient computation of different error indicators related to the computational mesh, the active polynomial chaos index set, and the TT rank. In particular, the curse of dimension is avoided.

Accountability Accentuates Interindividual-Intergroup Discontinuity by Enforcing Parochialism

OpenAIRE

Wildschut, T.; Van Horen, F.; Hart, C.

2015-01-01

Interindividual-intergroup discontinuity is the tendency for relations between groups to be more competitive than relations between individuals. We examined whether the discontinuity effect arises in part because group members experience normative pressure to favor the ingroup (parochialism). Building on the notion that accountability enhances normative pressure, we hypothesized that the discontinuity effect would be larger when accountability is present (compared to absent). A prisoner’s dil...

Discontinuities and the magnetospheric phenomena

International Nuclear Information System (INIS)

Rajaram, R.; Kalra, G.L.; Tandon, J.N.

1978-01-01

Wave coupling at contact discontinuities has an important bearing on the transmission of waves from the solar wind into the magnetosphere across the cusp region of the solar wind-magnetosphere boundary and on the propagation of geomagnetic pulsations in the polar exosphere. Keeping this in view, the problems of wave coupling across a contact discontinuity in a collisionless plasma, described by a set of double adiabatic fluid equations, is examined. The magnetic field is taken normal to the interface and it is shown that total reflection is not possible for any angle of incidence. The Alfven and the magneto-acoustic waves are not coupled. The transmission is most efficient for small density discontinuities. Inhibition of the transmission of the Alfven wave by the sharp density gradients above the F2-peak in the polar exosphere appears to account for the decrease in the pulsation amplitude, on the ground, as the poles are approached from the auroral zone. (author)

Strategies for discontinuation of proton pump inhibitors

DEFF Research Database (Denmark)

Haastrup, Peter; Paulsen, Maja S; Begtrup, Luise M

2014-01-01

PURPOSE: Proton pump inhibitors (PPIs) are considered to be overprescribed. Consensus on how to attempt discontinuation is, however, lacking. We therefore conducted a systematic review of clinical studies on discontinuation of PPIs. METHODS: Systematic review based on clinical studies investigating...

Constant Jacobian Matrix-Based Stochastic Galerkin Method for Probabilistic Load Flow

Directory of Open Access Journals (Sweden)

Yingyun Sun

2016-03-01

Full Text Available An intrusive spectral method of probabilistic load flow (PLF is proposed in the paper, which can handle the uncertainties arising from renewable energy integration. Generalized polynomial chaos (gPC expansions of dependent random variables are utilized to build a spectral stochastic representation of PLF model. Instead of solving the coupled PLF model with a traditional, cumbersome method, a modified stochastic Galerkin (SG method is proposed based on the P-Q decoupling properties of load flow in power system. By introducing two pre-calculated constant sparse Jacobian matrices, the computational burden of the SG method is significantly reduced. Two cases, IEEE 14-bus and IEEE 118-bus systems, are used to verify the computation speed and efficiency of the proposed method.

On the stability of rotational discontinuities and intermediate shocks

International Nuclear Information System (INIS)

Lee, L.C.; Huang, L.; Chao, J.K.

1989-01-01

The stability of rotational discontinuities and intermediate shocks is studied based on a hybrid simulation code. The simulation results show that rotational discontinuities are stable and intermediate shocks are not stationary. Intermediate shocks tend to evolve to rotational discontinuities and waves. The authors employ several different initial profiles for the magnetic field in the transition region and find that the final structure of the discontinuities or shocks is not sensitive to the initial magnetic field profile. The present results are different from those obtained from the resistive MHD simulations. Furthermore, their study indicates that the kinetic effect of particles plays an important role in the structure and stability of rotational discontinuities and intermediate shocks

Energy dependent mesh adaptivity of discontinuous isogeometric discrete ordinate methods with dual weighted residual error estimators

Science.gov (United States)

Owens, A. R.; Kópházi, J.; Welch, J. A.; Eaton, M. D.

2017-04-01

In this paper a hanging-node, discontinuous Galerkin, isogeometric discretisation of the multigroup, discrete ordinates (SN) equations is presented in which each energy group has its own mesh. The equations are discretised using Non-Uniform Rational B-Splines (NURBS), which allows the coarsest mesh to exactly represent the geometry for a wide range of engineering problems of interest; this would not be the case using straight-sided finite elements. Information is transferred between meshes via the construction of a supermesh. This is a non-trivial task for two arbitrary meshes, but is significantly simplified here by deriving every mesh from a common coarsest initial mesh. In order to take full advantage of this flexible discretisation, goal-based error estimators are derived for the multigroup, discrete ordinates equations with both fixed (extraneous) and fission sources, and these estimators are used to drive an adaptive mesh refinement (AMR) procedure. The method is applied to a variety of test cases for both fixed and fission source problems. The error estimators are found to be extremely accurate for linear NURBS discretisations, with degraded performance for quadratic discretisations owing to a reduction in relative accuracy of the "exact" adjoint solution required to calculate the estimators. Nevertheless, the method seems to produce optimal meshes in the AMR process for both linear and quadratic discretisations, and is ≈×100 more accurate than uniform refinement for the same amount of computational effort for a 67 group deep penetration shielding problem.

Element free Galerkin formulation of composite beam with longitudinal slip

Energy Technology Data Exchange (ETDEWEB)

Ahmad, Dzulkarnain; Mokhtaram, Mokhtazul Haizad [Department of Civil Engineering, Universiti Selangor, Bestari Jaya, Selangor (Malaysia); Badli, Mohd Iqbal; Yassin, Airil Y. Mohd [Faculty of Civil Engineering, Universiti Teknologi Malaysia, Skudai, Johor (Malaysia)

2015-05-15

Behaviour between two materials in composite beam is assumed partially interact when longitudinal slip at its interfacial surfaces is considered. Commonly analysed by the mesh-based formulation, this study used meshless formulation known as Element Free Galerkin (EFG) method in the beam partial interaction analysis, numerically. As meshless formulation implies that the problem domain is discretised only by nodes, the EFG method is based on Moving Least Square (MLS) approach for shape functions formulation with its weak form is developed using variational method. The essential boundary conditions are enforced by Langrange multipliers. The proposed EFG formulation gives comparable results, after been verified by analytical solution, thus signify its application in partial interaction problems. Based on numerical test results, the Cubic Spline and Quartic Spline weight functions yield better accuracy for the EFG formulation, compares to other proposed weight functions.

Socio-Economic Differentials in Contraceptive Discontinuation in India

Directory of Open Access Journals (Sweden)

Kiran Agrahari

2016-05-01

Full Text Available Fertility divergence amid declining in use of modern contraception in many states of India needs urgent research and programmatic attention. Although utilization of antenatal, natal, and post-natal care has shown spectacular increase in post National Rural Health Mission (NRHM period, the contraceptive use had shown a declining trend. Using the calendar data from the National Family Health Survey–3, this article examines the reasons of contraceptive discontinuation among spacing method users by socio-economic groups in India. Bivariate and multivariate analyses and life table discontinuation rates are used in the analyses. Results suggest that about half of the pill users, two fifths of the condom users, one third of traditional method users, and one fifth of IUD users discontinue a method in first 12 months of use. However, the discontinuation of all three modern spacing methods declines in subsequent period (within 12-36 months. The probability of method failure was highest among traditional method users and higher among poor and less educated that may lead to unwanted/mistimed birth. Although discontinuation of condom declines with economic status, it does not show any large variation for pill users. The contraceptive discontinuation was significantly associated with duration of use, age, parity, contraceptive method, religion, and contraceptive intention. Based on these findings, it is suggested that follow-up services to modern spacing method users, increasing counseling for spacing method users, motivating the traditional method user to use modern spacing method, and improving the overall quality of family planning services can reduce the discontinuation of spacing method.

Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients

KAUST Repository

Beck, Joakim

2011-12-22

In this work we first focus on the Stochastic Galerkin approximation of the solution u of an elliptic stochastic PDE. We rely on sharp estimates for the decay of the coefficients of the spectral expansion of u on orthogonal polynomials to build a sequence of polynomial subspaces that features better convergence properties compared to standard polynomial subspaces such as Total Degree or Tensor Product. We consider then the Stochastic Collocation method, and use the previous estimates to introduce a new effective class of Sparse Grids, based on the idea of selecting a priori the most profitable hierarchical surpluses, that, again, features better convergence properties compared to standard Smolyak or tensor product grids.

On numerical solution of compressible flow in time-dependent domains

Czech Academy of Sciences Publication Activity Database

Feistauer, M.; Horáček, Jaromír; Kučera, V.; Prokopová, Jaroslava

2012-01-01

Roč. 137, č. 1 (2012), s. 1-16 ISSN 0862-7959 R&D Projects: GA MŠk OC09019 Institutional research plan: CEZ:AV0Z20760514 Keywords : compressible Navier-Stokes equations * arbitrary Lagrangian-Eulerian method * discontinuous Galerkin finite element method * interior and boundary penalty Subject RIV: BI - Acoustics

The Galerkin finite element method for a multi-term time-fractional diffusion equation

KAUST Repository

Jin, Bangti

2015-01-01

© 2014 The Authors. We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite element method using continuous piecewise linear functions. Nearly optimal error estimates for both cases of initial data and inhomogeneous term are derived, which cover both smooth and nonsmooth data. Further we develop a fully discrete scheme based on a finite difference discretization of the time-fractional derivatives, and discuss its stability and error estimate. Extensive numerical experiments for one- and two-dimensional problems confirm the theoretical convergence rates.

A class of discontinuous Petrov–Galerkin methods. Part III: Adaptivity

KAUST Repository

Demkowicz, Leszek; Gopalakrishnan, Jay; Niemi, Antti H.

2012-01-01

space, we prove robustness (uniform stability with respect to the diffusion parameter) and mesh-independence of the energy norm of the FE error for the 1D problem. With hp-adaptivity and a proper scaling of the norms for the test functions, we establish

Continuous and discontinuous transitions to synchronization.

Science.gov (United States)

Wang, Chaoqing; Garnier, Nicolas B

2016-11-01

We describe how the transition to synchronization in a system of globally coupled Stuart-Landau oscillators changes from continuous to discontinuous when the nature of the coupling is moved from diffusive to reactive. We explain this drastic qualitative change as resulting from the co-existence of a particular synchronized macrostate together with the trivial incoherent macrostate, in a range of parameter values for which the latter is linearly stable. In contrast to the paradigmatic Kuramoto model, this particular state observed at the synchronization transition contains a finite, non-vanishing number of synchronized oscillators, which results in a discontinuous transition. We consider successively two situations where either a fully synchronized state or a partially synchronized state exists at the transition. Thermodynamic limit and finite size effects are briefly discussed, as well as connections with recently observed discontinuous transitions.

Actor Bonds in Situations of Discontinuous Business Activities

DEFF Research Database (Denmark)

Skaates, Maria Anne

2000-01-01

Demand in many industrial buying situations, e.g. project purchases or procurement related to virtual organizations, is discontinuous. In situations of discontinuity, networks are often more of an ad hos informational and social nature, as strong activity and resource links are not present....... Furthermore the governance structure of markets characterized by discontinuous business activities is either that of the "socially constructed market" (Skaates, 2000) or that of the (socially constructed) network (Håkansson and Johanson, 1993). Additionally relationships and actor bonds vary substantially...

Rotational discontinuities and the structure of the magnetopause

International Nuclear Information System (INIS)

Swift, D.W.; Lee, L.C.

1983-01-01

Symmetric and asymmetric rotational discontinuities are studied by means of a one-dimensional computer simulation and by single-particle trajectory calculations. The numerical simulations show the symmetric rotation to be stable for both ion and electron senses of rotation with a thickness of the order of a few ion gyroradii when the rotation angle of the tangential field is 180 0 or less. Larger rotation angles tend to be unstable. In an expansive discontinuity, when the magnetic field on the downstream side of the discontinuity is larger, an expanding transition layer separating the high-field from a low-field region develops on the downstream side, and a symmetric rotational discontinuity forms at the upstream edge. The implication of these results for magnetopause structure and energy flow through the magnetopause is described

Essential imposition of Neumann condition in Galerkin-Legendre elliptic solvers

CERN Document Server

Auteri, F; Quartapelle, L

2003-01-01

A new Galerkin-Legendre direct spectral solver for the Neumann problem associated with Laplace and Helmholtz operators in rectangular domains is presented. The algorithm differs from other Neumann spectral solvers by the high sparsity of the matrices, exploited in conjunction with the direct product structure of the problem. The homogeneous boundary condition is satisfied exactly by expanding the unknown variable into a polynomial basis of functions which are built upon the Legendre polynomials and have a zero slope at the interval extremes. A double diagonalization process is employed pivoting around the eigenstructure of the pentadiagonal mass matrices in both directions, instead of the full stiffness matrices encountered in the classical variational formulation of the problem with a weak natural imposition of the derivative boundary condition. Nonhomogeneous Neumann data are accounted for by means of a lifting. Numerical results are given to illustrate the performance of the proposed spectral elliptic solv...

Implementation of LDG method for 3D unstructured meshes

Directory of Open Access Journals (Sweden)

Filander A. Sequeira Chavarría

2012-07-01

Full Text Available This paper describes an implementation of the Local Discontinuous Galerkin method (LDG applied to elliptic problems in 3D. The implementation of the major operators is discussed. In particular the use of higher-order approximations and unstructured meshes. Efficient data structures that allow fast assembly of the linear system in the mixed formulation are described in detail. Keywords: Discontinuous finite element methods, high-order approximations, unstructured meshes, object-oriented programming. Mathematics Subject Classification: 65K05, 65N30, 65N55.

[Discontinuation of depression treatment from the perspective of suicide prevention].

Science.gov (United States)

Cho, Yoshinori

2012-01-01

It is assumed that discontinuation of treatment for depression may increase the risk of suicide. A population-based register study in Denmark did not find a lower risk among people over age 50 who followed treatment in comparison with those who discontinued treatment with antidepressants at an early stage. This result, however, does not allow us to think superficially that early discontinuation of treatment does not increase the risk of suicide. It is because the study has limitations without information of such as psychiatric diagnoses, severity of the depressed state, and reasons of discontinuation. It is safe for clinicians to aim at preventing discontinuation of treatment. Particularly, in Japan and South Korea where there is a sociocultural climate of tolerability for suicide, suicide can occur in milder depressed state and discontinuation of treatment should be taken more seriously than in Western countries.

A Galerkin Finite Element Method for Numerical Solutions of the Modified Regularized Long Wave Equation

Directory of Open Access Journals (Sweden)

Liquan Mei

2014-01-01

Full Text Available A Galerkin method for a modified regularized long wave equation is studied using finite elements in space, the Crank-Nicolson scheme, and the Runge-Kutta scheme in time. In addition, an extrapolation technique is used to transform a nonlinear system into a linear system in order to improve the time accuracy of this method. A Fourier stability analysis for the method is shown to be marginally stable. Three invariants of motion are investigated. Numerical experiments are presented to check the theoretical study of this method.

Galerkin method for unsplit 3-D Dirac equation using atomically/kinetically balanced B-spline basis

International Nuclear Information System (INIS)

Fillion-Gourdeau, F.; Lorin, E.; Bandrauk, A.D.

2016-01-01

A Galerkin method is developed to solve the time-dependent Dirac equation in prolate spheroidal coordinates for an electron–molecular two-center system. The initial state is evaluated from a variational principle using a kinetic/atomic balanced basis, which allows for an efficient and accurate determination of the Dirac spectrum and eigenfunctions. B-spline basis functions are used to obtain high accuracy. This numerical method is used to compute the energy spectrum of the two-center problem and then the evolution of eigenstate wavefunctions in an external electromagnetic field.

Risk of discontinuation of Advanced Therapy Medicinal Products clinical trials.

Science.gov (United States)

Hanna, Eve; Rémuzat, Cecile; Auquier, Pascal; Toumi, Mondher

2016-01-01

Advanced therapy medicinal products (ATMPs) constitute a class of innovative products that encompasses gene therapy, somatic cell therapy, and tissue-engineered products (TEP). There is an increased investment of commercial and non-commercial sponsors in this field and a growing number of ATMPs randomized clinical trials (RCT) and patients enrolled in such trials. RCT generate data to prove the efficacy of a new therapy, but the discontinuation of RCTs wastes scarce resources. Our objective is to identify the number and characteristics of discontinued ATMPs trials in order to evaluate the rate of discontinuation. We searched for ATMPs trials conducted between 1999 to June 2015 using three databases, which are Clinicaltrials.gov, the International Clinical Trials Registry Platform (ICTRP), and the EU Drug Regulating Authorities Clinical Trials (EudraCT). We selected the ATMPs trials after elimination of the duplicates. We identified the disease areas and the sponsors as commercial or non-commercial organizations. We classified ATMPs by type and trial status, that is, ongoing, completed, terminated, discontinued, and prematurely ended. Then, we calculated the rate of discontinuation. Between 1999 and June 2015, 143 withdrawn, terminated, or prematurely ended ATMPs clinical trials were identified. Between 1999 and June 2013, 474 ongoing and completed clinical trials were identified. Therefore, the rate of discontinuation of ATMPs trials is 23.18%, similar to that for non-ATMPs drugs in development. The probability of discontinuation is, respectively, 27.35, 16.28, and 16.34% for cell therapies, gene therapies, and TEP. The highest discontinuation rate is for oncology (43%), followed by cardiology (19.2%). It is almost the same for commercial and non-commercial sponsors; therefore, the discontinuation reason may not be financially driven. No failure risk rate per development phase is available for ATMPs. The discontinuation rate may prove helpful when assessing the

41 CFR 109-39.105 - Discontinuance or curtailment of service.

Science.gov (United States)

2010-07-01

... AVIATION, TRANSPORTATION, AND MOTOR VEHICLES 39-INTERAGENCY FLEET MANAGEMENT SYSTEMS 39.1-Establishment, Modification, and Discontinuance of Interagency Fleet Management Systems § 109-39.105 Discontinuance or... 41 Public Contracts and Property Management 3 2010-07-01 2010-07-01 false Discontinuance or...

What happens when people discontinue taking medications? Lessons from COMBINE.

Science.gov (United States)

Stout, Robert L; Braciszewski, Jordan M; Subbaraman, Meenakshi Sabina; Kranzler, Henry R; O'Malley, Stephanie S; Falk, Daniel

2014-12-01

We use intensive longitudinal data methods to illuminate processes affecting patients' drinking in relation to the discontinuation of medications within an alcohol treatment study. Although previous work has focused on broad measures of medication adherence, we focus on dynamic changes in drinking both before and after patients discontinue. We conducted secondary data analyses using the COMBINE (Combined Pharmacotherapies and Behavioral Interventions for Alcohol Dependence) study, focused on participants who discontinued medications prior to the planned end of treatment. Using an interrupted time-series analysis, we analysed drinking in the weeks before and after discontinuation and also studied outcomes at the end of the COMBINE follow-up. Unites States of America. We describe the subsample of COMBINE participants who discontinued medications (n = 450), and compare them with those who were medication-adherent (n = 559) and with those who discontinued but had substantial missing data (n = 217). The primary outcomes were percentage of days abstinent (PDA) and percentage of heavy drinking days (PHDD). Medication adherence data were used to approximate the date of discontinuation. For many patients, an increase in drinking began weeks before discontinuation (PDA: F(1,4803) = 19.07, P < 0.001; PHDD: F(1,4804) = 8.58, P = 0.003) then escalated at discontinuation (PDA: F(1,446) = 5.05, P = 0.025; PHDD: F(1,446) = 4.52, P = 0.034). Among other effects, the amount of change was moderated by the reason for discontinuation (e.g. adverse event; PDA: F(2,4803) = 3.85, P = 0.021; PHDD: F(2,4804) = 5.36, P = 0.005) and also whether it occurred in the first or second half of treatment (PDA: F(1,4803) = 5.23, P = 0.022; PHDD: F(1,4804) = 8.79, P = 0.003). A patient's decision to stop taking medications during alcohol treatment appears to take place during a weeks-long process of disengagement from treatment. Patients who discontinue medications early in treatment or without

To Be or Not to Be Intrusive? The Solution of Parametric and Stochastic Equations---the “Plain Vanilla” Galerkin Case

KAUST Repository

Giraldi, Loï c; Litvinenko, Alexander; Liu, Dishi; Matthies, Hermann G.; Nouy, Anthony

2014-01-01

In parametric equations---stochastic equations are a special case---one may want to approximate the solution such that it is easy to evaluate its dependence on the parameters. Interpolation in the parameters is an obvious possibility---in this context often labeled as a collocation method. In the frequent situation where one has a “solver” for a given fixed parameter value, this may be used “nonintrusively” as a black-box component to compute the solution at all the interpolation points independently of each other. By extension, all other methods, and especially simple Galerkin methods, which produce some kind of coupled system, are often classed as “intrusive.” We show how, for such “plain vanilla” Galerkin formulations, one may solve the coupled system in a nonintrusive way, and even the simplest form of block-solver has comparable efficiency. This opens at least two avenues for possible speed-up: first, to benefit from the coupling in the iteration by using more sophisticated block-solvers and, second, the possibility of nonintrusive successive rank-one updates as in the proper generalized decomposition (PGD).

Area Regge calculus and discontinuous metrics

International Nuclear Information System (INIS)

Wainwright, Chris; Williams, Ruth M

2004-01-01

Taking the triangle areas as independent variables in the theory of Regge calculus can lead to ambiguities in the edge lengths, which can be interpreted as discontinuities in the metric. We construct solutions to area Regge calculus using a triangulated lattice and find that on a spacelike or timelike hypersurface no such discontinuity can arise. On a null hypersurface however, we can have such a situation and the resulting metric can be interpreted as a so-called refractive wave

Physics-based process model approach for detecting discontinuity during friction stir welding

Energy Technology Data Exchange (ETDEWEB)

Shrivastava, Amber; Pfefferkorn, Frank E.; Duffie, Neil A.; Ferrier, Nicola J.; Smith, Christopher B.; Malukhin, Kostya; Zinn, Michael

2015-02-12

The goal of this work is to develop a method for detecting the creation of discontinuities during friction stir welding. This in situ weld monitoring method could significantly reduce the need for post-process inspection. A process force model and a discontinuity force model were created based on the state-of-the-art understanding of flow around an friction stir welding (FSW) tool. These models are used to predict the FSW forces and size of discontinuities formed in the weld. Friction stir welds with discontinuities and welds without discontinuities were created, and the differences in force dynamics were observed. In this paper, discontinuities were generated by reducing the tool rotation frequency and increasing the tool traverse speed in order to create "cold" welds. Experimental force data for welds with discontinuities and welds without discontinuities compared favorably with the predicted forces. The model currently overpredicts the discontinuity size.

Accountability Accentuates Interindividual-Intergroup Discontinuity by Enforcing Parochialism

NARCIS (Netherlands)

Wildschut, T.; Van Horen, F.; Hart, C.

2015-01-01

Interindividual-intergroup discontinuity is the tendency for relations between groups to be more competitive than relations between individuals. We examined whether the discontinuity effect arises in part because group members experience normative pressure to favor the ingroup (parochialism).

Accountability Accentuates Interindividual-Intergroup Discontinuity by Enforcing Parochialism.

Science.gov (United States)

Wildschut, Tim; van Horen, Femke; Hart, Claire

2015-01-01

Interindividual-intergroup discontinuity is the tendency for relations between groups to be more competitive than relations between individuals. We examined whether the discontinuity effect arises in part because group members experience normative pressure to favor the ingroup (parochialism). Building on the notion that accountability enhances normative pressure, we hypothesized that the discontinuity effect would be larger when accountability is present (compared to absent). A prisoner's dilemma game experiment supported this prediction. Specifically, intergroup (compared to interindividual) interaction activated an injunctive ingroup-favoring norm, and accountability enhanced the influence of this norm on competitive behavior.

A Simple Stochastic Differential Equation with Discontinuous Drift

DEFF Research Database (Denmark)

Simonsen, Maria; Leth, John-Josef; Schiøler, Henrik

2013-01-01

In this paper we study solutions to stochastic differential equations (SDEs) with discontinuous drift. We apply two approaches: The Euler-Maruyama method and the Fokker-Planck equation and show that a candidate density function based on the Euler-Maruyama method approximates a candidate density...... function based on the stationary Fokker-Planck equation. Furthermore, we introduce a smooth function which approximates the discontinuous drift and apply the Euler-Maruyama method and the Fokker-Planck equation with this input. The point of departure for this work is a particular SDE with discontinuous...

Probabilistic Solar Wind Forecasting Using Large Ensembles of Near-Sun Conditions With a Simple One-Dimensional "Upwind" Scheme.

Science.gov (United States)

Owens, Mathew J; Riley, Pete

2017-11-01

Long lead-time space-weather forecasting requires accurate prediction of the near-Earth solar wind. The current state of the art uses a coronal model to extrapolate the observed photospheric magnetic field to the upper corona, where it is related to solar wind speed through empirical relations. These near-Sun solar wind and magnetic field conditions provide the inner boundary condition to three-dimensional numerical magnetohydrodynamic (MHD) models of the heliosphere out to 1 AU. This physics-based approach can capture dynamic processes within the solar wind, which affect the resulting conditions in near-Earth space. However, this deterministic approach lacks a quantification of forecast uncertainty. Here we describe a complementary method to exploit the near-Sun solar wind information produced by coronal models and provide a quantitative estimate of forecast uncertainty. By sampling the near-Sun solar wind speed at a range of latitudes about the sub-Earth point, we produce a large ensemble (N = 576) of time series at the base of the Sun-Earth line. Propagating these conditions to Earth by a three-dimensional MHD model would be computationally prohibitive; thus, a computationally efficient one-dimensional "upwind" scheme is used. The variance in the resulting near-Earth solar wind speed ensemble is shown to provide an accurate measure of the forecast uncertainty. Applying this technique over 1996-2016, the upwind ensemble is found to provide a more "actionable" forecast than a single deterministic forecast; potential economic value is increased for all operational scenarios, but particularly when false alarms are important (i.e., where the cost of taking mitigating action is relatively large).

Probabilistic Solar Wind Forecasting Using Large Ensembles of Near-Sun Conditions With a Simple One-Dimensional "Upwind" Scheme

Science.gov (United States)

Owens, Mathew J.; Riley, Pete

2017-11-01

Long lead-time space-weather forecasting requires accurate prediction of the near-Earth solar wind. The current state of the art uses a coronal model to extrapolate the observed photospheric magnetic field to the upper corona, where it is related to solar wind speed through empirical relations. These near-Sun solar wind and magnetic field conditions provide the inner boundary condition to three-dimensional numerical magnetohydrodynamic (MHD) models of the heliosphere out to 1 AU. This physics-based approach can capture dynamic processes within the solar wind, which affect the resulting conditions in near-Earth space. However, this deterministic approach lacks a quantification of forecast uncertainty. Here we describe a complementary method to exploit the near-Sun solar wind information produced by coronal models and provide a quantitative estimate of forecast uncertainty. By sampling the near-Sun solar wind speed at a range of latitudes about the sub-Earth point, we produce a large ensemble (N = 576) of time series at the base of the Sun-Earth line. Propagating these conditions to Earth by a three-dimensional MHD model would be computationally prohibitive; thus, a computationally efficient one-dimensional "upwind" scheme is used. The variance in the resulting near-Earth solar wind speed ensemble is shown to provide an accurate measure of the forecast uncertainty. Applying this technique over 1996-2016, the upwind ensemble is found to provide a more "actionable" forecast than a single deterministic forecast; potential economic value is increased for all operational scenarios, but particularly when false alarms are important (i.e., where the cost of taking mitigating action is relatively large).

Accountability Accentuates Interindividual—Intergroup Discontinuity by Enforcing Parochialism

Directory of Open Access Journals (Sweden)

Tim eWildschut

2015-11-01

Full Text Available Interindividual-intergroup discontinuity is the tendency for relations between groups to be more competitive than relations between individuals. We examined whether the discontinuity effect arises in part because group members experience normative pressure to favor the ingroup (parochialism. Building on the notion that accountability enhances normative pressure, we hypothesized that the discontinuity effect would be larger when accountability is present (compared to absent. A prisoner’s dilemma game experiment supported this prediction. Specifically, intergroup (compared to interindividual interaction activated an injunctive ingroup-favoring norm, and accountability enhanced the influence of this norm on competitive behavior.

Dynamic Rupture Benchmarking of the ADER-DG Method

Science.gov (United States)

Gabriel, Alice; Pelties, Christian

2013-04-01

We will verify the arbitrary high-order derivative Discontinuous Galerkin (ADER-DG) method in various test cases of the 'SCEC/USGS Dynamic Earthquake Rupture Code Verification Exercise' benchmark suite (Harris et al. 2009). The ADER-DG scheme is able to solve the spontaneous rupture problem with high-order accuracy in space and time on three-dimensional unstructured tetrahedral meshes. Strong mesh coarsening or refinement at areas of interest can be applied to keep the computational costs feasible. Moreover, the method does not generate spurious high-frequency contributions in the slip rate spectra and therefore does not require any artificial damping as demonstrated in previous presentations and publications (Pelties et al. 2010 and 2012). We will show that the mentioned features hold also for more advanced setups as e.g. a branching fault system, heterogeneous background stresses and bimaterial faults. The advanced geometrical flexibility combined with an enhanced accuracy will make the ADER-DG method a useful tool to study earthquake dynamics on complex fault systems in realistic rheologies. References: Harris, R.A., M. Barall, R. Archuleta, B. Aagaard, J.-P. Ampuero, H. Bhat, V. Cruz-Atienza, L. Dalguer, P. Dawson, S. Day, B. Duan, E. Dunham, G. Ely, Y. Kaneko, Y. Kase, N. Lapusta, Y. Liu, S. Ma, D. Oglesby, K. Olsen, A. Pitarka, S. Song, and E. Templeton, The SCEC/USGS Dynamic Earthquake Rupture Code Verification Exercise, Seismological Research Letters, vol. 80, no. 1, pages 119-126, 2009 Pelties, C., J. de la Puente, and M. Kaeser, Dynamic Rupture Modeling in Three Dimensions on Unstructured Meshes Using a Discontinuous Galerkin Method, AGU 2010 Fall Meeting, abstract #S21C-2068 Pelties, C., J. de la Puente, J.-P. Ampuero, G. Brietzke, and M. Kaeser, Three-Dimensional Dynamic Rupture Simulation with a High-order Discontinuous Galerkin Method on Unstructured Tetrahedral Meshes, JGR. - Solid Earth, VOL. 117, B02309, 2012

Adaptive Finite Element Methods for Elliptic Problems with Discontinuous Coefficients

KAUST Repository

Bonito, Andrea; DeVore, Ronald A.; Nochetto, Ricardo H.

2013-01-01

Elliptic PDEs with discontinuous diffusion coefficients occur in application domains such as diffusions through porous media, electromagnetic field propagation on heterogeneous media, and diffusion processes on rough surfaces. The standard approach to numerically treating such problems using finite element methods is to assume that the discontinuities lie on the boundaries of the cells in the initial triangulation. However, this does not match applications where discontinuities occur on curves, surfaces, or manifolds, and could even be unknown beforehand. One of the obstacles to treating such discontinuity problems is that the usual perturbation theory for elliptic PDEs assumes bounds for the distortion of the coefficients in the L∞ norm and this in turn requires that the discontinuities are matched exactly when the coefficients are approximated. We present a new approach based on distortion of the coefficients in an Lq norm with q < ∞ which therefore does not require the exact matching of the discontinuities. We then use this new distortion theory to formulate new adaptive finite element methods (AFEMs) for such discontinuity problems. We show that such AFEMs are optimal in the sense of distortion versus number of computations, and report insightful numerical results supporting our analysis. © 2013 Societ y for Industrial and Applied Mathematics.

39 CFR 241.3 - Discontinuance of post offices.

Science.gov (United States)

2010-07-01

... CLASSIFICATION, AND DISCONTINUANCE § 241.3 Discontinuance of post offices. (a) Introduction—(1) Coverage. This... justify in sufficient detail to Postal Service management and affected customers the proposed service... inspection during normal business hours at each post office where the Final Determination is posted for 30...

Introduction to COFFE: The Next-Generation HPCMP CREATE-AV CFD Solver

Science.gov (United States)

Glasby, Ryan S.; Erwin, J. Taylor; Stefanski, Douglas L.; Allmaras, Steven R.; Galbraith, Marshall C.; Anderson, W. Kyle; Nichols, Robert H.

2016-01-01

HPCMP CREATE-AV Conservative Field Finite Element (COFFE) is a modular, extensible, robust numerical solver for the Navier-Stokes equations that invokes modularity and extensibility from its first principles. COFFE implores a flexible, class-based hierarchy that provides a modular approach consisting of discretization, physics, parallelization, and linear algebra components. These components are developed with modern software engineering principles to ensure ease of uptake from a user's or developer's perspective. The Streamwise Upwind/Petrov-Galerkin (SU/PG) method is utilized to discretize the compressible Reynolds-Averaged Navier-Stokes (RANS) equations tightly coupled with a variety of turbulence models. The mathematics and the philosophy of the methodology that makes up COFFE are presented.

A cubic B-spline Galerkin approach for the numerical simulation of the GEW equation

Directory of Open Access Journals (Sweden)

S. Battal Gazi Karakoç

2016-02-01

Full Text Available The generalized equal width (GEW wave equation is solved numerically by using lumped Galerkin approach with cubic B-spline functions. The proposed numerical scheme is tested by applying two test problems including single solitary wave and interaction of two solitary waves. In order to determine the performance of the algorithm, the error norms L2 and L∞ and the invariants I1, I2 and I3 are calculated. For the linear stability analysis of the numerical algorithm, von Neumann approach is used. As a result, the obtained findings show that the presented numerical scheme is preferable to some recent numerical methods.  

Discontinuation of nicotine replacement therapy among smoking-cessation attempters.

Science.gov (United States)

Burns, Emily K; Levinson, Arnold H

2008-03-01

Nicotine replacement therapy (NRT) doubles successful quitting, but more than half of NRT users do not comply with optimal treatment regimens. From the 2005 Colorado state tobacco survey, quit attempters who utilized NRT (N=366) were analyzed in spring 2007. Descriptive and regression analyses were used to examine reasons for discontinuing NRT, length of time on NRT, and quit intentions. The reasons for discontinuing NRT were resuming smoking (34%), side effects (17%), NRT not helping with quitting (14%), quitting smoking (10%), and cost (5%). Poverty, age, and non-Latino minority status were associated with reasons for discontinuation other than quitting smoking. Having side effects was associated with a short duration of NRT use and 95% lower odds of intending to quit in the next month. In the first population-level study examining reasons for discontinuing NRT, general-population smokers who initiate NRT use when attempting to quit are highly likely to discontinue NRT prematurely. Age and culturally-appropriate medication management interventions may increase NRT compliance and improve cessation outcomes.

Solutions of the Wheeler-Feynman equations with discontinuous velocities.

Science.gov (United States)

de Souza, Daniel Câmara; De Luca, Jayme

2015-01-01

We generalize Wheeler-Feynman electrodynamics with a variational boundary value problem for continuous boundary segments that might include velocity discontinuity points. Critical-point orbits must satisfy the Euler-Lagrange equations of the action functional at most points, which are neutral differential delay equations (the Wheeler-Feynman equations of motion). At velocity discontinuity points, critical-point orbits must satisfy the Weierstrass-Erdmann continuity conditions for the partial momenta and the partial energies. We study a special setup having the shortest time-separation between the (infinite-dimensional) boundary segments, for which case the critical-point orbit can be found using a two-point boundary problem for an ordinary differential equation. For this simplest setup, we prove that orbits can have discontinuous velocities. We construct a numerical method to solve the Wheeler-Feynman equations together with the Weierstrass-Erdmann conditions and calculate some numerical orbits with discontinuous velocities. We also prove that the variational boundary value problem has a unique solution depending continuously on boundary data, if the continuous boundary segments have velocity discontinuities along a reduced local space.

The optimal time of discontinuing methimazole before radioiodine therapy

International Nuclear Information System (INIS)

Moosavi, Z.; Zakavi, R.

2001-01-01

Hyperthyroidism is a common disease and one of the best methods for its treatment is radioiodine therapy with Treatment with antithyroid drugs brings patients to euthyroidism before radioiodine therapy. Antithyroid drugs should be discontinued before radioiodine therapy to increase thyroid uptake. The purpose of this study was to determine the optimal time of methimazole discontinuation. One hundred eighty four patients, who were referred for radioiodine therapy were classified in 3 groups according to the duration of methimazole discontinuation before thyroid uptake (RAIU) measurement. Group 1,2 and 3 were patients who discontinued methimazole (48-72 h rs), (72-120 h rs) and more than 120 h rs before RAIU measurement, respectively. Mean thyroid uptake in group 1, 2 and 3 was (64±151.1%), (60.1±14.1%) and (59.3±12.8), respectively. No significant difference was noted in thyroid uptake between these groups (F= 1.83, P<0.16). This study shows that 48-72 h rs of methimazole discontinuation before radioiodine therapy is enough and longer term abstention is not associated with higher uptake

Soliton shock wave fronts and self-similar discontinuities in dispersion hydrodynamics

International Nuclear Information System (INIS)

Gurevich, A.V.; Meshcherkin, A.P.

1987-01-01

Nonlinear flows in nondissipative dispersion hydrodynamics are examined. It is demonstrated that in order to describe such flows it is necessary to incorporate a new concept: a special discontinuity called a ''self-similar'' discontinuity consisting of a nondissipative shock wave and a powerful slow wave discontinuity in regular hydrodynamics. The ''self similar discontinuity'' expands linearly over time. It is demonstrated that this concept may be introduced in a solution to Euler equations. The boundary conditions of the ''self similar discontinuity'' that allow closure of Euler equations for dispersion hydrodynamics are formulated, i.e., those that replace the shock adiabatic curve of standard dissipative hydrodynamics. The structure of the soliton front and of the trailing edge of the shock wave is investigated. A classification and complete solution are given to the problem of the decay of random initial discontinuities in the hydrodynamics of highly nonisothermic plasma. A solution is derived to the problem of the decay of initial discontinuities in the hydrodynamics of magnetized plasma. It is demonstrated that in this plasma, a feature of current density arises at the point of soliton inversion

Minimizers with discontinuous velocities for the electromagnetic variational method

International Nuclear Information System (INIS)

De Luca, Jayme

2010-01-01

The electromagnetic two-body problem has neutral differential delay equations of motion that, for generic boundary data, can have solutions with discontinuous derivatives. If one wants to use these neutral differential delay equations with arbitrary boundary data, solutions with discontinuous derivatives must be expected and allowed. Surprisingly, Wheeler-Feynman electrodynamics has a boundary value variational method for which minimizer trajectories with discontinuous derivatives are also expected, as we show here. The variational method defines continuous trajectories with piecewise defined velocities and accelerations, and electromagnetic fields defined by the Euler-Lagrange equations on trajectory points. Here we use the piecewise defined minimizers with the Lienard-Wierchert formulas to define generalized electromagnetic fields almost everywhere (but on sets of points of zero measure where the advanced/retarded velocities and/or accelerations are discontinuous). Along with this generalization we formulate the generalized absorber hypothesis that the far fields vanish asymptotically almost everywhere and show that localized orbits with far fields vanishing almost everywhere must have discontinuous velocities on sewing chains of breaking points. We give the general solution for localized orbits with vanishing far fields by solving a (linear) neutral differential delay equation for these far fields. We discuss the physics of orbits with discontinuous derivatives stressing the differences to the variational methods of classical mechanics and the existence of a spinorial four-current associated with the generalized variational electrodynamics.

Discontinuation risk comparison among 'real-world' newly anticoagulated atrial fibrillation patients

DEFF Research Database (Denmark)

Lip, Gregory Y H; Pan, Xianying; Kamble, Shital

2018-01-01

Discontinuation of oral anticoagulants may expose non-valvular atrial fibrillation (NVAF) patients to an increased risk of stroke. This study describes the real-world discontinuation rates and compared the risk of drug discontinuation among NVAF patients initiating apixaban, warfarin, dabigatran,...

Lagrange–Galerkin methods for the incompressible Navier-Stokes equations: a review

Directory of Open Access Journals (Sweden)

Bermejo Rodolfo

2016-09-01

Full Text Available We review in this paper the development of Lagrange-Galerkin (LG methods to integrate the incompressible Navier-Stokes equations (NSEs for engineering applications. These methods were introduced in the computational fluid dynamics community in the early eighties of the past century, and at that time they were considered good methods for both their theoretical stability properties and the way of dealing with the nonlinear terms of the equations; however, the numerical experience gained with the application of LG methods to different problems has identified drawbacks of them, such as the calculation of specific integrals that arise in their formulation and the calculation of the ow trajectories, which somehow have hampered the applicability of LG methods. In this paper, we focus on these issues and summarize the convergence results of LG methods; furthermore, we shall briefly introduce a new stabilized LG method suitable for high Reynolds numbers.

A Galerkin discretisation-based identification for parameters in nonlinear mechanical systems

Science.gov (United States)

Liu, Zuolin; Xu, Jian

2018-04-01

In the paper, a new parameter identification method is proposed for mechanical systems. Based on the idea of Galerkin finite-element method, the displacement over time history is approximated by piecewise linear functions, and the second-order terms in model equation are eliminated by integrating by parts. In this way, the lost function of integration form is derived. Being different with the existing methods, the lost function actually is a quadratic sum of integration over the whole time history. Then for linear or nonlinear systems, the optimisation of the lost function can be applied with traditional least-squares algorithm or the iterative one, respectively. Such method could be used to effectively identify parameters in linear and arbitrary nonlinear mechanical systems. Simulation results show that even under the condition of sparse data or low sampling frequency, this method could still guarantee high accuracy in identifying linear and nonlinear parameters.

Derivative discontinuity with localized Hartree-Fock potential

Energy Technology Data Exchange (ETDEWEB)

Nazarov, V. U. [Research Center for Applied Sciences, Academia Sinica, Taipei 11529, Taiwan (China); Vignale, G. [Department of Physics, University of Missouri-Columbia, Columbia, Missouri 65211 (United States)

2015-08-14

The localized Hartree-Fock potential has proven to be a computationally efficient alternative to the optimized effective potential, preserving the numerical accuracy of the latter and respecting the exact properties of being self-interaction free and having the correct −1/r asymptotics. In this paper we extend the localized Hartree-Fock potential to fractional particle numbers and observe that it yields derivative discontinuities in the energy as required by the exact theory. The discontinuities are numerically close to those of the computationally more demanding Hartree-Fock method. Our potential enjoys a “direct-energy” property, whereby the energy of the system is given by the sum of the single-particle eigenvalues multiplied by the corresponding occupation numbers. The discontinuities c{sub ↑} and c{sub ↓} of the spin-components of the potential at integer particle numbers N{sub ↑} and N{sub ↓} satisfy the condition c{sub ↑}N{sub ↑} + c{sub ↓}N{sub ↓} = 0. Thus, joining the family of effective potentials which support a derivative discontinuity, but being considerably easier to implement, the localized Hartree-Fock potential becomes a powerful tool in the broad area of applications in which the fundamental gap is an issue.

Convergent piecewise affine systems : analysis and design Part II: discontinuous case

NARCIS (Netherlands)

Pavlov, A.V.; Pogromski, A.Y.; Wouw, van de N.; Nijmeijer, H.; Rooda, J.E.

2005-01-01

In this paper convergence properties of piecewise affine (PWA) systems with discontinuous right-hand sides are studied. It is shown that for discontinuous PWA systems existence of a common quadratic Lyapunov function is not sufficient for convergence. For discontinuous bimodal PWA systems necessary

A hybrid Pade-Galerkin technique for differential equations

Science.gov (United States)

Geer, James F.; Andersen, Carl M.

1993-01-01

A three-step hybrid analysis technique, which successively uses the regular perturbation expansion method, the Pade expansion method, and then a Galerkin approximation, is presented and applied to some model boundary value problems. In the first step of the method, the regular perturbation method is used to construct an approximation to the solution in the form of a finite power series in a small parameter epsilon associated with the problem. In the second step of the method, the series approximation obtained in step one is used to construct a Pade approximation in the form of a rational function in the parameter epsilon. In the third step, the various powers of epsilon which appear in the Pade approximation are replaced by new (unknown) parameters (delta(sub j)). These new parameters are determined by requiring that the residual formed by substituting the new approximation into the governing differential equation is orthogonal to each of the perturbation coordinate functions used in step one. The technique is applied to model problems involving ordinary or partial differential equations. In general, the technique appears to provide good approximations to the solution even when the perturbation and Pade approximations fail to do so. The method is discussed and topics for future investigations are indicated.

Work Package 1B.2 under the European Commission, Integrated Wind Turbine Design (UPWIND): Verification of long-term load measurement technique

Energy Technology Data Exchange (ETDEWEB)

Schmidt Paulsen, U.

2011-02-15

The present report is the final effort of tasks carried out under UPWIND WP1B2 transmission and conversion, which describes: 1) results and recommendations developed in the course of developing the long-term load measurement technique. 2) the hardware details, type of sensors and location, data storage and. 3) data analysis technique to verify design load assumptions. The work is carried out under Contract no 019945 (SES6) 'UPWIND' within the European Commission The interaction between the mechanical and electrical generator subsystems is described rudimentarily, based primarily on HAWC2 simulations below stall of the mechanical system with simple generator and gearbox systems. The electrical system simulations were not carried out as intended in DOW[2], but indications of the conditions for establishing the interaction have been described by measurements and by argument, that this might have an effect as indicated. The hypothesis stating, that the power signal can be utilized as a basic signal for extended analysis of mechanical as well as electrical power signal with static and dynamic features, has been demonstrated on performance and dynamic bandwidth capability. It is however from present analysis obvious that improved signal conditions could be achieved with other mechanical joint solutions than with the present torque signal as measured with the cardan joint. For the reasons mentioned, the comparison with a signal showing the mechanical properties could be improved, with a likely gain on the accuracy as a result. (Author)

Efficient Galerkin solution of stochastic fractional differential equations using second kind Chebyshev wavelets

Directory of Open Access Journals (Sweden)

Fakhrodin Mohammadi

2017-10-01

Full Text Available ‎Stochastic fractional differential equations (SFDEs have been used for modeling many physical problems in the fields of turbulance‎, ‎heterogeneous‎, ‎flows and matrials‎, ‎viscoelasticity and electromagnetic theory‎. ‎In this paper‎, ‎an‎ efficient wavelet Galerkin method based on the second kind Chebyshev wavelets are proposed for approximate solution of SFDEs‎. ‎In ‎this ‎app‎roach‎‎, ‎o‎perational matrices of the second kind Chebyshev wavelets ‎are used ‎for reducing SFDEs to a linear system of algebraic equations that can be solved easily‎. ‎C‎onvergence and error analysis of the proposed method is ‎considered‎.‎ ‎Some numerical examples are performed to confirm the applicability and efficiency of the proposed method‎.

Efficient C1-continuous phase-potential upwind (C1-PPU) schemes for coupled multiphase flow and transport with gravity

Science.gov (United States)

Jiang, Jiamin; Younis, Rami M.

2017-10-01

In the presence of counter-current flow, nonlinear convergence problems may arise in implicit time-stepping when the popular phase-potential upwinding (PPU) scheme is used. The PPU numerical flux is non-differentiable across the co-current/counter-current flow regimes. This may lead to cycles or divergence in the Newton iterations. Recently proposed methods address improved smoothness of the numerical flux. The objective of this work is to devise and analyze an alternative numerical flux scheme called C1-PPU that, in addition to improving smoothness with respect to saturations and phase potentials, also improves the level of scalar nonlinearity and accuracy. C1-PPU involves a novel use of the flux limiter concept from the context of high-resolution methods, and allows a smooth variation between the co-current/counter-current flow regimes. The scheme is general and applies to fully coupled flow and transport formulations with an arbitrary number of phases. We analyze the consistency property of the C1-PPU scheme, and derive saturation and pressure estimates, which are used to prove the solution existence. Several numerical examples for two- and three-phase flows in heterogeneous and multi-dimensional reservoirs are presented. The proposed scheme is compared to the conventional PPU and the recently proposed Hybrid Upwinding schemes. We investigate three properties of these numerical fluxes: smoothness, nonlinearity, and accuracy. The results indicate that in addition to smoothness, nonlinearity may also be critical for convergence behavior and thus needs to be considered in the design of an efficient numerical flux scheme. Moreover, the numerical examples show that the C1-PPU scheme exhibits superior convergence properties for large time steps compared to the other alternatives.

Stacking and discontinuous buffers in capillary zone electrophoresis.

Science.gov (United States)

Shihabi, Z K

2000-08-01

Discontinuous buffers for capillary zone electrophoresis (CZE) can be used under less rigid conditions compared to those for isotachophoresis for stacking. They can be prepared simply by modifying the sample itself, either by addition of small inorganic ions, low conductivity diluents, or both, and also by adjusting its pH, meanwhile injecting a large volume on the capillary. Zwitterionic and organic-based buffers such as triethanolamine and tris(hydroxymethyl)aminomethane (Tris) are well suited for stacking due to their low conductivity, provided the buffer is discontinuous as demonstrated here. A simple mechanism based on discontinuous buffers is described to explain many of the observed stacking types in CZE, pointing out the many similarities to transient isotachophoresis.

Comparison between results of solution of Burgers' equation and Laplace's equation by Galerkin and least-square finite element methods

Science.gov (United States)

Adib, Arash; Poorveis, Davood; Mehraban, Farid

2018-03-01

In this research, two equations are considered as examples of hyperbolic and elliptic equations. In addition, two finite element methods are applied for solving of these equations. The purpose of this research is the selection of suitable method for solving each of two equations. Burgers' equation is a hyperbolic equation. This equation is a pure advection (without diffusion) equation. This equation is one-dimensional and unsteady. A sudden shock wave is introduced to the model. This wave moves without deformation. In addition, Laplace's equation is an elliptical equation. This equation is steady and two-dimensional. The solution of Laplace's equation in an earth dam is considered. By solution of Laplace's equation, head pressure and the value of seepage in the directions X and Y are calculated in different points of earth dam. At the end, water table is shown in the earth dam. For Burgers' equation, least-square method can show movement of wave with oscillation but Galerkin method can not show it correctly (the best method for solving of the Burgers' equation is discrete space by least-square finite element method and discrete time by forward difference.). For Laplace's equation, Galerkin and least square methods can show water table correctly in earth dam.

Airline loyalty (programs) across borders : A geographic discontinuity approach

NARCIS (Netherlands)

de Jong, Gerben; Behrens, Christiaan; van Ommeren, Jos

2018-01-01

We analyze brand loyalty advantages of national airlines in their domestic countries using geocoded data from a major international frequent flier program. We employ a geographic discontinuity design that estimates discontinuities in program activity at the national borders of the program's

Waiting-time distributions of magnetic discontinuities: Clustering or Poisson process?

International Nuclear Information System (INIS)

Greco, A.; Matthaeus, W. H.; Servidio, S.; Dmitruk, P.

2009-01-01

Using solar wind data from the Advanced Composition Explorer spacecraft, with the support of Hall magnetohydrodynamic simulations, the waiting-time distributions of magnetic discontinuities have been analyzed. A possible phenomenon of clusterization of these discontinuities is studied in detail. We perform a local Poisson's analysis in order to establish if these intermittent events are randomly distributed or not. Possible implications about the nature of solar wind discontinuities are discussed.

Preparation and Mechanical Properties of Aligned Discontinuous Carbon Fiber Composites

OpenAIRE

DENG Hua; GAO Junpeng; BAO Jianwen

2018-01-01

Aligned discontinuous carbon fiber composites were fabricated from aligned discontinuous carbon fiber prepreg, which was prepared from continuous carbon fiber prepreg via mechanical high-frequency cutting. The internal quality and mechanical properties were characterized and compared with continuous carbon fiber composites. The results show that the internal quality of the aligned discontinuous carbon fiber composites is fine and the mechanical properties have high retention rate after the fi...

Simulation of upwind maneuvering of a sailing yacht

Science.gov (United States)

Harris, Daniel Hartrick

A time domain maneuvering simulation of an IACC class yacht suitable for the analysis of unsteady upwind sailing including tacking is presented. The simulation considers motions in six degrees of freedom. The hydrodynamic and aerodynamic loads are calculated primarily with unsteady potential theory supplemented by empirical viscous models. The hydrodynamic model includes the effects of incident waves. Control of the rudder is provided by a simple rate feedback autopilot which is augmented with open loop additions to mimic human steering. The hydrodynamic models are based on the superposition of force components. These components fall into two groups, those which the yacht will experience in calm water, and those due to incident waves. The calm water loads are further divided into zero Froude number, or "double body" maneuvering loads, hydrostatic loads, gravitational loads, free surface radiation loads, and viscous/residual loads. The maneuvering loads are calculated with an unsteady panel code which treats the instantaneous geometry of the yacht below the undisturbed free surface. The free surface radiation loads are calculated via convolution of impulse response functions derived from seakeeping strip theory. The viscous/residual loads are based upon empirical estimates. The aerodynamic model consists primarily of a database of steady state sail coefficients. These coefficients treat the individual contributions to the total sail force of a number of chordwise strips on both the main and jib. Dynamic effects are modeled by using the instantaneous incident wind velocity and direction as the independent variables for the sail load contribution of each strip. The sail coefficient database was calculated numerically with potential methods and simple empirical viscous corrections. Additional aerodynamic load calculations are made to determine the parasitic contributions of the rig and hull. Validation studies compare the steady sailing hydro and aerodynamic loads

A non-conventional discontinuous Lagrangian for viscous flow

Science.gov (United States)

Marner, F.

2017-01-01

Drawing an analogy with quantum mechanics, a new Lagrangian is proposed for a variational formulation of the Navier–Stokes equations which to-date has remained elusive. A key feature is that the resulting Lagrangian is discontinuous in nature, posing additional challenges apropos the mathematical treatment of the related variational problem, all of which are resolvable. In addition to extending Lagrange's formalism to problems involving discontinuous behaviour, it is demonstrated that the associated equations of motion can self-consistently be interpreted within the framework of thermodynamics beyond local equilibrium, with the limiting case recovering the classical Navier–Stokes equations. Perspectives for applying the new formalism to discontinuous physical phenomena such as phase and grain boundaries, shock waves and flame fronts are provided. PMID:28386415

The structure of rotational discontinuities. [in solar wind

Science.gov (United States)

Neugebauer, M.

1989-01-01

This study examines the structures of a set of rotational discontinuities detected in the solar wind by the ISEE-3 spacecraft. It is found that the complexity of the structure increases as the angle theta between the propagation vector k and the magnetic field decreases. For rotational discontinuities that propagate at a large angle to the field with an ion (left-hand) sense of rotation, the magnetic hodograms tend to be flattened, in agreement with prior numerical simulations. When theta is large, angular 'overshoots' are often observed at one or both ends of the discontinuity. When the propagation is nearly parallel to the field (when theta is small), many different types of structure are seen, ranging from straight lines, to S-shaped curves, to complex, disorganized shapes.

News and views in discontinuous phase transitions

Science.gov (United States)

Nagler, Jan

2014-03-01

Recent progress in the theory of discontinuous percolation allow us to better understand the the sudden emergence of large-scale connectedness both in networked systems and on the lattice. We analytically study mechanisms for the amplification of critical fluctuations at the phase transition point, non-self-averaging and power law fluctuations. A single event analysis allow to establish criteria for discontinuous percolation transitions, even on the high-dimensional lattice. Some applications such as salad bowl percolation, and inverse fragmentation are discussed.

Dynamic stability and failure modes of slopes in discontinuous rock mass

International Nuclear Information System (INIS)

Shimizu, Yasuhiro; Aydan, O.; Ichikawa, Yasuaki; Kawamoto, Toshikazu.

1988-01-01

The stability of rock slopes during earthquakes are of great concern in rock engineering works such as highway, dam, and nuclear power station constructions. As rock mass in nature is usually discontinuous, the stability of rock slopes will be geverned by the spatial distribution of discontinuities in relation with the geometry of slope and their mechanical properties rather than the rock element. The authors have carried out some model tests on discontinuous rock slopes using three different model tests techniques in order to investigate the dynamic behaviour and failure modes of the slopes in discontinuous rock mass. This paper describes the findings and observations made on model rock slopes with various discontinuity patterns and slope geometry. In addition some stability criterions are developed and the calculated results are compared with those of experiments. (author)

Steady and transient analyses of natural convection in a horizontal porous annulus with Galerkin method

International Nuclear Information System (INIS)

Rao, Y.F.; Fukuda, K.; Hasegawa, S.

1986-01-01

Steady and transient analytical investigation with the Galerkin method has been performed on natural convection in a horizontal porous annulus heated from the inner surface. Three families of convergent solutions, appearing one after another with increasing RaDa numbers, were obtained corresponding to different initial conditions. Despite the fact that the flow structures of two branching solutions are quite different, there exists a critical RaDa number at which their overall heat transfer rates have the same value. The bifurcation point was determined numerically, which coincided very well with that from experimental observation. The solutions in which higher wavenumber modes are dominant agree better with experimental data of overall heat transfer

Discontinuity of maximum entropy inference and quantum phase transitions

International Nuclear Information System (INIS)

Chen, Jianxin; Ji, Zhengfeng; Yu, Nengkun; Zeng, Bei; Li, Chi-Kwong; Poon, Yiu-Tung; Shen, Yi; Zhou, Duanlu

2015-01-01

In this paper, we discuss the connection between two genuinely quantum phenomena—the discontinuity of quantum maximum entropy inference and quantum phase transitions at zero temperature. It is shown that the discontinuity of the maximum entropy inference of local observable measurements signals the non-local type of transitions, where local density matrices of the ground state change smoothly at the transition point. We then propose to use the quantum conditional mutual information of the ground state as an indicator to detect the discontinuity and the non-local type of quantum phase transitions in the thermodynamic limit. (paper)

Incompressible Turbulent Flow Simulation Using the κ-ɛ Model and Upwind Schemes

Directory of Open Access Journals (Sweden)

V. G. Ferreira

2007-01-01

Full Text Available In the computation of turbulent flows via turbulence modeling, the treatment of the convective terms is a key issue. In the present work, we present a numerical technique for simulating two-dimensional incompressible turbulent flows. In particular, the performance of the high Reynolds κ-ɛ model and a new high-order upwind scheme (adaptative QUICKEST by Kaibara et al. (2005 is assessed for 2D confined and free-surface incompressible turbulent flows. The model equations are solved with the fractional-step projection method in primitive variables. Solutions are obtained by using an adaptation of the front tracking GENSMAC (Tomé and McKee (1994 methodology for calculating fluid flows at high Reynolds numbers. The calculations are performed by using the 2D version of the Freeflow simulation system (Castello et al. (2000. A specific way of implementing wall functions is also tested and assessed. The numerical procedure is tested by solving three fluid flow problems, namely, turbulent flow over a backward-facing step, turbulent boundary layer over a flat plate under zero-pressure gradients, and a turbulent free jet impinging onto a flat surface. The numerical method is then applied to solve the flow of a horizontal jet penetrating a quiescent fluid from an entry port beneath the free surface.

MHD intermediate shock discontinuities: Pt. 1

International Nuclear Information System (INIS)

Kennel, C.F.; Blandford, R.D.; Coppi, P.

1989-01-01

Recent numerical investigations have focused attention once more on the role of intermediate shocks in MHD. Four types of intermediate shock are identified using a graphical representation of the MHD Rankine-Hugoniot conditions. This same representation can be used to exhibit the close relationship of intermediate shocks to switch-on shocks and rotational discontinuities. The conditions under which intermediate discontinuities can be found are elucidated. The variations in velocity, pressure, entropy and magnetic-field jumps with upstream parameters in intermediate shocks are exhibited graphically. The evolutionary arguments traditionally advanced against intermediate shocks may fail because the equations of classical MHD are not strictly hyperbolic. (author)

OPTIMAL ESTIMATES FOR THE SEMIDISCRETE GALERKIN METHOD APPLIED TO PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS WITH NONSMOOTH DATA

KAUST Repository

GOSWAMI, DEEPJYOTI; PANI, AMIYA K.; YADAV, SANGITA

2014-01-01

AWe propose and analyse an alternate approach to a priori error estimates for the semidiscrete Galerkin approximation to a time-dependent parabolic integro-differential equation with nonsmooth initial data. The method is based on energy arguments combined with repeated use of time integration, but without using parabolic-type duality techniques. An optimal L2-error estimate is derived for the semidiscrete approximation when the initial data is in L2. A superconvergence result is obtained and then used to prove a maximum norm estimate for parabolic integro-differential equations defined on a two-dimensional bounded domain. © 2014 Australian Mathematical Society.

Contribution of Strong Discontinuities to the Power Spectrum of the Solar Wind

International Nuclear Information System (INIS)

Borovsky, Joseph E.

2010-01-01

Eight and a half years of magnetic field measurements (2 22 samples) from the ACE spacecraft in the solar wind at 1 A.U. are analyzed. Strong (large-rotation-angle) discontinuities in the solar wind are collected and measured. An artificial time series is created that preserves the timing and amplitudes of the discontinuities. The power spectral density of the discontinuity series is calculated and compared with the power spectral density of the solar-wind magnetic field. The strong discontinuities produce a power-law spectrum in the ''inertial subrange'' with a spectral index near the Kolmogorov -5/3 index. The discontinuity spectrum contains about half of the power of the full solar-wind magnetic field over this ''inertial subrange.'' Warnings are issued about the significant contribution of discontinuities to the spectrum of the solar wind, complicating interpretation of spectral power and spectral indices.

Multidimensional upwind hydrodynamics on unstructured meshes using graphics processing units - I. Two-dimensional uniform meshes

Science.gov (United States)

Paardekooper, S.-J.

2017-08-01

We present a new method for numerical hydrodynamics which uses a multidimensional generalization of the Roe solver and operates on an unstructured triangular mesh. The main advantage over traditional methods based on Riemann solvers, which commonly use one-dimensional flux estimates as building blocks for a multidimensional integration, is its inherently multidimensional nature, and as a consequence its ability to recognize multidimensional stationary states that are not hydrostatic. A second novelty is the focus on graphics processing units (GPUs). By tailoring the algorithms specifically to GPUs, we are able to get speedups of 100-250 compared to a desktop machine. We compare the multidimensional upwind scheme to a traditional, dimensionally split implementation of the Roe solver on several test problems, and we find that the new method significantly outperforms the Roe solver in almost all cases. This comes with increased computational costs per time-step, which makes the new method approximately a factor of 2 slower than a dimensionally split scheme acting on a structured grid.

Clopidogrel discontinuation and platelet reactivity following coronary stenting

LENUS (Irish Health Repository)

2011-01-01

Summary. Aims: Antiplatelet therapy with aspirin and clopidogrel is recommended for 1 year after drug-eluting stent (DES) implantation or myocardial infarction. However, the discontinuation of antiplatelet therapy has become an important issue as recent studies have suggested a clustering of ischemic events within 90 days of clopidogrel withdrawal. The objective of this investigation was to explore the hypothesis that there is a transient ‘rebound’ increase in platelet reactivity within 3 months of clopidogrel discontinuation. Methods and Results: In this prospective study, platelet function was assessed in patients taking aspirin and clopidogrel for at least 1 year following DES implantation. Platelet aggregation was measured using a modification of light transmission aggregometry in response to multiple concentrations of adenosine diphosphate (ADP), epinephrine, arachidonic acid, thrombin receptor activating peptide and collagen. Clopidogrel was stopped and platelet function was reassessed 1 week, 1 month and 3 months later. Thirty-two patients on dual antiplatelet therapy were recruited. Discontinuation of clopidogrel increased platelet aggregation to all agonists, except arachidonic acid. Platelet aggregation in response to ADP (2.5, 5, 10, and 20 μm) and epinephrine (5 and 20 μm) was significantly increased at 1 month compared with 3 months following clopidogrel withdrawal. Thus, a transient period of increased platelet reactivity to both ADP and epinephrine was observed 1 month after clopidogrel discontinuation. Conclusions: This study demonstrates a transient increase in platelet reactivity 1 month after clopidogrel withdrawal. This phenomenon may, in part, explain the known clustering of thrombotic events observed after clopidogrel discontinuation. This observation requires confirmation in larger populations.

New formulations on the finite element method for boundary value problems with internal/external boundary layers; Novas formulacoes de elementos finitos para problemas de valor de contorno com camadas limite interna/externa

Energy Technology Data Exchange (ETDEWEB)

Pereira, Luis Carlos Martins

1998-06-15

New Petrov-Galerkin formulations on the finite element methods for convection-diffusion problems with boundary layers are presented. Such formulations are based on a consistent new theory on discontinuous finite element methods. Existence and uniqueness of solutions for these problems in the new finite element spaces are demonstrated. Some numerical experiments shows how the new formulation operate and also their efficacy. (author)

New formulations on the finite element method for boundary value problems with internal/external boundary layers

International Nuclear Information System (INIS)

Pereira, Luis Carlos Martins

1998-06-01

New Petrov-Galerkin formulations on the finite element methods for convection-diffusion problems with boundary layers are presented. Such formulations are based on a consistent new theory on discontinuous finite element methods. Existence and uniqueness of solutions for these problems in the new finite element spaces are demonstrated. Some numerical experiments shows how the new formulation operate and also their efficacy. (author)

A Discontinuous Galerkin Finite Element Method for Dynamic of Fully Saturated Soil / Rzwiazanie Zadania Dynamiki Całkowicie Nawodnionego Gruntu Przy Zastosowaniu Mes Z Nieciagłym Sformułowaniem Galerkina W Czasie

Directory of Open Access Journals (Sweden)

Wrana B.

2011-03-01

Full Text Available Artykuł podejmuje zagadnienie analizy rozchodzenia sie fal naprezeniowych w gruncie w ujeciu metody elementów skonczonych bazujac na sformułowaniu rozwiazania ciagłego w przestrzeni i nieciagłego w dziedzinie czasu Galerkina (space and time-discontinous Galerkin TDG finite element method. W tym sformułowaniu zarówno przemieszczenia jak i predkosci sa wielkosciami nieznanymi wzajemnie niezaleznymi aproksymowanymi ciagłymi funkcjami kształtu w przestrzeni i nieciagłymi funkcjami kształtu w czasie. Do opisu zachowania sie gruntu w pełni nasyconego woda zastosowano sformułowanie u-p w ujeciu metody elementów skonczonych. Grunt traktowany jest, jako osrodek dwufazowy składajacy sie ze szkieletu i wody w porach. Zastosowane sformułowanie uwzglednia tłumienie osrodka przez uwzglednienie dyssypacji energii proporcjonalnej do predkosci wody wzgledem szkieletu. W artykule przedstawiono porównanie proponowanej metody rozwiazania numerycznego w dziedzinie czasu do metod obecnie stosowanych, takich jak: metoda róznicy centralnej, metoda Houbolta, Wilsona θ, HHT-α oraz najczesciej stosowanej metody Newmarka. Z porównania wynika, ze proponowana metoda jest metoda stabilna o małym błedzie numerycznego rozwiazania.

Research progress on criteria for discontinuation of EGFR inhibitor therapy

Directory of Open Access Journals (Sweden)

Zhuang HQ

2012-10-01

Full Text Available Hong-qing Zhuang, Zhi-yong Yuan, Jun Wang, Ping Wang, Lu-jun Zhao, Bai-lin ZhangDepartment of Radiotherapy, Tianjin Medical University Cancer Institute and Hospital, Tianjin Key Laboratory of Cancer Prevention and Therapy, Tianjin Lung Cancer Center, Tianjin, People's Republic of ChinaAbstract: The clinical success of the epidermal growth factor receptor (EGFR tyrosine kinase inhibitors (TKI as therapeutic agents has prompted great interest in their further development and clinical testing for a wide variety of malignancies. However, most studies have focused on the efficacy of TKI, and few studies have been done on the criteria for their discontinuation. The current standard for drug discontinuation is “until progression”, based on change in tumor size. However, tumor size is not related to the gene expression which determines the efficacy of TKI in the final analysis, and it is also difficult to make a thorough and correct prediction based on tumor size when the TKI is discontinued. Nevertheless, clinical evaluation of the criteria for TKI discontinuation is still in its early days. Some promising findings have started to emerge. With the improving knowledge of EGFR and its inhibitors, it is expected that the criteria for discontinuation of EGFR inhibitor therapy will become clearer.Keywords: epidermal growth factor receptor, drug discontinuation, acquired drug-resistance

Divergence-Conforming Discontinuous Galerkin Methods and $C^0$ Interior Penalty Methods

KAUST Repository

Kanschat, Guido; Sharma, Natasha

2014-01-01

© 2014 Society for Industrial and Applied Mathematics. In this paper, we show that recently developed divergence-conforming methods for the Stokes problem have discrete stream functions. These stream functions in turn solve a continuous interior

A Moving Discontinuous Galerkin Finite Element Method for Flows with Interfaces

Science.gov (United States)

2017-12-07

compressible (Euler) flow , both in steady and spacetime form. The Euler flow state variable is given by y = (r,rv1, . . . ,rvn,rE) 2 Rm, (18) where m = n+2...analogous flow was computed using a larger spatial velocity vx = 32 using MDG-ICE(p = 0), as shown in Figure 3. In this case, the upstream state ...spacetime domainW= (0,1)⇥ 0, 12 with six quadrilateral cells is shown in Figure 4. The flow state variable y was discretized using Q2 elements, while the

Discontinuous Galerkin Subgrid Finite Element Method for Heterogeneous Brinkman’s Equations

KAUST Repository

Iliev, Oleg P.; Lazarov, Raytcho D.; Willems, Joerg

2010-01-01

We present a two-scale finite element method for solving Brinkman's equations with piece-wise constant coefficients. This system of equations model fluid flows in highly porous, heterogeneous media with complex topology of the heterogeneities. We

Convergence Improvement of Response Matrix Method with Large Discontinuity Factors

International Nuclear Information System (INIS)

Yamamoto, Akio

2003-01-01

In the response matrix method, a numerical divergence problem has been reported when extremely small or large discontinuity factors are utilized in the calculations. In this paper, an alternative response matrix formulation to solve the divergence problem is discussed, and properties of iteration matrixes are investigated through eigenvalue analyses. In the conventional response matrix formulation, partial currents between adjacent nodes are assumed to be discontinuous, and outgoing partial currents are converted into incoming partial currents by the discontinuity factor matrix. Namely, the partial currents of the homogeneous system (i.e., homogeneous partial currents) are treated in the conventional response matrix formulation. In this approach, the spectral radius of an iteration matrix for the partial currents may exceed unity when an extremely small or large discontinuity factor is used. Contrary to this, an alternative response matrix formulation using heterogeneous partial currents is discussed in this paper. In the latter approach, partial currents are assumed to be continuous between adjacent nodes, and discontinuity factors are directly considered in the coefficients of a response matrix. From the eigenvalue analysis of the iteration matrix for the one-group, one-dimensional problem, the spectral radius for the heterogeneous partial current formulation does not exceed unity even if an extremely small or large discontinuity factor is used in the calculation; numerical stability of the alternative formulation is superior to the conventional one. The numerical stability of the heterogeneous partial current formulation is also confirmed by the two-dimensional light water reactor core analysis. Since the heterogeneous partial current formulation does not require any approximation, the converged solution exactly reproduces the reference solution when the discontinuity factors are directly derived from the reference calculation

Schroedinger propagation of initial discontinuities leads to divergence of moments

International Nuclear Information System (INIS)

Marchewka, A.; Schuss, Z.

2009-01-01

We show that the large phase expansion of the Schroedinger propagation of an initially discontinuous wave function leads to the divergence of average energy, momentum, and displacement, rendering them unphysical states. If initially discontinuous wave functions are considered to be approximations to continuous ones, the determinant of the spreading rate of these averages is the maximal gradient of the initial wave function. Therefore a dilemma arises between the inclusion of discontinuous wave functions in quantum mechanics and the requirement of finite moments.

Schroedinger propagation of initial discontinuities leads to divergence of moments

Energy Technology Data Exchange (ETDEWEB)

Marchewka, A., E-mail: avi.marchewka@gmail.co [Ruppin Academic Center, Emek-Hefer 40250 (Israel); Schuss, Z., E-mail: schuss@post.tau.ac.i [Department of Mathematics, Tel-Aviv University, Ramat-Aviv, 69978 Tel-Aviv (Israel)

2009-09-21

We show that the large phase expansion of the Schroedinger propagation of an initially discontinuous wave function leads to the divergence of average energy, momentum, and displacement, rendering them unphysical states. If initially discontinuous wave functions are considered to be approximations to continuous ones, the determinant of the spreading rate of these averages is the maximal gradient of the initial wave function. Therefore a dilemma arises between the inclusion of discontinuous wave functions in quantum mechanics and the requirement of finite moments.

Forensic Excavation of Rock Masses: A Technique to Investigate Discontinuity Persistence

Science.gov (United States)

Shang, J.; Hencher, S. R.; West, L. J.; Handley, K.

2017-11-01

True persistence of rock discontinuities (areas with insignificant tensile strength) is an important factor controlling the engineering behaviour of fractured rock masses, but is extremely difficult to quantify using current geological survey methodologies, even where there is good rock exposure. Trace length as measured in the field or using remote measurement devices is actually only broadly indicative of persistence for rock engineering practice and numerical modelling. Visible traces of discontinuities are treated as if they were open fractures within rock mass classifications, despite many such traces being non-persistent and actually retaining considerable strength. The common assumption of 100% persistence, based on trace length, is generally extremely conservative in terms of strength and stiffness, but not always so and may lead to a wrong prediction of failure mechanism or of excavatability. Assuming full persistence would give hopelessly incorrect predictions of hydraulic conductivity. A new technique termed forensic excavation of rock masses is introduced, as a procedure for directly investigating discontinuity persistence. This technique involves non-explosive excavation of rock masses by injecting an expansive chemical splitter along incipient discontinuities. On expansion, the splitter causes the incipient traces to open as true joints. Experiments are described in which near-planar rock discontinuities, through siltstone and sandstone, were opened up by injecting the splitter into holes drilled along the lines of visible traces of the discontinuities in the laboratory and in the field. Once exposed the surfaces were examined to investigate the pre-existing persistence characteristics of the incipient discontinuities. One conclusion from this study is that visible trace length of a discontinuity can be a poor indicator of true persistence (defined for a fracture area with negligible tensile strength). An observation from this series of experiments

The effect of discontinuities on the corrosion behaviour of copper canisters

International Nuclear Information System (INIS)

King, F.

2004-03-01

Discontinuities may remain in the weld region of copper canisters following the final closure welding and inspection procedures. Although the shell of the copper canister is expected to exhibit excellent corrosion properties in the repository environment, the question remains what impact these discontinuities might have on the long-term performance and service life of the canister. A review of the relevant corrosion literature has been carried out and an expert opinion of the impact of these discontinuities on the canister lifetime has been developed. Since the amount of oxidant in the repository is limited and the maximum wall penetration is expected to be 2 O/Cu(OH) 2 film at a critical electrochemical potential determines where and when pits initiate, not the presence of pit-shaped surface discontinuities. The factors controlling pit growth and death are well understood. There is evidence for a maximum pit radius for copper in chloride solutions, above which the small anodic: cathodic surface area ratio required for the formation of deep pits cannot be sustained. This maximum pit radius is of the order of 0.1-0.5 mm. Surface discontinuities larger than this size are unlikely to propagate as pits, and pits generated from smaller discontinuities will die once they reach this maximum size. Death of propagating pits will be compounded by the decrease in oxygen flux to the canister as the repository environment becomes anoxic. Surface discontinuities could impact the SCC behaviour either through their effect on the local environment or via stress concentration or intensification. There is no evidence that surface discontinuities will affect the initiation of SCC by ennoblement of the corrosion potential or the formation of locally aggressive conditions. Stress concentration at pits could lead to crack initiation under some circumstances, but the stress intensity factor for the resultant cracks, or for pre-existing crack-like discontinuities, will be smaller than the

A Streamline-Upwind Petrov-Galerkin Finite Element Scheme for Non-Ionized Hypersonic Flows in Thermochemical Nonequilibrium

Science.gov (United States)

Kirk, Benjamin S.; Bova, Stephen W.; Bond, Ryan B.

2011-01-01

Presentation topics include background and motivation; physical modeling including governing equations and thermochemistry; finite element formulation; results of inviscid thermal nonequilibrium chemically reacting flow and viscous thermal equilibrium chemical reacting flow; and near-term effort.

Automatic extraction of discontinuity orientation from rock mass surface 3D point cloud

Science.gov (United States)

Chen, Jianqin; Zhu, Hehua; Li, Xiaojun

2016-10-01

This paper presents a new method for extracting discontinuity orientation automatically from rock mass surface 3D point cloud. The proposed method consists of four steps: (1) automatic grouping of discontinuity sets using an improved K-means clustering method, (2) discontinuity segmentation and optimization, (3) discontinuity plane fitting using Random Sample Consensus (RANSAC) method, and (4) coordinate transformation of discontinuity plane. The method is first validated by the point cloud of a small piece of a rock slope acquired by photogrammetry. The extracted discontinuity orientations are compared with measured ones in the field. Then it is applied to a publicly available LiDAR data of a road cut rock slope at Rockbench repository. The extracted discontinuity orientations are compared with the method proposed by Riquelme et al. (2014). The results show that the presented method is reliable and of high accuracy, and can meet the engineering needs.

A gradient estimate for solutions to parabolic equations with discontinuous coefficients

Directory of Open Access Journals (Sweden)

Jishan Fan

2013-04-01

Full Text Available Li-Vogelius and Li-Nirenberg gave a gradient estimate for solutions of strongly elliptic equations and systems of divergence forms with piecewise smooth coefficients, respectively. The discontinuities of the coefficients are assumed to be given by manifolds of codimension 1, which we called them emph{manifolds of discontinuities}. Their gradient estimate is independent of the distances between manifolds of discontinuities. In this paper, we gave a parabolic version of their results. That is, we gave a gradient estimate for parabolic equations of divergence forms with piecewise smooth coefficients. The coefficients are assumed to be independent of time and their discontinuities are likewise the previous elliptic equations. As an application of this estimate, we also gave a pointwise gradient estimate for the fundamental solution of a parabolic operator with piecewise smooth coefficients. Both gradient estimates are independent of the distances between manifolds of discontinuities.

Stress intensity factor analysis of friction sliding at discontinuity interfaces and junctions

CSIR Research Space (South Africa)

Phan, AV

2003-12-01

Full Text Available ]) and boundary element method (BEM) [2?5]. The key feature of the integral equation approach is that only the boundary of the domain is discretized and only boundary quantities are determined. As a result, for fracture analy- sis, the singular stress field ahead... collocation ap- proach enforces the BIE (1) and HBIE (2) at discrete source points whereas these equations are satisfied in an averaged sense with the Galerkin approximation. The additional boundary integration is the key to obtaining a symmetric coefficient...

A simple model of discontinuous firm’s growth

OpenAIRE

D'Elia, Enrico

2011-01-01

Typically, firms change their size through a row of discrete leaps over time. Sunk costs, regulatory, financial and organizational constraints, talent distribution and other factors may explain this fact. However, firms tend to grow or fall discontinuously even if those inertial factors were removed. For instance, a very essential model of discontinuous growth can be based on a couple of assumptions concerning only technology and entrepreneurs’ strategy, that is: (a) in the short run, the...

Reciprocity principle for scattered fields from discontinuities in waveguides.

Science.gov (United States)

Pau, Annamaria; Capecchi, Danilo; Vestroni, Fabrizio

2015-01-01

This study investigates the scattering of guided waves from a discontinuity exploiting the principle of reciprocity in elastodynamics, written in a form that applies to waveguides. The coefficients of reflection and transmission for an arbitrary mode can be derived as long as the principle of reciprocity is satisfied at the discontinuity. Two elastodynamic states are related by the reciprocity. One is the response of the waveguide in the presence of the discontinuity, with the scattered fields expressed as a superposition of wave modes. The other state is the response of the waveguide in the absence of the discontinuity oscillating according to an arbitrary mode. The semi-analytical finite element method is applied to derive the needed dispersion relation and wave mode shapes. An application to a solid cylinder with a symmetric double change of cross-section is presented. This model is assumed to be representative of a damaged rod. The coefficients of reflection and transmission of longitudinal waves are investigated for selected values of notch length and varying depth. Copyright © 2014 Elsevier B.V. All rights reserved.

Early Discontinuation of Montelukast Treatment; A Danish Nationwide Utilization Study

DEFF Research Database (Denmark)

Farah, Rahmo I; Damkier, Per; Christiansen, Anders

2018-01-01

Montelukast, a leukotriene receptor antagonist, was marketed in 1998 as an oral supplementary treatment to patients with mild to moderate asthma. The aim of this study was to describe the early discontinuation pattern among montelukast users in Denmark in the period of 1 March 1998 to 31 December....... Early discontinuation was defined as failing to fill a second prescription for montelukast within at least a year after the initial montelukast prescription. Among 135,271 included montelukast users, 47,480 (35%) discontinued the use of montelukast after a single redeemed prescription. The trend...

Risk of Vascular Thrombotic Events Following Discontinuation of Antithrombotics After Peptic Ulcer Bleeding.

Science.gov (United States)

Kim, Seung Young; Hyun, Jong Jin; Suh, Sang Jun; Jung, Sung Woo; Jung, Young Kul; Koo, Ja Seol; Yim, Hyung Joon; Park, Jong Jae; Chun, Hoon Jai; Lee, Sang Woo

2016-04-01

To evaluate whether the risk of cardiovascular events increases when antithrombotics are discontinued after ulcer bleeding. Peptic ulcer bleeding associated with antithrombotics has increased due to the increase in the proportion of elderly population. Little is known about the long-term effects of discontinuing antithrombotics after peptic ulcer bleeding. The aim of this study was to evaluate whether the risk of cardiovascular events increases when antithrombotics are discontinued after ulcer bleeding. We reviewed the medical records of patients with ulcer bleeding who were taking antiplatelet agents or anticoagulants at the time of ulcer bleeding. Cox-regression model was used to adjust for potential confounders, and analyzed association between discontinuation of antithrombotic drugs after ulcer bleeding and thrombotic events such as ischemic heart disease or stroke. Of the 544 patients with ulcer bleeding, 72 patients who were taking antithrombotics and followed up for >2 months were analyzed. Forty patients discontinued antithrombotics after ulcer bleeding (discontinuation group) and 32 patients continued antithrombotics with or without transient interruption (continuation group). Thrombotic events developed more often in discontinuation group than in the continuation group [7/32 (21.9%) vs. 1/40 (2.5%), P=0.019]. Hazard ratio for thrombotic event when antithrombotics were continuously discontinued was 10.9 (95% confidence interval, 1.3-89.7). There were no significant differences in recurrent bleeding events between the 2 groups. Discontinuation of antithrombotics after peptic ulcer bleeding increases the risk of cardiovascular events. Therefore, caution should be taken when discontinuing antithrombotics after ulcer bleeding.

ANÁLISIS DE LA ESTABILIDAD ESPACIO-TEMPORAL DEL MÉTODO PETROV-GALERKIN EN CONTRACORRIENTE PARA LA ECUACIONES DE DIFUSIÓN-ADVECCIÓN

Directory of Open Access Journals (Sweden)

DIEGO GARZÓN

2010-01-01

Full Text Available El presente artículo analiza la estabilidad espacial y temporal de una solución numérica de la ecuación de difusiónadvección, a través del método de PetrovGalerkin en contracorriente (SUPG, junto con una discretización temporal BackwardEuler. En la primera parte del artículo se plantean los conceptos fundamentales de la técnica de estabilización espacial SUPG para dos dimensiones y posteriormente se presentan las consideraciones empleadas para la discretización temporal. A continuación se trata la metodología y las expresiones necesarias para la implementación computacional del método. Se analizan dos casos de estudio en los cuales se compara la estabilidad espacial y temporal de la solución implementada, con la obtenida por medio de la aproximación convencional BubnovGalerkin. Se emplea el error en norma de energía para analizar la estabilidad de las aproximaciones obtenidas. Videos y gráficas adicionales de los problemas presentados en este artículo pueden ser descargados de www.gnum.unal.edu.co

Low-Dissipation Advection Schemes Designed for Large Eddy Simulations of Hypersonic Propulsion Systems

Science.gov (United States)

White, Jeffrey A.; Baurle, Robert A.; Fisher, Travis C.; Quinlan, Jesse R.; Black, William S.

2012-01-01

The 2nd-order upwind inviscid flux scheme implemented in the multi-block, structured grid, cell centered, finite volume, high-speed reacting flow code VULCAN has been modified to reduce numerical dissipation. This modification was motivated by the desire to improve the codes ability to perform large eddy simulations. The reduction in dissipation was accomplished through a hybridization of non-dissipative and dissipative discontinuity-capturing advection schemes that reduces numerical dissipation while maintaining the ability to capture shocks. A methodology for constructing hybrid-advection schemes that blends nondissipative fluxes consisting of linear combinations of divergence and product rule forms discretized using 4th-order symmetric operators, with dissipative, 3rd or 4th-order reconstruction based upwind flux schemes was developed and implemented. A series of benchmark problems with increasing spatial and fluid dynamical complexity were utilized to examine the ability of the candidate schemes to resolve and propagate structures typical of turbulent flow, their discontinuity capturing capability and their robustness. A realistic geometry typical of a high-speed propulsion system flowpath was computed using the most promising of the examined schemes and was compared with available experimental data to demonstrate simulation fidelity.

New implementation method for essential boundary condition to extended element-free Galerkin method. Application to nonlinear problem

International Nuclear Information System (INIS)

Saitoh, Ayumu; Matsui, Nobuyuki; Itoh, Taku; Kamitani, Atsushi; Nakamura, Hiroaki

2011-01-01

A new method has been proposed for implementing essential boundary conditions to the Element-Free Galerkin Method (EFGM) without using the Lagrange multiplier. Furthermore, the performance of the proposed method has been investigated for a nonlinear Poisson problem. The results of computations show that, as interpolation functions become closer to delta functions, the accuracy of the solution is improved on the boundary. In addition, the accuracy of the proposed method is higher than that of the conventional EFGM. Therefore, it might be concluded that the proposed method is useful for solving the nonlinear Poisson problem. (author)

Discontinuous precipitation and ordering in Ni2V-Cu alloys

International Nuclear Information System (INIS)

Sukhanov, V.D; Boyarshinova, T.S.; Shashkov, O.D.

1986-01-01

Ni-V-Cu system alloys were used to investigate the effect of ordering on over-saturated solid solution decomposition. It was discovered that ordering in the process of grain boundary migration (discontinuous disordering), stimulated changing of continuous precipitation mechanism for discontinuous one

A gradient estimate for solutions to parabolic equations with discontinuous coefficients

OpenAIRE

Fan, Jishan; Kim, Kyoungsun; Nagayasu, Sei; Nakamura, Gen

2011-01-01

Li-Vogelius and Li-Nirenberg gave a gradient estimate for solutions of strongly elliptic equations and systems of divergence forms with piecewise smooth coefficients, respectively. The discontinuities of the coefficients are assumed to be given by manifolds of codimension 1, which we called them emph{manifolds of discontinuities}. Their gradient estimate is independent of the distances between manifolds of discontinuities. In this paper, we gave a parabolic version of their results. T...

Factors Influencing Contraceptive Choice and Discontinuation ...

African Journals Online (AJOL)

Erah

2010-03-30

women indicated that their HIV status dictated contraceptive decisions, particularly with ... Women reported method discontinuation because of side effects, having met desired parity, ...... Washington, D.C., 2009. ... Accessed March 30, 2010.

Finite element analysis of nonlinear creeping flows

International Nuclear Information System (INIS)

Loula, A.F.D.; Guerreiro, J.N.C.

1988-12-01

Steady-state creep problems with monotone constitutive laws are studied. Finite element approximations are constructed based on mixed Petrov-Galerkin formulations for constrained problems. Stability, convergence and a priori error estimates are proved for equal-order discontinuous stress and continuous velocity interpolations. Numerical results are presented confirming the rates of convergence predicted in the analysis and the good performance of this formulation. (author) [pt

41 CFR 101-39.105 - Discontinuance or curtailment of service.

Science.gov (United States)

2010-07-01

..., AND MOTOR VEHICLES 39-INTERAGENCY FLEET MANAGEMENT SYSTEMS 39.1-Establishment, Modification, and Discontinuance of Interagency Fleet Management Systems § 101-39.105 Discontinuance or curtailment of service. (a... efficiencies are realized from the operation of any fleet management system, the Administrator, GSA, will...

How do horizontal, frictional discontinuities affect reverse fault-propagation folding?

Science.gov (United States)

Bonanno, Emanuele; Bonini, Lorenzo; Basili, Roberto; Toscani, Giovanni; Seno, Silvio

2017-09-01

The development of new reverse faults and related folds is strongly controlled by the mechanical characteristics of the host rocks. In this study we analyze the impact of a specific kind of anisotropy, i.e. thin mechanical and frictional discontinuities, in affecting the development of reverse faults and of the associated folds using physical scaled models. We perform analog modeling introducing one or two initially horizontal, thin discontinuities above an initially blind fault dipping at 30° in one case, and 45° in another, and then compare the results with those obtained from a fully isotropic model. The experimental results show that the occurrence of thin discontinuities affects both the development and the propagation of new faults and the shape of the associated folds. New faults 1) accelerate or decelerate their propagation depending on the location of the tips with respect to the discontinuities, 2) cross the discontinuities at a characteristic angle (∼90°), and 3) produce folds with different shapes, resulting not only from the dip of the new faults but also from their non-linear propagation history. Our results may have direct impact on future kinematic models, especially those aimed to reconstruct the tectonic history of faults that developed in layered rocks or in regions affected by pre-existing faults.

A higher order space-time Galerkin scheme for time domain integral equations

KAUST Repository

Pray, Andrew J.

2014-12-01

Stability of time domain integral equation (TDIE) solvers has remained an elusive goal formany years. Advancement of this research has largely progressed on four fronts: 1) Exact integration, 2) Lubich quadrature, 3) smooth temporal basis functions, and 4) space-time separation of convolutions with the retarded potential. The latter method\\'s efficacy in stabilizing solutions to the time domain electric field integral equation (TD-EFIE) was previously reported for first-order surface descriptions (flat elements) and zeroth-order functions as the temporal basis. In this work, we develop the methodology necessary to extend the scheme to higher order surface descriptions as well as to enable its use with higher order basis functions in both space and time. These basis functions are then used in a space-time Galerkin framework. A number of results are presented that demonstrate convergence in time. The viability of the space-time separation method in producing stable results is demonstrated experimentally for these examples.

A higher order space-time Galerkin scheme for time domain integral equations

KAUST Repository

Pray, Andrew J.; Beghein, Yves; Nair, Naveen V.; Cools, Kristof; Bagci, Hakan; Shanker, Balasubramaniam

2014-01-01

Stability of time domain integral equation (TDIE) solvers has remained an elusive goal formany years. Advancement of this research has largely progressed on four fronts: 1) Exact integration, 2) Lubich quadrature, 3) smooth temporal basis functions, and 4) space-time separation of convolutions with the retarded potential. The latter method's efficacy in stabilizing solutions to the time domain electric field integral equation (TD-EFIE) was previously reported for first-order surface descriptions (flat elements) and zeroth-order functions as the temporal basis. In this work, we develop the methodology necessary to extend the scheme to higher order surface descriptions as well as to enable its use with higher order basis functions in both space and time. These basis functions are then used in a space-time Galerkin framework. A number of results are presented that demonstrate convergence in time. The viability of the space-time separation method in producing stable results is demonstrated experimentally for these examples.

Application of stochastic Galerkin FEM to the complete electrode model of electrical impedance tomography

International Nuclear Information System (INIS)

Leinonen, Matti; Hakula, Harri; Hyvönen, Nuutti

2014-01-01

The aim of electrical impedance tomography is to determine the internal conductivity distribution of some physical body from boundary measurements of current and voltage. The most accurate forward model for impedance tomography is the complete electrode model, which consists of the conductivity equation coupled with boundary conditions that take into account the electrode shapes and the contact resistances at the corresponding interfaces. If the reconstruction task of impedance tomography is recast as a Bayesian inference problem, it is essential to be able to solve the complete electrode model forward problem with the conductivity and the contact resistances treated as a random field and random variables, respectively. In this work, we apply a stochastic Galerkin finite element method to the ensuing elliptic stochastic boundary value problem and compare the results with Monte Carlo simulations

A variational multiscale method for particle-cloud tracking in turbomachinery flows

Science.gov (United States)

Corsini, A.; Rispoli, F.; Sheard, A. G.; Takizawa, K.; Tezduyar, T. E.; Venturini, P.

2014-11-01

We present a computational method for simulation of particle-laden flows in turbomachinery. The method is based on a stabilized finite element fluid mechanics formulation and a finite element particle-cloud tracking method. We focus on induced-draft fans used in process industries to extract exhaust gases in the form of a two-phase fluid with a dispersed solid phase. The particle-laden flow causes material wear on the fan blades, degrading their aerodynamic performance, and therefore accurate simulation of the flow would be essential in reliable computational turbomachinery analysis and design. The turbulent-flow nature of the problem is dealt with a Reynolds-Averaged Navier-Stokes model and Streamline-Upwind/Petrov-Galerkin/Pressure-Stabilizing/Petrov-Galerkin stabilization, the particle-cloud trajectories are calculated based on the flow field and closure models for the turbulence-particle interaction, and one-way dependence is assumed between the flow field and particle dynamics. We propose a closure model utilizing the scale separation feature of the variational multiscale method, and compare that to the closure utilizing the eddy viscosity model. We present computations for axial- and centrifugal-fan configurations, and compare the computed data to those obtained from experiments, analytical approaches, and other computational methods.

Father's Labour Migration and Children's School Discontinuation in Rural Mozambique.

Science.gov (United States)

Yabiku, Scott T; Agadjanian, Victor

2017-08-01

We examine how the discontinuation of schooling among left-behind children is related to multiple dimensions of male labor migration: the accumulation of migration experience, the timing of these migration experiences in the child's life course, and the economic success of the migration. Our setting is rural southern Mozambique, an impoverished area with massive male labor out-migration. Results show that fathers' economically successful labor migration is more beneficial for children's schooling than unsuccessful migration or non-migration. There are large differences, however, by gender: compared to sons of non-migrants, sons of migrant fathers (regardless of migration success) have lower rates of school discontinuation, while daughters of migrant fathers have rates of school discontinuation no different than daughters of non-migrants. Furthermore, accumulated labor migration across the child's life course is beneficial for boys' schooling, but not girls'. Remittances sent in the past year reduce the rate of discontinuation for sons, but not daughters.