#### Sample records for discontinuous galerkin solution

1. Solution of 3D heat conduction equations using the discontinuous Galerkin method on unstructured grids

Directory of Open Access Journals (Sweden)

Ruslan V. Zhalnin

2015-09-01

Full Text Available The discontinuous Galerkin method with discontinuous basic functions which is characterized by a high order of accuracy of the obtained solution is now widely used. In this paper a new way of approximation of diffusion terms for discontinuous Galerkin method for solving diffusion-type equations is proposed. The method uses piecewise polynomials that are continuous on a macroelement surrounding the nodes in the unstructured mesh but discontinuous between the macroelements. In the proposed numerical scheme the spaced grid is used. On one grid an approximation of the unknown quantity is considered, on the other is the approximation of additional variables. Additional variables are components of the heat flux. For the numerical experiment the initial-boundary problem for three-dimensional heat conduction equation is chosen. Calculations of three-dimensional modeling problems including explosive factors show a good accuracy of offered method.

2. 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.

3. Efficient Implementation of Smoothness-Increasing Accuracy-Conserving (SIAC) Filters for Discontinuous Galerkin Solutions

NARCIS (Netherlands)

Mirzaee, H.; Ryan, J.K.; Kirby, R.M.

2011-01-01

The discontinuous Galerkin (DG) methods provide a high-order extension of the finite volume method in much the same way as high-order or spectral/hp elements extend standard finite elements. However, lack of inter-element continuity is often contrary to the smoothness assumptions upon which many

4. Adaptive backward difference formula - Discontinuous Galerkin finite element method for the solution of conservation laws

Czech Academy of Sciences Publication Activity Database

Dolejší, V.; Kůs, Pavel

2008-01-01

Roč. 73, č. 12 (2008), s. 1739-1766 ISSN 0029-5981 Keywords : backward difference formula * discontinuous Galerkin method * adaptive choice of the time step Subject RIV: BA - General Mathematics Impact factor: 2.229, year: 2008 http://onlinelibrary.wiley.com/doi/10.1002/nme.2143/abstract

5. 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.

6. Discontinuous Galerkin finite element methods for hyperbolic differential equations

NARCIS (Netherlands)

van der Vegt, Jacobus J.W.; van der Ven, H.; Boelens, O.J.; Boelens, O.J.; Toro, E.F.

2002-01-01

In this paper a suryey is given of the important steps in the development of discontinuous Galerkin finite element methods for hyperbolic partial differential equations. Special attention is paid to the application of the discontinuous Galerkin method to the solution of the Euler equations of gas

7. Discontinuous Galerkin Method for Hyperbolic Conservation Laws

KAUST Repository

Mousikou, Ioanna

2016-11-11

Hyperbolic conservation laws form a special class of partial differential equations. They describe phenomena that involve conserved quantities and their solutions show discontinuities which reflect the formation of shock waves. We consider one-dimensional systems of hyperbolic conservation laws and produce approximations using finite difference, finite volume and finite element methods. Due to stability issues of classical finite element methods for hyperbolic conservation laws, we study the discontinuous Galerkin method, which was recently introduced. The method involves completely discontinuous basis functions across each element and it can be considered as a combination of finite volume and finite element methods. We illustrate the implementation of discontinuous Galerkin method using Legendre polynomials, in case of scalar equations and in case of quasi-linear systems, and we review important theoretical results about stability and convergence of the method. The applications of finite volume and discontinuous Galerkin methods to linear and non-linear scalar equations, as well as to the system of elastodynamics, are exhibited.

8. A Priori Estimates of Solution of a Homogeneous Boundary Value Problem for Parabolic Type Equations by the Discontinuous Galerkin Method on Staggered Grids

Directory of Open Access Journals (Sweden)

Ruslan V. Zhalnin

2017-12-01

Full Text Available Introduction: In this paper, we present a priori error analysis of the solution of a homogeneous boundary value problem for a second-order differential equation by the discontinuous Galerkin method on staggered grids. Materials and Methods: This study is based on the unified hp-version error analysis of local discontinuous Galerkin method proposed by Castillo et al. [Optimal a priori error estimates for the hp-version of the local discontinuous Galerkin method for convection-diffusion problems, 2002]. The purpose of this paper is to present a new approach to the error analysis of the solution of parabolic equations by the discontinuous Galerkin method on staggered grids. Results: We suggest that approximation errors depend on the characteristic size of the cells and the degree of polynomials used in the basis functions. The necessary lemmas are formulated for the problem solution. The complete proof of the lemmas formulated is carried out. We formulated and proved a theorem, in which a priori error estimates are given for solving parabolic equations using the discontinuous Galerkin method on staggered grids Discussion and Conclusions: The obtained results are consistent with similar studies of other authors and complement them. Further work on this topic involves the study of diffusion-type equations of order higher than the first and the production of a posteriori error estimates.

9. Class of reconstructed discontinuous Galerkin methods in computational fluid dynamics

International Nuclear Information System (INIS)

Luo, Hong; Xia, Yidong; Nourgaliev, Robert

2011-01-01

A class of reconstructed discontinuous Galerkin (DG) methods is presented to solve compressible flow problems on arbitrary grids. The idea is to combine the efficiency of the reconstruction methods in finite volume methods and the accuracy of the DG methods to obtain a better numerical algorithm in computational fluid dynamics. The beauty of the resulting reconstructed discontinuous Galerkin (RDG) methods is that they provide a unified formulation for both finite volume and DG methods, and contain both classical finite volume and standard DG methods as two special cases of the RDG methods, and thus allow for a direct efficiency comparison. Both Green-Gauss and least-squares reconstruction methods and a least-squares recovery method are presented to obtain a quadratic polynomial representation of the underlying linear discontinuous Galerkin solution on each cell via a so-called in-cell reconstruction process. The devised in-cell reconstruction is aimed to augment the accuracy of the discontinuous Galerkin method by increasing the order of the underlying polynomial solution. These three reconstructed discontinuous Galerkin methods are used to compute a variety of compressible flow problems on arbitrary meshes to assess their accuracy. The numerical experiments demonstrate that all three reconstructed discontinuous Galerkin methods can significantly improve the accuracy of the underlying second-order DG method, although the least-squares reconstructed DG method provides the best performance in terms of both accuracy, efficiency, and robustness. (author)

10. Discontinuous Galerkin for the Radiative Transport Equation

KAUST Repository

Guermond, Jean-Luc

2013-10-11

This note presents some recent results regarding the approximation of the linear radiative transfer equation using discontinuous Galerkin methods. The locking effect occurring in the diffusion limit with the upwind numerical flux is investigated and a correction technique is proposed.

11. 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)

12. A Multi-wavelet type limiter for discontinuous Galerkin approximations

NARCIS (Netherlands)

Cheruvu, V.; Ryan, J.K.

2010-01-01

In this report, we present a multi-wavelet type limiter for the discontinuous Galerkin method for limiting the solution when spurious oscillations develop near a shock. This limiting leads to a loss of information in the approximation that can be detrimental to a higher order approximation (k > 2).

13. 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.

14. Discontinuous Galerkin algorithms for fully kinetic plasmas

Science.gov (United States)

Juno, J.; Hakim, A.; TenBarge, J.; Shi, E.; Dorland, W.

2018-01-01

We present a new algorithm for the discretization of the non-relativistic Vlasov-Maxwell system of equations for the study of plasmas in the kinetic regime. Using the discontinuous Galerkin finite element method for the spatial discretization, we obtain a high order accurate solution for the plasma's distribution function. Time stepping for the distribution function is done explicitly with a third order strong-stability preserving Runge-Kutta method. Since the Vlasov equation in the Vlasov-Maxwell system is a high dimensional transport equation, up to six dimensions plus time, we take special care to note various features we have implemented to reduce the cost while maintaining the integrity of the solution, including the use of a reduced high-order basis set. A series of benchmarks, from simple wave and shock calculations, to a five dimensional turbulence simulation, are presented to verify the efficacy of our set of numerical methods, as well as demonstrate the power of the implemented features.

15. Hybridized Multiscale Discontinuous Galerkin Methods for Multiphysics

Science.gov (United States)

2015-09-14

Helmholtz equation for a very wide range of wave frequencies, 4) presented an embedded discontinuous Galerkin (EDG) method for numerically ...of freedom (for the same mesh and polynomial degree of the approximation) in comparison to the well-established finite element methods for diffusion... equations , J. Comput. Phys., 228 (2009), pp. 8841–8855. [4] N.-C. NGUYEN, J. PERAIRE, AND B. COCKBURN, A comparison of HDG methods for Stokes flow, J.

16. Error Analysis for Discontinuous Galerkin Method for Parabolic Problems

Science.gov (United States)

Kaneko, Hideaki

2004-01-01

In the proposal, the following three objectives are stated: (1) A p-version of the discontinuous Galerkin method for a one dimensional parabolic problem will be established. It should be recalled that the h-version in space was used for the discontinuous Galerkin method. An a priori error estimate as well as a posteriori estimate of this p-finite element discontinuous Galerkin method will be given. (2) The parameter alpha that describes the behavior double vertical line u(sub t)(t) double vertical line 2 was computed exactly. This was made feasible because of the explicitly specified initial condition. For practical heat transfer problems, the initial condition may have to be approximated. Also, if the parabolic problem is proposed on a multi-dimensional region, the parameter alpha, for most cases, would be difficult to compute exactly even in the case that the initial condition is known exactly. The second objective of this proposed research is to establish a method to estimate this parameter. This will be done by computing two discontinuous Galerkin approximate solutions at two different time steps starting from the initial time and use them to derive alpha. (3) The third objective is to consider the heat transfer problem over a two dimensional thin plate. The technique developed by Vogelius and Babuska will be used to establish a discontinuous Galerkin method in which the p-element will be used for through thickness approximation. This h-p finite element approach, that results in a dimensional reduction method, was used for elliptic problems, but the application appears new for the parabolic problem. The dimension reduction method will be discussed together with the time discretization method.

17. On cell entropy inequality for discontinuous Galerkin methods

Science.gov (United States)

Jiang, Guangshan; Shu, Chi-Wang

1993-01-01

We prove a cell entropy inequality for a class of high order discontinuous Galerkin finite element methods approximating conservation laws, which implies convergence for the one dimensional scalar convex case.

18. A coupled electro-thermal Discontinuous Galerkin method

Science.gov (United States)

Homsi, L.; Geuzaine, C.; Noels, L.

2017-11-01

This paper presents a Discontinuous Galerkin scheme in order to solve the nonlinear elliptic partial differential equations of coupled electro-thermal problems. In this paper we discuss the fundamental equations for the transport of electricity and heat, in terms of macroscopic variables such as temperature and electric potential. A fully coupled nonlinear weak formulation for electro-thermal problems is developed based on continuum mechanics equations expressed in terms of energetically conjugated pair of fluxes and fields gradients. The weak form can thus be formulated as a Discontinuous Galerkin method. The existence and uniqueness of the weak form solution are proved. The numerical properties of the nonlinear elliptic problems i.e., consistency and stability, are demonstrated under specific conditions, i.e. use of high enough stabilization parameter and at least quadratic polynomial approximations. Moreover the prior error estimates in the H1-norm and in the L2-norm are shown to be optimal in the mesh size with the polynomial approximation degree.

19. Discontinuous Galerkin flood model formulation: Luxury or necessity?

Science.gov (United States)

Kesserwani, Georges; Wang, Yueling

2014-08-01

The finite volume Godunov-type flood model formulation is the most comprehensive amongst those currently employed for flood risk modeling. The local Discontinuous Galerkin method constitutes a more complex, rigorous, and extended local Godunov-type formulation. However, the practical merit associated with such an increase in the level of complexity of the formulation is yet to be decided. This work makes the case for a second-order Runge-Kutta Discontinuous Galerkin (RKDG2) formulation and contrasts it with the equivalently accurate finite volume (MUSCL) formulation, both of which solve the Shallow Water Equations (SWE) in two space dimensions. The numerical complexity of both formulations are presented and their capabilities are explored for wide-ranging diagnostic and real-scale tests, incorporating all challenging features relevant to flood inundation modeling. Our findings reveal that the extra complexity associated with the RKDG2 model pays off by providing higher-quality solution behavior on very coarse meshes and improved velocity predictions. The practical implication of this is that improved accuracy for flood modeling simulations will result when terrain data are limited or of a low resolution.

20. A discontinuous Galerkin method for solving transient Maxwell equations with nonlinear material properties

KAUST Repository

Sirenko, Kostyantyn

2014-07-01

Discontinuous Galerkin time-domain method (DGTD) has been used extensively in computational electromagnetics for analyzing transient electromagnetic wave interactions on structures described with linear constitutive relations. DGTD expands unknown fields independently on disconnected mesh elements and uses numerical flux to realize information exchange between fields on different elements (J. S. Hesthaven and T. Warburton, Nodal Discontinuous Galerkin Method, 2008). The numerical flux of choice for \\'linear\\' Maxwell equations is the upwind flux, which mimics accurately the physical behavior of electromagnetic waves on discontinuous boundaries. It is obtained from the analytical solution of the Riemann problem defined on the boundary of two neighboring mesh elements.

1. A Parallel Reconstructed Discontinuous Galerkin Method for the Compressible Flows on Aritrary Grids

Energy Technology Data Exchange (ETDEWEB)

Hong Luo; Amjad Ali; Robert Nourgaliev; Vincent A. Mousseau

2010-01-01

A reconstruction-based discontinuous Galerkin method is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. In this method, an in-cell reconstruction is used to obtain a higher-order polynomial representation of the underlying discontinuous Galerkin polynomial solution and an inter-cell reconstruction is used to obtain a continuous polynomial solution on the union of two neighboring, interface-sharing cells. The in-cell reconstruction is designed to enhance the accuracy of the discontinuous Galerkin method by increasing the order of the underlying polynomial solution. The inter-cell reconstruction is devised to remove an interface discontinuity of the solution and its derivatives and thus to provide a simple, accurate, consistent, and robust approximation to the viscous and heat fluxes in the Navier-Stokes equations. A parallel strategy is also devised for the resulting reconstruction discontinuous Galerkin method, which is based on domain partitioning and Single Program Multiple Data (SPMD) parallel programming model. The RDG method is used to compute a variety of compressible flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results demonstrate that this RDG method is third-order accurate at a cost slightly higher than its underlying second-order DG method, at the same time providing a better performance than the third order DG method, in terms of both computing costs and storage requirements.

2. Analysis of Adaptive Mesh Refinement for IMEX Discontinuous Galerkin Solutions of the Compressible Euler Equations with Application to Atmospheric Simulations

Science.gov (United States)

2013-01-01

parent side of the face 1∫ −1 ( qR(ξ)− q̃R(ξ) ) ψi(ξ)dξ = 0, (31) where qR is the continuous projection of the variables qR1 and qR2 from children sides...to a parent side, and q̃R(ξ) =  q R1(z(1)) = qR1 ( ξ−o(1) s ) for − 1 ≤ ξ ≤ 0−, qR2(z(2)) = qR2 ( ξ−o(2) s ) for 0+ ≤ ξ ≤ 1. (32) Note that q̃R(ξ...allows for a discontinuity at ξ = 0. Substituting (32) into (31) yields 0∫ −1 ( qR(ξ)− qR1 ( ξ − o(1) s )) ψi(ξ)dξ + 1∫ 0 ( qR(ξ)− qR2 ( ξ − o(2) s

3. 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

4. Local discontinuous Galerkin methods for phase transition problems

NARCIS (Netherlands)

Tian, Lulu

2015-01-01

In this thesis we develop a local discontinuous Galerkin (LDG) finite element method to solve mathematical models for phase transitions in solids and fluids. The first model we study is called a viscosity-capillarity (VC) system associated with phase transitions in elastic bars and Van der Waals

5. An implicit discontinuous Galerkin finite element model for water waves

NARCIS (Netherlands)

van der Vegt, Jacobus J.W.; Tomar, S.K.; Yao, Z.H.; Yuan, M.W.; Zhong, W.X.

2004-01-01

An overview is given of a discontinuous Galerkin finite element method for linear free surface water waves. The method uses an implicit time integration method which is unconditionally stable and does not suffer from the frequently encountered mesh dependent saw-tooth type instability at the free

6. An implicit discontinuous Galerkin finite element model for water waves

NARCIS (Netherlands)

van der Vegt, Jacobus J.W.; Ambati, V.R.; Bokhove, Onno

2005-01-01

We discuss a new higher order accurate discontinuous Galerkin finite element method for non-linear free surface gravity waves. The algorithm is based on an arbitrary Lagrangian Eulerian description of the flow field using deforming elements and a moving mesh, which makes it possible to represent

7. Space-time discontinuous Galerkin finite element methods

NARCIS (Netherlands)

van der Vegt, Jacobus J.W.; Deconinck, H.; Ricchiuto, M.

2006-01-01

In these notes an introduction is given to space-time discontinuous Galerkin (DG) finite element methods for hyperbolic and parabolic conservation laws on time dependent domains. the space-time DG discretization is explained in detail, including the definition of the numerical fluxes and

8. Space-time discontinuous Galerkin method for compressible flow

NARCIS (Netherlands)

Klaij, C.M.

2006-01-01

The space-time discontinuous Galerkin method allows the simulation of compressible flow in complex aerodynamical applications requiring moving, deforming and locally refined meshes. This thesis contains the space-time discretization of the physical model, a fully explicit solver for the resulting

9. Space-time discontinuous Galerkin method for parabolic problems in time-dependent domains

NARCIS (Netherlands)

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

2004-01-01

In this report a space-time discontinuous Galerkin (DG) finite element method for the solution of the advection-diffusion-reaction equation in time-dependent domains is presented and analyzed. The variational formulation is based on a combination of the space-time DG method developed by van der Vegt

10. Space-time discontinuous Galerkin finite element method for inviscid gas dynamics

NARCIS (Netherlands)

van der Ven, H.; van der Vegt, Jacobus J.W.; Bouwman, E.G.; Bathe, K.J.

2003-01-01

In this paper an overview is given of the space-time discontinuous Galerkin finite element method for the solution of the Euler equations of gas dynamics. This technique is well suited for problems which require moving meshes to deal with changes in the domain boundary. The method is demonstrated

11. A Discontinuous Galerkin Model for Fluorescence Loss in Photobleaching

DEFF Research Database (Denmark)

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

2018-01-01

Galerkin method, the computational complexity is drastically reduced compared to continuous Galerkin methods. Using this approach on green uorescent protein (GFP), we can determine its intracellular di usion constant, the strength of localized hindrance to di usion as well as the permeability......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...

12. 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...

13. 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...

14. An asynchronous spacetime discontinuous Galerkin finite element method for time domain electromagnetics

Science.gov (United States)

Abedi, Reza; Mudaliar, Saba

2017-12-01

We present an asynchronous spacetime discontinuous Galerkin (aSDG) method for time domain electromagnetics in which space and time are directly discretized. By using differential forms we express Maxwell's equations and consequently their discontinuous Galerkin discretization for arbitrary domains in spacetime. The elements are discretized with electric and magnetic basis functions that are discontinuous across all inter-element boundaries and can have arbitrary high and per element spacetime orders. When restricted to unstructured grids that satisfy a specific causality constraint, the method has a local and asynchronous solution procedure with linear solution complexity in terms of the number of elements. We numerically investigate the convergence properties of the method for 1D to 3D uniform grids for energy dissipation, an error relative to the exact solution, and von Neumann dissipation and dispersion errors. Two dimensional simulations demonstrate the effectiveness of the method in resolving sharp wave fronts.

15. 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 $20K. Current cycle-accurate simulations for discretizations of the 3-D compressible flow equations yield approximately 40-50% of the peak performance of the Merrimac streaming processor chip. Ongoing work includes the assessment of the performance of the same algorithm on the 2 Teraflop desktop board with a target goal of achieving 1 Teraflop performance. 16. Stability Analysis of Discontinuous Galerkin Approximations to the Elastodynamics Problem KAUST Repository Antonietti, Paola F. 2015-11-21 We consider semi-discrete discontinuous Galerkin approximations of both displacement and displacement-stress formulations of the elastodynamics problem. We prove the stability analysis in the natural energy norm and derive optimal a-priori error estimates. For the displacement-stress formulation, schemes preserving the total energy of the system are introduced and discussed. We verify our theoretical estimates on two and three dimensions test problems. 17. A discontinuous Galerkin method on kinetic flocking models OpenAIRE Tan, Changhui 2014-01-01 We study kinetic representations of flocking models. They arise from agent-based models for self-organized dynamics, such as Cucker-Smale and Motsch-Tadmor models. We prove flocking behavior for the kinetic descriptions of flocking systems, which indicates a concentration in velocity variable in infinite time. We propose a discontinuous Galerkin method to treat the asymptotic$\\delta$-singularity, and construct high order positive preserving scheme to solve kinetic flocking systems. 18. Very high order discontinuous Galerkin method in elliptic problems Science.gov (United States) Jaśkowiec, Jan 2017-09-01 The paper deals with high-order discontinuous Galerkin (DG) method with the approximation order that exceeds 20 and reaches 100 and even 1000 with respect to one-dimensional case. To achieve such a high order solution, the DG method with finite difference method has to be applied. The basis functions of this method are high-order orthogonal Legendre or Chebyshev polynomials. These polynomials are defined in one-dimensional space (1D), but they can be easily adapted to two-dimensional space (2D) by cross products. There are no nodes in the elements and the degrees of freedom are coefficients of linear combination of basis functions. In this sort of analysis the reference elements are needed, so the transformations of the reference element into the real one are needed as well as the transformations connected with the mesh skeleton. Due to orthogonality of the basis functions, the obtained matrices are sparse even for finite elements with more than thousands degrees of freedom. In consequence, the truncation errors are limited and very high-order analysis can be performed. The paper is illustrated with a set of benchmark examples of 1D and 2D for the elliptic problems. The example presents the great effectiveness of the method that can shorten the length of calculation over hundreds times. 19. Numerical Analysis of the Electro-Magnetic Perfectly Matched Layer in a Discontinuous Galerkin Discretization OpenAIRE Schulz, Andreas 2015-01-01 This work is devoted to the numerical analysis of time-domain linear Maxwell's equations in a discontinuous Galerkin discretization. We focus on Berenger's perfectly matched layer and have a detailed look at construction, well-posedness, and semi-discrete error analysis. We present an analytic solution to the system, that can be utilized to efficiently determine optimal parameter values for the layer and state a way to avoid an exponential growth in time of the semi-discrete error bound. 20. 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. 1. A discontinuous Galerkin method for two-dimensional PDE models of Asian options Science.gov (United States) Hozman, J.; Tichý, T.; Cvejnová, D. 2016-06-01 In our previous research we have focused on the problem of plain vanilla option valuation using discontinuous Galerkin method for numerical PDE solution. Here we extend a simple one-dimensional problem into two-dimensional one and design a scheme for valuation of Asian options, i.e. options with payoff depending on the average of prices collected over prespecified horizon. The algorithm is based on the approach combining the advantages of the finite element methods together with the piecewise polynomial generally discontinuous approximations. Finally, an illustrative example using DAX option market data is provided. 2. 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 ... 3. Discontinuous Galerkin finite element method for shallow two-phase flows NARCIS (Netherlands) Rhebergen, Sander; Bokhove, Onno; van der Vegt, Jacobus J.W. We present a discontinuous Galerkin finite element method for two depth-averaged two-phase flow models. One of these models contains nonconservative products for which we developed a discontinuous Galerkin finite element formulation in Rhebergen et al. (2008) J. Comput. Phys. 227, 1887-1922. The 4. Simplified Discontinuous Galerkin Methods for Systems of Conservation Laws with Convex Extension Science.gov (United States) Barth, Timothy J. 1999-01-01 Simplified forms of the space-time discontinuous Galerkin (DG) and discontinuous Galerkin least-squares (DGLS) finite element method are developed and analyzed. The new formulations exploit simplifying properties of entropy endowed conservation law systems while retaining the favorable energy properties associated with symmetric variable formulations. 5. 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 6. SpECTRE: A task-based discontinuous Galerkin code for relativistic astrophysics Science.gov (United States) Kidder, Lawrence E.; Field, Scott E.; Foucart, Francois; Schnetter, Erik; Teukolsky, Saul A.; Bohn, Andy; Deppe, Nils; Diener, Peter; Hébert, François; Lippuner, Jonas; Miller, Jonah; Ott, Christian D.; Scheel, Mark A.; Vincent, Trevor 2017-04-01 We introduce a new relativistic astrophysics code, SpECTRE, that combines a discontinuous Galerkin method with a task-based parallelism model. SpECTRE's goal is to achieve more accurate solutions for challenging relativistic astrophysics problems such as core-collapse supernovae and binary neutron star mergers. The robustness of the discontinuous Galerkin method allows for the use of high-resolution shock capturing methods in regions where (relativistic) shocks are found, while exploiting high-order accuracy in smooth regions. A task-based parallelism model allows efficient use of the largest supercomputers for problems with a heterogeneous workload over disparate spatial and temporal scales. We argue that the locality and algorithmic structure of discontinuous Galerkin methods will exhibit good scalability within a task-based parallelism framework. We demonstrate the code on a wide variety of challenging benchmark problems in (non)-relativistic (magneto)-hydrodynamics. We demonstrate the code's scalability including its strong scaling on the NCSA Blue Waters supercomputer up to the machine's full capacity of 22 , 380 nodes using 671 , 400 threads. 7. Discontinuous Galerkin Methods for NonLinear Differential Systems Science.gov (United States) Barth, Timothy; Mansour, Nagi (Technical Monitor) 2001-01-01 This talk considers simplified finite element discretization techniques for first-order systems of conservation laws equipped with a convex (entropy) extension. Using newly developed techniques in entropy symmetrization theory, simplified forms of the discontinuous Galerkin (DG) finite element method have been developed and analyzed. The use of symmetrization variables yields numerical schemes which inherit global entropy stability properties of the PDE (partial differential equation) system. Central to the development of the simplified DG methods is the Eigenvalue Scaling Theorem which characterizes right symmetrizers of an arbitrary first-order hyperbolic system in terms of scaled eigenvectors of the corresponding flux Jacobian matrices. A constructive proof is provided for the Eigenvalue Scaling Theorem with detailed consideration given to the Euler equations of gas dynamics and extended conservation law systems derivable as moments of the Boltzmann equation. Using results from kinetic Boltzmann moment closure theory, we then derive and prove energy stability for several approximate DG fluxes which have practical and theoretical merit. 8. 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. 9. 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. 10. 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. 11. 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. 12. A Reconstructed Discontinuous Galerkin Method for the Compressible Euler Equations on Arbitrary Grids Energy Technology Data Exchange (ETDEWEB) Hong Luo; Luquing Luo; Robert Nourgaliev; Vincent Mousseau 2009-06-01 A reconstruction-based discontinuous Galerkin (DG) method is presented for the solution of the compressible Euler equations on arbitrary grids. By taking advantage of handily available and yet invaluable information, namely the derivatives, in the context of the discontinuous Galerkin methods, a solution polynomial of one degree higher is reconstructed using a least-squares method. The stencils used in the reconstruction involve only the van Neumann neighborhood (face-neighboring cells) and are compact and consistent with the underlying DG method. The resulting DG method can be regarded as an improvement of a recovery-based DG method in the sense that it shares the same nice features as the recovery-based DG method, such as high accuracy and efficiency, and yet overcomes some of its shortcomings such as a lack of flexibility, compactness, and robustness. The developed DG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate the accuracy and efficiency of the method. The numerical results indicate that this reconstructed DG method is able to obtain a third-order accurate solution at a slightly higher cost than its second-order DG method and provide an increase in performance over the third order DG method in terms of computing time and storage requirement. 13. Regional wave propagation using the discontinuous Galerkin method Directory of Open Access Journals (Sweden) S. Wenk 2013-01-01 Full Text Available We present an application of the discontinuous Galerkin (DG method to regional wave propagation. The method makes use of unstructured tetrahedral meshes, combined with a time integration scheme solving the arbitrary high-order derivative (ADER Riemann problem. This ADER-DG method is high-order accurate in space and time, beneficial for reliable simulations of high-frequency wavefields over long propagation distances. Due to the ease with which tetrahedral grids can be adapted to complex geometries, undulating topography of the Earth's surface and interior interfaces can be readily implemented in the computational domain. The ADER-DG method is benchmarked for the accurate radiation of elastic waves excited by an explosive and a shear dislocation source. We compare real data measurements with synthetics of the 2009 L'Aquila event (central Italy. We take advantage of the geometrical flexibility of the approach to generate a European model composed of the 3-D EPcrust model, combined with the depth-dependent ak135 velocity model in the upper mantle. The results confirm the applicability of the ADER-DG method for regional scale earthquake simulations, which provides an alternative to existing methodologies. 14. EXPLICIT LEAST-DEGREE BOUNDARY FILTERS FOR DISCONTINUOUS GALERKIN* Science.gov (United States) Nguyen, Dang-Manh; Peters, Jörg 2017-01-01 Convolving the output of Discontinuous Galerkin (DG) computations using spline filters can improve both smoothness and accuracy of the output. At domain boundaries, these filters have to be one-sided for non-periodic boundary conditions. Recently, position-dependent smoothness-increasing accuracy-preserving (PSIAC) filters were shown to be a superset of the well-known one-sided RLKV and SRV filters. Since PSIAC filters can be formulated symbolically, PSIAC filtering amounts to forming linear products with local DG output and so offers a more stable and efficient implementation. The paper introduces a new class of PSIAC filters NP0 that have small support and are piecewise constant. Extensive numerical experiments for the canonical hyperbolic test equation show NP0 filters outperform the more complex known boundary filters. NP0 filters typically reduce the L∞ error in the boundary region below that of the interior where optimally superconvergent symmetric filters of the same support are applied. NP0 filtering can be implemented as forming linear combinations of the data with short rational weights. Exact derivatives of the convolved output are easy to compute. PMID:29081643 15. A discontinuous Galerkin method for studying elasticity and variable viscosity Stokes problems Science.gov (United States) Schnepp, Sascha M.; Charrier, Dominic; May, Dave 2015-04-01 Traditionally in the geodynamics community, staggered grid finite difference schemes and mixed Finite Elements (FE) have been utilised to discretise the variable viscosity (VV) Stokes problem. These methods have been demonstrated to be sufficiently robust and accurate for a wide range of variable viscosity problems involving both smooth viscosity structures possessing large spatial variations, and for discontinuous viscosity structures. One caveat of the aforementioned discretisations is that they tend to have inf-sup constants which are highly dependent on the cell aspect ratio. Whilst high order mixed FE approaches utilising spaces defined via Qk - Qk-2, k ≥ 3, alleviate this shortcoming, such elements are seldomly used as they are computationally expensive, the definition of multi-level preconditioners is complex, and spectral accuracy is often not obtained. Discontinuous Galerkin (DG) methods offer the advantage that spaces can be constructed which have both low order in velocity and pressure and inf-sup constants which are not sensitive to the element aspect ratio. To date, DG discretisations have not been extensively used within geodynamic applications associated with VV Stokes formulations. Here we rigorously evaluate the applicability of two Interior Penalty Discontinuous Galerkin methods, namely the Nonsymmetric and Symmetric Interior Penalty Galerkin methods (NIPG and SIPG) for compressible elasticity and incompressible, variable viscosity Stokes problems. Through a suite of numerical experiments, our evaluation considers the stability, order of accuracy and robustness of the NIPG and SIPG discretisations for cases with both smooth and discontinuous coefficients. Using manufactured solutions, we confirm that both DG formulations are stable and result in convergent solutions for displacement based elasticity formulations, even in the limit of Poisson ratio approaching 0.5. With regards to incompressible flow simulations, using the analytic solution Sol 16. Convergence of Discontinuous Galerkin Methods for Incompressible Two-Phase Flow in Heterogeneous Media KAUST Repository Kou, Jisheng 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. 17. Application of discontinuous Galerkin method for solving a compressible five-equation two-phase flow model Directory of Open Access Journals (Sweden) M. Rehan Saleem 2018-03-01 Full Text Available 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. Keywords: Two-phase compressible flows, Non-conservative system, Shock discontinuities, Discontinuous Galerkin method, Central scheme 18. 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. 19. 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. 20. 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. 1. A Level Set Discontinuous Galerkin Method for Free Surface Flows - and Water-Wave Modeling DEFF Research Database (Denmark) Grooss, Jesper 2005-01-01 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 a level set technique. We describe the discontinuous Galerkin method in general, and its application to the flow equations...... equations in time are discussed. We investigate theory of di erential algebraic equations, and connect the theory to current methods for solving the unsteady fluid flow equations. We explore the use of a semi-implicit spectral deferred correction method having potential to achieve high temporal order....... The deferred correction method is applied on the fluid flow equations and show good results in periodic domains. We describe the design of a level set method for the free surface modeling. The level set utilize the high order accurate discontinuous Galerkin method fully and represent smooth surfaces very... 2. 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. 3. Shock capturing in discontinuous Galerkin spectral elements via the entropy viscosity method Science.gov (United States) Hackl, Jason; Shringarpure, Mrugesh; Fischer, Paul; Balachandar, Sivaramakrishnan 2017-11-01 We present a 3D discontinuous Galerkin spectral element solver for compressible flows with shock waves using artificial viscosity to regularize the solution for representation by nested tensor products of high-order Lagrange polynomials. The viscosity is constructed from a smoothed evaluation of the residual of an entropy inequality, localizing the artificial viscosity around shock waves and other flow features that would otherwise not be representable in spectral elements without thermodynamic violations due to Gibbs oscillations. Applied to the Guermond-Popov (2014) stress tensor, this smoothed, continuous artificial viscosity is easily integrated with the non-symmetric numerical fluxes of Baumann and Oden (1999). The method is implemented on top of nek5000, leveraging an outstanding high-performance spectral element code to solve shocked flows over curved surfaces. The interaction of a Mach 3 shock with a sphere is shown to demonstrate this capability. Supported by the Department of Energy Predictive Science Academic Alliance Program Contract DE-NA0002378. 4. 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... 5. Asymptotic Analysis of Upwind Discontinuous Galerkin Approximation of the Radiative Transport Equation in the Diffusive Limit KAUST Repository Guermond, Jean-Luc 2010-01-01 We revisit some results from M. L. Adams [Nu cl. Sci. Engrg., 137 (2001), pp. 298- 333]. Using functional analytic tools we prove that a necessary and sufficient condition for the standard upwind discontinuous Galerkin approximation to converge to the correct limit solution in the diffusive regime is that the approximation space contains a linear space of continuous functions, and the restrictions of the functions of this space to each mesh cell contain the linear polynomials. Furthermore, the discrete diffusion limit converges in the Sobolev space H1 to the continuous one if the boundary data is isotropic. With anisotropic boundary data, a boundary layer occurs, and convergence holds in the broken Sobolev space H with s < 1/2 only © 2010 Society for Industrial and Applied Mathematics. 6. 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. 7. 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 8. A Reconstructed Discontinuous Galerkin Method for the Compressible Navier-Stokes Equations on Arbitrary Grids Energy Technology Data Exchange (ETDEWEB) Hong Luo; Luqing Luo; Robert Nourgaliev; Vincent A. Mousseau 2010-01-01 A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier-Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need to judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on arbitrary grids. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG method is able to deliver the same accuracy as the well-known Bassi-Rebay II scheme, at a half of its computing costs for the discretization of the viscous fluxes in the Navier-Stokes equations, clearly demonstrating its superior performance over the existing DG methods for solving the compressible Navier-Stokes equations. 9. Discontinuous Galerkin finite element methods for (non)conservative partial differential equations NARCIS (Netherlands) Rhebergen, Sander 2010-01-01 The first research topic in this thesis is the development of discontinuous Galerkin (DG) finite element methods for partial differential equations containing nonconservative products, which are present in many two-phase flow models. For this, we combine the theory of Dal Maso, LeFloch and Murat, in 10. Two fluid space-time discontinuous Galerkin finite element method. Part II: Applications NARCIS (Netherlands) Sollie, W.E.H.; van der Vegt, Jacobus J.W. 2009-01-01 The numerical method for two fluid flow computations presented in Sollie, Bokhove \\& van der Vegt, Two Fluid Space-Time Discontinuous Galerkin Finite Element Method. Part I: Numerical Algorithm is applied to a number of one and two dimensional single and two fluid test problems, including a magma - 11. 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 12. Fully Discrete Local Discontinuous Galerkin Approximation for Time-Space Fractional Subdiffusion/Superdiffusion Equations Directory of Open Access Journals (Sweden) Meilan Qiu 2017-01-01 Full Text Available We focus on developing the finite difference (i.e., backward Euler difference or second-order central difference/local discontinuous Galerkin finite element mixed method to construct and analyze a kind of efficient, accurate, flexible, numerical schemes for approximately solving time-space fractional subdiffusion/superdiffusion equations. Discretizing the time Caputo fractional derivative by using the backward Euler difference for the derivative parameter (0<α<1 or second-order central difference method for (1<α<2, combined with local discontinuous Galerkin method to approximate the spatial derivative which is defined by a fractional Laplacian operator, two high-accuracy fully discrete local discontinuous Galerkin (LDG schemes of the time-space fractional subdiffusion/superdiffusion equations are proposed, respectively. Through the mathematical induction method, we show the concrete analysis for the stability and the convergence under the L2 norm of the LDG schemes. Several numerical experiments are presented to validate the proposed model and demonstrate the convergence rate of numerical schemes. The numerical experiment results show that the fully discrete local discontinuous Galerkin (LDG methods are efficient and powerful for solving fractional partial differential equations. 13. Sequential limiting in continuous and discontinuous Galerkin methods for the Euler equations Science.gov (United States) Dobrev, V.; Kolev, Tz.; Kuzmin, D.; Rieben, R.; Tomov, V. 2018-03-01 We present a new predictor-corrector approach to enforcing local maximum principles in piecewise-linear finite element schemes for the compressible Euler equations. The new element-based limiting strategy is suitable for continuous and discontinuous Galerkin methods alike. In contrast to synchronized limiting techniques for systems of conservation laws, we constrain the density, momentum, and total energy in a sequential manner which guarantees positivity preservation for the pressure and internal energy. After the density limiting step, the total energy and momentum gradients are adjusted to incorporate the irreversible effect of density changes. Antidiffusive corrections to bounds-compatible low-order approximations are limited to satisfy inequality constraints for the specific total and kinetic energy. An accuracy-preserving smoothness indicator is introduced to gradually adjust lower bounds for the element-based correction factors. The employed smoothness criterion is based on a Hessian determinant test for the density. A numerical study is performed for test problems with smooth and discontinuous solutions. 14. A parallel code base on discontinuous Galerkin method on three dimensional unstructured meshes for MHD equations Science.gov (United States) Li, Xujing; Zheng, Weiying 2016-10-01 A new parallel code based on discontinuous Galerkin (DG) method for hyperbolic conservation laws on three dimensional unstructured meshes is developed recently. This code can be used for simulations of MHD equations, which are very important in magnetic confined plasma research. The main challenges in MHD simulations in fusion include the complex geometry of the configurations, such as plasma in tokamaks, the possibly discontinuous solutions and large scale computing. Our new developed code is based on three dimensional unstructured meshes, i.e. tetrahedron. This makes the code flexible to arbitrary geometries. Second order polynomials are used on each element and HWENO type limiter are applied. The accuracy tests show that our scheme reaches the desired three order accuracy and the nonlinear shock test demonstrate that our code can capture the sharp shock transitions. Moreover, One of the advantages of DG compared with the classical finite element methods is that the matrices solved are localized on each element, making it easy for parallelization. Several simulations including the kink instabilities in toroidal geometry will be present here. Chinese National Magnetic Confinement Fusion Science Program 2015GB110003. 15. A Flexible Galerkin Finite Element Method with an A Posteriori Discontinuous Finite Element Error Estimation for Hyperbolic Problems OpenAIRE Massey, Thomas Christopher 2002-01-01 A Flexible Galerkin Finite Element Method (FGM) is a hybrid class of finite element methods that combine the usual continuous Galerkin method with the now popular discontinuous Galerkin method (DGM). A detailed description of the formulation of the FGM on a hyperbolic partial differential equation, as well as the data structures used in the FGM algorithm is presented. Some hp-convergence results and computational cost are included. Additionally, an a posteriori error estimate f... 16. 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. 17. 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. 18. Discontinuous Galerkin methods for plasma physics in the scrape-off layer of tokamaks Energy Technology Data Exchange (ETDEWEB) Michoski, C., E-mail: michoski@ices.utexas.edu [Institute for Computational Engineering and Sciences (ICES), Department of Aerospace Engineering and Engineering Mechanics, University of Texas at Austin, Austin, TX 78712 (United States); Meyerson, D. [Institute for Fusion Studies (IFS), Department of Physics, University of Texas at Austin, Austin, TX 78712 (United States); Isaac, T. [Institute for Computational Engineering and Sciences (ICES), University of Texas at Austin, Austin, TX 78712 (United States); Waelbroeck, F. [Institute for Fusion Studies (IFS), Department of Physics, University of Texas at Austin, Austin, TX 78712 (United States) 2014-10-01 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. 19. Robust and Accurate Shock Capturing Method for High-Order Discontinuous Galerkin Methods Science.gov (United States) Atkins, Harold L.; Pampell, Alyssa 2011-01-01 A simple yet robust and accurate approach for capturing shock waves using a high-order discontinuous Galerkin (DG) method is presented. The method uses the physical viscous terms of the Navier-Stokes equations as suggested by others; however, the proposed formulation of the numerical viscosity is continuous and compact by construction, and does not require the solution of an auxiliary diffusion equation. This work also presents two analyses that guided the formulation of the numerical viscosity and certain aspects of the DG implementation. A local eigenvalue analysis of the DG discretization applied to a shock containing element is used to evaluate the robustness of several Riemann flux functions, and to evaluate algorithm choices that exist within the underlying DG discretization. A second analysis examines exact solutions to the DG discretization in a shock containing element, and identifies a "model" instability that will inevitably arise when solving the Euler equations using the DG method. This analysis identifies the minimum viscosity required for stability. The shock capturing method is demonstrated for high-speed flow over an inviscid cylinder and for an unsteady disturbance in a hypersonic boundary layer. Numerical tests are presented that evaluate several aspects of the shock detection terms. The sensitivity of the results to model parameters is examined with grid and order refinement studies. 20. 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. 1. 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. 2. Finite element, discontinuous Galerkin, and finite difference evolution schemes in spacetime International Nuclear Information System (INIS) Zumbusch, G 2009-01-01 Numerical schemes for Einstein's vacuum equation are developed. Einstein's equation in harmonic gauge is second-order symmetric hyperbolic. It is discretized in four-dimensional spacetime by finite differences, finite elements and interior penalty discontinuous Galerkin methods, the latter being related to Regge calculus. The schemes are split into space and time and new time-stepping schemes for wave equations are derived. The methods are evaluated for linear and nonlinear test problems of the Apples-with-Apples collection. 3. 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. 4. A Leap-Frog Discontinuous Galerkin Method for the Time-Domain Maxwell's Equations in Metamaterials Energy Technology Data Exchange (ETDEWEB) Li, J., Waters, J. W., Machorro, E. A. 2012-06-01 Numerical simulation of metamaterials play a very important role in the design of invisibility cloak, and sub-wavelength imaging. In this paper, we propose a leap-frog discontinuous Galerkin method to solve the time-dependent Maxwell’s equations in metamaterials. Conditional stability and error estimates are proved for the scheme. The proposed algorithm is implemented and numerical results supporting the analysis are provided. 5. A spectral-element discontinuous Galerkin lattice Boltzmann method for nearly incompressible flows Science.gov (United States) Min, Misun; Lee, Taehun 2011-01-01 We present a spectral-element discontinuous Galerkin lattice Boltzmann method for solving nearly incompressible flows. Decoupling the collision step from the streaming step offers numerical stability at high Reynolds numbers. In the streaming step, we employ high-order spectral-element discontinuous Galerkin discretizations using a tensor product basis of one-dimensional Lagrange interpolation polynomials based on Gauss-Lobatto-Legendre grids. Our scheme is cost-effective with a fully diagonal mass matrix, advancing time integration with the fourth-order Runge-Kutta method. We present a consistent treatment for imposing boundary conditions with a numerical flux in the discontinuous Galerkin approach. We show convergence studies for Couette flows and demonstrate two benchmark cases with lid-driven cavity flows for Re = 400-5000 and flows around an impulsively started cylinder for Re = 550-9500. Computational results are compared with those of other theoretical and computational work that used a multigrid method, a vortex method, and a spectral element model. 6. 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. 7. 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. 8. A nodal discontinuous Galerkin finite element method for nonlinear elastic wave propagation. Science.gov (United States) Bou Matar, Olivier; Guerder, Pierre-Yves; Li, YiFeng; Vandewoestyne, Bart; Van Den Abeele, Koen 2012-05-01 A nodal discontinuous Galerkin finite element method (DG-FEM) to solve the linear and nonlinear elastic wave equation in heterogeneous media with arbitrary high order accuracy in space on unstructured triangular or quadrilateral meshes is presented. This DG-FEM method combines the geometrical flexibility of the finite element method, and the high parallelization potentiality and strongly nonlinear wave phenomena simulation capability of the finite volume method, required for nonlinear elastodynamics simulations. In order to facilitate the implementation based on a numerical scheme developed for electromagnetic applications, the equations of nonlinear elastodynamics have been written in a conservative form. The adopted formalism allows the introduction of different kinds of elastic nonlinearities, such as the classical quadratic and cubic nonlinearities, or the quadratic hysteretic nonlinearities. Absorbing layers perfectly matched to the calculation domain of the nearly perfectly matched layers type have been introduced to simulate, when needed, semi-infinite or infinite media. The developed DG-FEM scheme has been verified by means of a comparison with analytical solutions and numerical results already published in the literature for simple geometrical configurations: Lamb's problem and plane wave nonlinear propagation. 9. 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. 10. On Formulations of Discontinuous Galerkin and Related Methods for Conservation Laws Science.gov (United States) Huynh, H. T. 2014-01-01 A formulation for the discontinuous Galerkin (DG) method that leads to solutions using the differential form of the equation (as opposed to the standard integral form) is presented. The formulation includes (a) a derivative calculation that involves only data within each cell with no data interaction among cells, and (b) for each cell, corrections to this derivative that deal with the jumps in fluxes at the cell boundaries and allow data across cells to interact. The derivative with no interaction is obtained by a projection, but for nodal-type methods, evaluating this derivative by interpolation at the nodal points is more economical. The corrections are derived using the approximate (Dirac) delta functions. The formulation results in a family of schemes: different approximate delta functions give rise to different methods. It is shown that the current formulation is essentially equivalent to the flux reconstruction (FR) formulation. Due to the use of approximate delta functions, an energy stability proof simpler than that of Vincent, Castonguay, and Jameson (2011) for a family of schemes is derived. Accuracy and stability of resulting schemes are discussed via Fourier analyses. Similar to FR, the current formulation provides a unifying framework for high-order methods by recovering the DG, spectral difference (SD), and spectral volume (SV) schemes. It also yields stable, accurate, and economical methods. 11. A hybridizable discontinuous Galerkin method for computing nonlocal electromagnetic effects in three-dimensional metallic nanostructures Science.gov (United States) Vidal-Codina, F.; Nguyen, N. C.; Oh, S.-H.; Peraire, J. 2018-02-01 The interaction of light with metallic nanostructures produces a collective excitation of electrons at the metal surface, also known as surface plasmons. These collective excitations lead to resonances that enable the confinement of light in deep-subwavelength regions, thereby leading to large near-field enhancements. The simulation of plasmon resonances presents notable challenges. From the modeling perspective, the realistic behavior of conduction-band electrons in metallic nanostructures is not captured by Maxwell's equations, thus requiring additional modeling. From the simulation perspective, the disparity in length scales stemming from the extreme field localization demands efficient and accurate numerical methods. In this paper, we develop the hybridizable discontinuous Galerkin (HDG) method to solve Maxwell's equations augmented with the hydrodynamic model for the conduction-band electrons in noble metals. This method enables the efficient simulation of plasmonic nanostructures while accounting for the nonlocal interactions between electrons and the incident light. We introduce a novel postprocessing scheme to recover superconvergent solutions and demonstrate the convergence of the proposed HDG method for the simulation of a 2D gold nanowire and a 3D periodic annular nanogap structure. The results of the hydrodynamic model are compared to those of a simplified local response model, showing that differences between them can be significant at the nanoscale. 12. A Parallel Implicit Reconstructed Discontinuous Galerkin Method for Compressible Flows on Hybrid Grids Science.gov (United States) Xia, Yidong The objective this work is to develop a parallel, implicit reconstructed discontinuous Galerkin (RDG) method using Taylor basis for the solution of the compressible Navier-Stokes equations on 3D hybrid grids. This third-order accurate RDG method is based on a hierarchical weighed essentially non- oscillatory reconstruction scheme, termed as HWENO(P1P 2) to indicate that a quadratic polynomial solution is obtained from the underlying linear polynomial DG solution via a hierarchical WENO reconstruction. The HWENO(P1P2) is designed not only to enhance the accuracy of the underlying DG(P1) method but also to ensure non-linear stability of the RDG method. In this reconstruction scheme, a quadratic polynomial (P2) solution is first reconstructed using a least-squares approach from the underlying linear (P1) discontinuous Galerkin solution. The final quadratic solution is then obtained using a Hermite WENO reconstruction, which is necessary to ensure the linear stability of the RDG method on 3D unstructured grids. The first derivatives of the quadratic polynomial solution are then reconstructed using a WENO reconstruction in order to eliminate spurious oscillations in the vicinity of strong discontinuities, thus ensuring the non-linear stability of the RDG method. The parallelization in the RDG method is based on a message passing interface (MPI) programming paradigm, where the METIS library is used for the partitioning of a mesh into subdomain meshes of approximately the same size. Both multi-stage explicit Runge-Kutta and simple implicit backward Euler methods are implemented for time advancement in the RDG method. In the implicit method, three approaches: analytical differentiation, divided differencing (DD), and automatic differentiation (AD) are developed and implemented to obtain the resulting flux Jacobian matrices. The automatic differentiation is a set of techniques based on the mechanical application of the chain rule to obtain derivatives of a function given as 13. Convergent High-Order Compact WENO Discontinuity Capturing with Positivity Preserving for Unstructured Discontinuous Galerkin Schemes Data.gov (United States) National Aeronautics and Space Administration — Challenges: Our recent investigation revealed that the more advanced discontinuity capturing weighted essentially nonoscillatory (WENO) technique, which is of... 14. An HP Adaptive Discontinuous Galerkin Method for Hyperbolic Conservation Laws. Ph.D. Thesis Science.gov (United States) Bey, Kim S. 1994-01-01 This dissertation addresses various issues for model classes of hyperbolic conservation laws. The basic approach developed in this work employs a new family of adaptive, hp-version, finite element methods based on a special discontinuous Galerkin formulation for hyperbolic problems. The discontinuous Galerkin formulation admits high-order local approximations on domains of quite general geometry, while providing a natural framework for finite element approximations and for theoretical developments. The use of hp-versions of the finite element method makes possible exponentially convergent schemes with very high accuracies in certain cases; the use of adaptive hp-schemes allows h-refinement in regions of low regularity and p-enrichment to deliver high accuracy, while keeping problem sizes manageable and dramatically smaller than many conventional approaches. The use of discontinuous Galerkin methods is uncommon in applications, but the methods rest on a reasonable mathematical basis for low-order cases and has local approximation features that can be exploited to produce very efficient schemes, especially in a parallel, multiprocessor environment. The place of this work is to first and primarily focus on a model class of linear hyperbolic conservation laws for which concrete mathematical results, methodologies, error estimates, convergence criteria, and parallel adaptive strategies can be developed, and to then briefly explore some extensions to more general cases. Next, we provide preliminaries to the study and a review of some aspects of the theory of hyperbolic conservation laws. We also provide a review of relevant literature on this subject and on the numerical analysis of these types of problems. 15. Numerical modelling of MPA-CVD reactors with the discontinuous Galerkin finite element method Science.gov (United States) Houston, Paul; Sime, Nathan 2017-07-01 In this article we develop a fully self consistent mathematical model describing the formation of a hydrogen plasma in a microwave power assisted chemical vapour deposition (MPA-CVD) reactor employed for the manufacture of synthetic diamond. The underlying multi-physics model includes constituent equations for the background gas mass average velocity, gas temperature, electromagnetic field energy and plasma density. The proposed mathematical model is numerically approximated based on exploiting the discontinuous Galerkin finite element method. We demonstrate the practical performance of this computational approach on a variety of CVD reactor geometries for a range of operating conditions. 16. 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. 17. Energy Stable Flux Formulas For The Discontinuous Galerkin Discretization Of First Order Nonlinear Conservation Laws Science.gov (United States) Barth, Timothy; Charrier, Pierre; Mansour, Nagi N. (Technical Monitor) 2001-01-01 We consider the discontinuous Galerkin (DG) finite element discretization of first order systems of conservation laws derivable as moments of the kinetic Boltzmann equation. This includes well known conservation law systems such as the Euler For the class of first order nonlinear conservation laws equipped with an entropy extension, an energy analysis of the DG method for the Cauchy initial value problem is developed. Using this DG energy analysis, several new variants of existing numerical flux functions are derived and shown to be energy stable. 18. Accurate traveltime computation in complex anisotropic media with discontinuous Galerkin method Science.gov (United States) Le Bouteiller, P.; Benjemaa, M.; Métivier, L.; Virieux, J. 2017-12-01 Travel time computation is of major interest for a large range of geophysical applications, among which source localization and characterization, phase identification, data windowing and tomography, from decametric scale up to global Earth scale.Ray-tracing tools, being essentially 1D Lagrangian integration along a path, have been used for their efficiency but present some drawbacks, such as a rather difficult control of the medium sampling. Moreover, they do not provide answers in shadow zones. Eikonal solvers, based on an Eulerian approach, have attracted attention in seismology with the pioneering work of Vidale (1988), while such approach has been proposed earlier by Riznichenko (1946). They have been used now for first-arrival travel-time tomography at various scales (Podvin & Lecomte (1991). The framework for solving this non-linear partial differential equation is now well understood and various finite-difference approaches have been proposed, essentially for smooth media. We propose a novel finite element approach which builds a precise solution for strongly heterogeneous anisotropic medium (still in the limit of Eikonal validity). The discontinuous Galerkin method we have developed allows local refinement of the mesh and local high orders of interpolation inside elements. High precision of the travel times and its spatial derivatives is obtained through this formulation. This finite element method also honors boundary conditions, such as complex topographies and absorbing boundaries for mimicking an infinite medium. Applications from travel-time tomography, slope tomography are expected, but also for migration and take-off angles estimation, thanks to the accuracy obtained when computing first-arrival times.References:Podvin, P. and Lecomte, I., 1991. Finite difference computation of traveltimes in very contrasted velocity model: a massively parallel approach and its associated tools, Geophys. J. Int., 105, 271-284.Riznichenko, Y., 1946. Geometrical 19. 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 20. 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. 1. A Discontinuous Galerkin Method for Two-Dimensional Shock Wave Modeling Directory of Open Access Journals (Sweden) W. Lai 2011-01-01 Full Text Available A numerical scheme based on discontinuous Galerkin method is proposed for the two-dimensional shallow water flows. The scheme is applied to model flows with shock waves. The form of shallow water equations that can eliminate numerical imbalance between flux term and source term and simplify computation is adopted here. The HLL approximate Riemann solver is employed to calculate the mass and momentum flux. A slope limiting procedure that is suitable for incompressible two-dimensional flows is presented. A simple method is adapted for flow over initially dry bed. A new formulation is introduced for modeling the net pressure force and gravity terms in discontinuous Galerkin method. To validate the scheme, numerical tests are performed to model steady and unsteady shock waves. Applications include circular dam break with shock, shock waves in channel contraction, and dam break in channel with 45∘ bend. Numerical results show that the scheme is accurate and efficient to model two-dimensional shallow water flows with shock waves. 2. Hybridizable discontinuous Galerkin method for the 2-D frequency-domain elastic wave equations Science.gov (United States) Bonnasse-Gahot, Marie; Calandra, Henri; Diaz, Julien; Lanteri, Stéphane 2018-04-01 Discontinuous Galerkin (DG) methods are nowadays actively studied and increasingly exploited for the simulation of large-scale time-domain (i.e. unsteady) seismic wave propagation problems. Although theoretically applicable to frequency-domain problems as well, their use in this context has been hampered by the potentially large number of coupled unknowns they incur, especially in the 3-D case, as compared to classical continuous finite element methods. In this paper, we address this issue in the framework of the so-called hybridizable discontinuous Galerkin (HDG) formulations. As a first step, we study an HDG method for the resolution of the frequency-domain elastic wave equations in the 2-D case. We describe the weak formulation of the method and provide some implementation details. The proposed HDG method is assessed numerically including a comparison with a classical upwind flux-based DG method, showing better overall computational efficiency as a result of the drastic reduction of the number of globally coupled unknowns in the resulting discrete HDG system. 3. 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. 4. Upwind discontinuous Galerkin methods with mass conservation of both phases for incompressible two-phase flow in porous media KAUST Repository Kou, Jisheng 2014-03-22 Discontinuous Galerkin methods with interior penalties and upwind schemes are applied to the original formulation modeling incompressible two-phase flow in porous media with the capillary pressure. The pressure equation is obtained by summing the discretized conservation equations of two phases. This treatment is very different from the conventional approaches, and its great merit is that the mass conservations hold for both phases instead of only one phase in the conventional schemes. By constructing a new continuous map and using the fixed-point theorem, we prove the global existence of discrete solutions under the proper conditions, and furthermore, we obtain a priori hp error estimates of the pressures in L 2 (H 1) and the saturations in L ∞(L 2) and L 2 (H 1). © 2014 Wiley Periodicals, Inc. 5. 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. 6. 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. 7. 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. 8. Existence of solutions to nonlocal and singular elliptic problems via Galerkin method Directory of Open Access Journals (Sweden) Francisco Julio S. A. Correa 2004-02-01 Full Text Available We study the existence of solutions to the nonlocal elliptic equation $$-M(|u|^2Delta u = f(x,u$$ with zero Dirichlet boundary conditions on a bounded and smooth domain of$mathbb{R}^n$. We consider the$M$-linear case with$fin H^{-1}(Omega $, and the sub-linear case$f(u=u^{alpha}$,$0Galerkin method for both cases when $M$ continuous and when $M$ is discontinuous.

9. 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

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

DEFF Research Database (Denmark)

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...

11. Error Analysis of p-Version Discontinuous Galerkin Method for Heat Transfer in Built-up Structures

Science.gov (United States)

Kaneko, Hideaki; Bey, Kim S.

2004-01-01

The purpose of this paper is to provide an error analysis for the p-version of the discontinuous Galerkin finite element method for heat transfer in built-up structures. As a special case of the results in this paper, a theoretical error estimate for the numerical experiments recently conducted by James Tomey is obtained.

12. 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.

13. 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.

14. 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.

15. 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.

16. A discontinuous Galerkin front tracking method for two-phase flows with surface tension

Energy Technology Data Exchange (ETDEWEB)

Nguyen, V.-T.; Peraire, J.; Cheong, K.B.; Persson, P.-O.

2008-12-28

A Discontinuous Galerkin method for solving hyperbolic systems of conservation laws involving interfaces is presented. The interfaces are represented by a collection of element boundaries and their position is updated using an arbitrary Lagrangian-Eulerian method. The motion of the interfaces and the numerical fluxes are obtained by solving a Riemann problem. As the interface is propagated, a simple and effective remeshing technique based on distance functions regenerates the grid to preserve its quality. Compared to other interface capturing techniques, the proposed approach avoids smearing of the jumps across the interface which leads to an improvement in accuracy. Numerical results are presented for several typical two-dimensional interface problems, including flows with surface tension.

17. A Third Order Accurate Cellwise Relaxation Implicit Discontinuous Galerkin Scheme for Unstructured Hybrid Meshes

Directory of Open Access Journals (Sweden)

2014-01-01

Full Text Available A third order accurate cellwise relaxation implicit Discontinuous Galerkin (DG scheme for RANS simulations using unstructured hybrid meshes is presented. A scalar parabolic equation is first examined to clarify what is really important in construction of implicit matrix to keep its diagonal dominance for the third and fourth order cellwise relaxation implicit DG schemes. In addition, discussions are given to approximated construction of implicit matrix for reducing computational cost. Then, the third order accurate cellwise relaxation implicit DG scheme for RANS simulations is successfully developed utilizing the expertise learned in the study of solving the parabolic equation. Superior spatial accuracy of the third order accurate cellwise relaxation implicit DG scheme for RANS simulations, while retaining reasonable convergence properties, is demonstrated for typical aerospace applications.

18. 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.

19. 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.

20. 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.

1. 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.

2. 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.

3. High-order triangle-based discontinuous Galerkin methods for hyperbolic equations on a rotating sphere

International Nuclear Information System (INIS)

Giraldo, Francis X.

2006-01-01

High-order triangle-based discontinuous Galerkin (DG) methods for hyperbolic equations on a rotating sphere are presented. The DG method can be characterized as the fusion of finite elements with finite volumes. This DG formulation uses high-order Lagrange polynomials on the triangle using nodal sets up to 15th order. The finite element-type area integrals are evaluated using order 2N Gauss cubature rules. This leads to a full mass matrix which, unlike for continuous Galerkin (CG) methods such as the spectral element (SE) method presented in Giraldo and Warburton [A nodal triangle-based spectral element method for the shallow water equations on the sphere, J. Comput. Phys. 207 (2005) 129-150], is small, local and efficient to invert. Two types of finite volume-type flux integrals are studied: a set based on Gauss-Lobatto quadrature points (order 2N - 1) and a set based on Gauss quadrature points (order 2N). Furthermore, we explore conservation and advection forms as well as strong and weak forms. Seven test cases are used to compare the different methods including some with scale contractions and shock waves. All three strong forms performed extremely well with the strong conservation form with 2N integration being the most accurate of the four DG methods studied. The strong advection form with 2N integration performed extremely well even for flows with shock waves. The strong conservation form with 2N - 1 integration yielded results almost as good as those with 2N while being less expensive. All the DG methods performed better than the SE method for almost all the test cases, especially for those with strong discontinuities. Finally, the DG methods required less computing time than the SE method due to the local nature of the mass matrix

4. Physical-constraint-preserving Central Discontinuous Galerkin Methods for Special Relativistic Hydrodynamics with a General Equation of State

Science.gov (United States)

Wu, Kailiang; Tang, Huazhong

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 L1-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.

5. A penalty-based nodal discontinuous Galerkin method for spontaneous rupture dynamics

Science.gov (United States)

Ye, R.; De Hoop, M. V.; Kumar, K.

2017-12-01

Numerical simulation of the dynamic rupture processes with slip is critical to understand the earthquake source process and the generation of ground motions. However, it can be challenging due to the nonlinear friction laws interacting with seismicity, coupled with the discontinuous boundary conditions across the rupture plane. In practice, the inhomogeneities in topography, fault geometry, elastic parameters and permiability add extra complexity. We develop a nodal discontinuous Galerkin method to simulate seismic wave phenomenon with slipping boundary conditions, including the fluid-solid boundaries and ruptures. By introducing a novel penalty flux, we avoid solving Riemann problems on interfaces, which makes our method capable for general anisotropic and poro-elastic materials. Based on unstructured tetrahedral meshes in 3D, the code can capture various geometries in geological model, and use polynomial expansion to achieve high-order accuracy. We consider the rate and state friction law, in the spontaneous rupture dynamics, as part of a nonlinear transmitting boundary condition, which is weakly enforced across the fault surface as numerical flux. An iterative coupling scheme is developed based on implicit time stepping, containing a constrained optimization process that accounts for the nonlinear part. To validate the method, we proof the convergence of the coupled system with error estimates. We test our algorithm on a well-established numerical example (TPV102) of the SCEC/USGS Spontaneous Rupture Code Verification Project, and benchmark with the simulation of PyLith and SPECFEM3D with agreeable results.

6. A GPU-accelerated nodal discontinuous Galerkin method with high-order absorbing boundary conditions and corner/edge compatibility

Science.gov (United States)

Modave, A.; Atle, A.; Chan, J.; Warburton, T.

2017-12-01

Discontinuous Galerkin finite element schemes exhibit attractive features for accurate large-scale wave-propagation simulations on modern parallel architectures. For many applications, these schemes must be coupled with non-reflective boundary treatments to limit the size of the computational domain without losing accuracy or computational efficiency, which remains a challenging task. In this paper, we present a combination of a nodal discontinuous Galerkin method with high-order absorbing boundary conditions (HABCs) for cuboidal computational domains. Compatibility conditions are derived for HABCs intersecting at the edges and the corners of a cuboidal domain. We propose a GPU implementation of the computational procedure, which results in a multidimensional solver with equations to be solved on 0D, 1D, 2D and 3D spatial regions. Numerical results demonstrate both the accuracy and the computational efficiency of our approach.

7. A priori error estimates for an hp-version of the discontinuous Galerkin method for hyperbolic conservation laws

Science.gov (United States)

Bey, Kim S.; Oden, J. Tinsley

1993-01-01

A priori error estimates are derived for hp-versions of the finite element method for discontinuous Galerkin approximations of a model class of linear, scalar, first-order hyperbolic conservation laws. These estimates are derived in a mesh dependent norm in which the coefficients depend upon both the local mesh size h(sub K) and a number p(sub k) which can be identified with the spectral order of the local approximations over each element.

8. 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.

9. 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.

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

KAUST Repository

Amler, Thomas

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.

11. 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.

12. 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.

13. 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.

14. 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.

15. 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.

16. 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.

17. 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.

18. 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.

19. 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

20. 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.

1. 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.

2. 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.

3. 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.

4. 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

5. 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

6. 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

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. science direct.com/ science /article/pii/S0096300315002453/pdfft?md5=02d46bc730e3a7fb8a5008aaab1da786&pid=1-s2.0-S0096300315002453-main.pdf

7. 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.

8. 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.

9. 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.

10. Modeling of Multicomponent Diffusions and Natural Convection in Unfractured and Fractured Media by Discontinuous Galerkin and Mixed Methods

KAUST Repository

Hoteit, Hussein

2017-12-29

Computation of the distribution of species in hydrocarbon reservoirs from diffusions (thermal, molecular, and pressure) and natural convection is an important step in reservoir initialization. Current methods, which are mainly based on the conventional finite difference approach, may not be numerically efficient in fractured and other media with complex heterogeneities. In this work, the discontinuous Galerkin (DG) method combined with the mixed finite element (MFE) method is used for the calculation of compositional variation in fractured hydrocarbon reservoirs. The use of unstructured gridding allows efficient computations for fractured media when the crossflow equilibrium concept is invoked. The DG method has less numerical dispersion than the upwind finite difference (FD) methods. The MFE method ensures continuity of fluxes at the interface of the grid elements. We also use the local discontinuous Galerkin (LDG) method instead of the MFE calculate the diffusion fluxes. Results from several numerical examples are presented to demonstrate the efficiency, robustness, and accuracy of the model. Various features of convection and diffusion in homogeneous, layered, and fractured media are also discussed.

11. 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.

12. PWR thermal-hydraulic analysis for subchannels using Petrov-Galerkin formulations of finite elements and a frontal method for the solution of linear systems

International Nuclear Information System (INIS)

Pereira, L.C.M.

1991-05-01

A methodology for thermo-hydraulic analysis of pressurized water reactor cores using a discontinuous Petrov-Galerkin formulation and a frontal method for solution of linear systems with hard disk storage is presented. this procedure aims at achieving significant economy of computer memory. the complete development of the subchannel equations is presented, beginning in the conservation equations. The cast in variational and finite element formulations is also presented. (author). 30 refs, 14 tabs

13. 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)

14. Numerical solution of fuzzy boundary value problems using Galerkin ...

Abstract. This paper proposes a new technique based on Galerkin method for solving nth order fuzzy boundary value problem. The proposed method has been illustrated by considering three different cases depending upon the sign of coefficients with benchmark example problems. To show the applicability of the.

15. 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.

16. 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.

17. A high-order discontinuous Galerkin method for 1D wave propagation in a nonlinear heterogeneous medium

Science.gov (United States)

Chabot, S.; Glinsky, N.; Mercerat, E. D.; Bonilla Hidalgo, L. F.

2018-02-01

We propose a nodal high-order discontinuous Galerkin method for 1D wave propagation in nonlinear media. We solve the elastodynamic equations written in the velocity-strain formulation and apply an upwind flux adapted to heterogeneous media with nonlinear constitutive behavior coupling stress and strain. Accuracy, convergence and stability of the method are studied through several numerical applications. Hysteresis loops distinguishing loading and unloading-reloading paths are also taken into account. We investigate several effects of nonlinearity in wave propagation, such as the generation of high frequencies and the frequency shift of resonant peaks to lower frequencies. Finally, we compare the results for both nonlinear models, with and without hysteresis, and highlight the effects of the former on the stabilization of the numerical scheme.

18. Weight-adjusted discontinuous Galerkin methods: Matrix-valued weights and elastic wave propagation in heterogeneous media

Science.gov (United States)

Chan, Jesse

2018-03-01

Weight-adjusted inner products are easily invertible approximations to weighted $L^2$ inner products. These approximations can be paired with a discontinuous Galerkin (DG) discretization to produce a time-domain method for wave propagation which is low storage, energy stable, and high order accurate for arbitrary heterogeneous media and curvilinear meshes. In this work, we extend weight-adjusted DG (WADG) methods to the case of matrix-valued weights, with the linear elastic wave equation as an application. We present a DG formulation of the symmetric form of the linear elastic wave equation, with upwind-like dissipation incorporated through simple penalty fluxes. A semi-discrete convergence analysis is given, and numerical results confirm the stability and high order accuracy of WADG for several problems in elastic wave propagation.

19. Stability of a Leap-Frog Discontinuous Galerkin Method for Time-Domain Maxwell's Equations in Anisotropic Materials

Science.gov (United States)

Araújo, Adérito; Barbeiro, Sílvia; Ghalati, Maryam Khaksar

2017-05-01

In this work we discuss the numerical discretization of the time-dependent Maxwell's equations using a fully explicit leap-frog type discontinuous Galerkin method. We present a sufficient condition for the stability, for cases of typical boundary conditions, either perfect electric, perfect magnetic or first order Silver-M\\"uller. The bounds of the stability region point out the influence of not only the mesh size but also the dependence on the choice of the numerical flux and the degree of the polynomials used in the construction of the finite element space, making possible to balance accuracy and computational efficiency. In the model we consider heterogeneous anisotropic permittivity tensors which arise naturally in many applications of interest. Numerical results supporting the analysis are provided.

20. 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.

1. 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.

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

International Nuclear Information System (INIS)

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)

3. 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

4. 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

5. An operator-based local discontinuous Galerkin method compatible with the BSSN formulation of the Einstein equations

International Nuclear Information System (INIS)

Miller, Jonah M; Schnetter, Erik

2017-01-01

Discontinuous Galerkin finite element (DGFE) methods offer a mathematically beautiful, computationally efficient, and efficiently parallelizable way to solve partial differential equations (PDEs). These properties make them highly desirable for numerical calculations in relativistic astrophysics and many other fields. The BSSN formulation of the Einstein equations has repeatedly demonstrated its robustness. The formulation is not only stable but allows for puncture-type evolutions of black hole systems. To-date no one has been able to solve the full (3  +  1)-dimensional BSSN equations using DGFE methods. This is partly because DGFE discretization often occurs at the level of the equations, not the derivative operator, and partly because DGFE methods are traditionally formulated for manifestly flux-conservative systems. By discretizing the derivative operator, we generalize a particular flavor of DGFE methods, Local DG methods, to solve arbitrary second-order hyperbolic equations. Because we discretize at the level of the derivative operator, our method can be interpreted as either a DGFE method or as a finite differences stencil with non-constant coefficients. (paper)

6. 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.

7. Discontinuous Galerkin Finite Element Investigation on the Fully-Compressible Navier–Stokes Equations for Microscale Shock-Channels

Directory of Open Access Journals (Sweden)

Alberto Zingaro

2018-02-01

Full Text Available Microfluidics is a multidisciplinary area founding applications in several fields such as the aerospace industry. Microelectromechanical systems (MEMS are mainly adopted for flow control, micropower generation and for life support and environmental control for space applications. Microflows are modeled relying on both a continuum and molecular approach. In this paper, the compressible Navier–Stokes (CNS equations have been adopted to solve a two-dimensional unsteady flow for a viscous micro shock-channel problem. In microflows context, as for the most gas dynamics applications, the CNS equations are usually discretized in space using finite volume method (FVM. In the present paper, the PDEs are discretized with the nodal discontinuous Galerkin finite element method (DG–FEM in order to understand how the method performs at microscale level for compressible flows. Validation is performed through a benchmark test problem for microscale applications. The error norms, order of accuracy and computational cost are investigated in a grid refinement study, showing a good agreement and increasing accuracy with reference data as the mesh is refined. The effects of different explicit Runge–Kutta schemes and of different time step sizes have also been studied. We found that the choice of the temporal scheme does not really affect the accuracy of the numerical results.

8. Krylov implicit integration factor methods for spatial discretization on high dimensional unstructured meshes: Application to discontinuous Galerkin methods

Science.gov (United States)

Chen, Shanqin; Zhang, Yong-Tao

2011-05-01

Integration factor methods are a class of "exactly linear part" time discretization methods. In [Q. Nie, Y.-T. Zhang, R. Zhao, Efficient semi-implicit schemes for stiff systems, Journal of Computational Physics, 214 (2006) 521-537], a class of efficient implicit integration factor (IIF) methods were developed for solving systems with both stiff linear and nonlinear terms, arising from spatial discretization of time-dependent partial differential equations (PDEs) with linear high order terms and stiff lower order nonlinear terms. The tremendous challenge in applying IIF temporal discretization for PDEs on high spatial dimensions is how to evaluate the matrix exponential operator efficiently. For spatial discretization on unstructured meshes to solve PDEs on complex geometrical domains, how to efficiently apply the IIF temporal discretization was open. In this paper, we solve this problem by applying the Krylov subspace approximations to the matrix exponential operator. Then we apply this novel time discretization technique to discontinuous Galerkin (DG) methods on unstructured meshes for solving reaction-diffusion equations. Numerical examples are shown to demonstrate the accuracy, efficiency and robustness of the method in resolving the stiffness of the DG spatial operator for reaction-diffusion PDEs. Application of the method to a mathematical model in pattern formation during zebrafish embryo development shall be shown.

9. 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.

10. 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.

11. 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.

12. 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.

13. Efficient Galerkin solution of stochastic fractional differential equations using second kind Chebyshev wavelets

Directory of Open Access Journals (Sweden)

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.

14. 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.

15. 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.

16. A residual-based shock capturing scheme for the continuous/discontinuous spectral element solution of the 2D shallow water equations

Science.gov (United States)

Marras, Simone; Kopera, Michal A.; Constantinescu, Emil M.; Suckale, Jenny; Giraldo, Francis X.

2018-04-01

The high-order numerical solution of the non-linear shallow water equations is susceptible to Gibbs oscillations in the proximity of strong gradients. In this paper, we tackle this issue by presenting a shock capturing model based on the numerical residual of the solution. Via numerical tests, we demonstrate that the model removes the spurious oscillations in the proximity of strong wave fronts while preserving their strength. Furthermore, for coarse grids, it prevents energy from building up at small wave-numbers. When applied to the continuity equation to stabilize the water surface, the addition of the shock capturing scheme does not affect mass conservation. We found that our model improves the continuous and discontinuous Galerkin solutions alike in the proximity of sharp fronts propagating on wet surfaces. In the presence of wet/dry interfaces, however, the model needs to be enhanced with the addition of an inundation scheme which, however, we do not address in this paper.

17. 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.

18. Variation formulae for the solutions of delay differential equations with discontinuous initial conditions

International Nuclear Information System (INIS)

2005-01-01

Variation formulae are proved for solutions of non-linear differential equations with variable delays and discontinuous initial conditions. The discontinuity of the initial condition means that at the initial moment of time the values of the initial function and the trajectory, generally speaking, do not coincide. The formulae obtained contain a new summand connected with the discontinuity of the initial condition and the variation of the initial moment.

19. Galerkin finite element methods for wave problems

these methods. Keywords. hp-Finite element method; continuous Galerkin methods; wave solutions; Gibbs' phenomenon. 1. Introduction. Galerkin methods belong to the class of solution methods for PDEs where the solution residue is minimized giving rise to the well-known weak formulation of problems. In this approach,.

20. 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.

1. MIB Galerkin method for elliptic interface problems.

Science.gov (United States)

Xia, Kelin; Zhan, Meng; Wei, Guo-Wei

2014-12-15

Material interfaces are omnipresent in the real-world structures and devices. Mathematical modeling of material interfaces often leads to elliptic partial differential equations (PDEs) with discontinuous coefficients and singular sources, which are commonly called elliptic interface problems. The development of high-order numerical schemes for elliptic interface problems has become a well defined field in applied and computational mathematics and attracted much attention in the past decades. Despite of significant advances, challenges remain in the construction of high-order schemes for nonsmooth interfaces, i.e., interfaces with geometric singularities, such as tips, cusps and sharp edges. The challenge of geometric singularities is amplified when they are associated with low solution regularities, e.g., tip-geometry effects in many fields. The present work introduces a matched interface and boundary (MIB) Galerkin method for solving two-dimensional (2D) elliptic PDEs with complex interfaces, geometric singularities and low solution regularities. The Cartesian grid based triangular elements are employed to avoid the time consuming mesh generation procedure. Consequently, the interface cuts through elements. To ensure the continuity of classic basis functions across the interface, two sets of overlapping elements, called MIB elements, are defined near the interface. As a result, differentiation can be computed near the interface as if there is no interface. Interpolation functions are constructed on MIB element spaces to smoothly extend function values across the interface. A set of lowest order interface jump conditions is enforced on the interface, which in turn, determines the interpolation functions. The performance of the proposed MIB Galerkin finite element method is validated by numerical experiments with a wide range of interface geometries, geometric singularities, low regularity solutions and grid resolutions. Extensive numerical studies confirm the

2. The existence of semiregular solutions to elliptic spectral problems with discontinuous nonlinearities

International Nuclear Information System (INIS)

Pavlenko, V N; Potapov, D K

2015-01-01

This paper is concerned with the existence of semiregular solutions to the Dirichlet problem for an equation of elliptic type with discontinuous nonlinearity and when the differential operator is not assumed to be formally self-adjoint. Theorems on the existence of semiregular (positive and negative) solutions for the problem under consideration are given, and a principle of upper and lower solutions giving the existence of semiregular solutions is established. For positive values of the spectral parameter, elliptic spectral problems with discontinuous nonlinearities are shown to have nontrivial semiregular (positive and negative) solutions. Bibliography: 32 titles

3. Wavelet=Galerkin discretization of hyperbolic equations

Energy Technology Data Exchange (ETDEWEB)

Restrepo, J.M.; Leaf, G.K.

1994-12-31

The relative merits of the wavelet-Galerkin solution of hyperbolic partial differential equations, typical of geophysical problems, are quantitatively and qualitatively compared to traditional finite difference and Fourier-pseudo-spectral methods. The wavelet-Galerkin solution presented here is found to be a viable alternative to the two conventional techniques.

4. A Galerkin Solution for Burgers' Equation Using Cubic B-Spline Finite Elements

OpenAIRE

Soliman, A. A.

2012-01-01

Numerical solutions for Burgers’ equation based on the Galerkins’ method using cubic B-splines as both weight and interpolation functions are set up. It is shown that this method is capable of solving Burgers’ equation accurately for values of viscosity ranging from very small to large. Three standard problems are used to validate the proposed algorithm. A linear stability analysis shows that a numerical scheme based on a Cranck-Nicolson approximation in time is unconditionally stable.

5. A Galerkin Solution for Burgers' Equation Using Cubic B-Spline Finite Elements

Directory of Open Access Journals (Sweden)

A. A. Soliman

2012-01-01

Full Text Available Numerical solutions for Burgers’ equation based on the Galerkins’ method using cubic B-splines as both weight and interpolation functions are set up. It is shown that this method is capable of solving Burgers’ equation accurately for values of viscosity ranging from very small to large. Three standard problems are used to validate the proposed algorithm. A linear stability analysis shows that a numerical scheme based on a Cranck-Nicolson approximation in time is unconditionally stable.

6. The Entropy Solutions for the Lighthill-Whitham-Richards Traffic Flow Model with a Discontinuous Flow-Density Relationship

National Research Council Canada - National Science Library

Lu, Yadong; Wong, S. C; Zhang, Mengping; Shu, Chi-Wang

2007-01-01

... initial condition and piecewise constant boundary conditions. The existence and uniqueness of entropy solutions for such conservation laws with discontinuous fluxes are not known mathematically...

7. Infinitely Many Solutions for a Boundary Value Problem with Discontinuous Nonlinearities

Directory of Open Access Journals (Sweden)

2009-03-01

Full Text Available The existence of infinitely many solutions for a Sturm-Liouville boundary value problem, under an appropriate oscillating behavior of the possibly discontinuous nonlinear term, is obtained. Several special cases and consequences are pointed out and some examples are presented. The technical approach is mainly based on a result of infinitely many critical points for locally Lipschitz functions.

8. A combined continuous-discontinuous finite element method for convection-diffusion problems

OpenAIRE

Devloo, PRB; Forti, T; Gomes, SM

2007-01-01

Discontinuous Galerkin (DGM) method combines the advantages of stability of finite volume method and the accuracy of continuous finite element method (FEIVI). Applications of the DGM are particularly valuable where the solution presents high-gradients or discontinuities, such as boundary layers and shock problems. A disadvantage of the DGM is the higher computational cost when comparing to classic finite element method, due to the increased number of degrees of freedom. With this motivation, ...

9. To Be or Not to Be Intrusive? The Solution of Parametric and Stochastic Equations---the “Plain Vanilla” Galerkin Case

KAUST Repository

Giraldi, Loïc

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).

10. Galerkin and weighted Galerkin methods for a forward-backward heat equation

NARCIS (Netherlands)

Lu, H.

1997-01-01

Galerkin and weighted Galerkin methods are proposed for the numerical solution of parabolic partial differential equations where the diffusion coefficient takes different signs. The approach is based on a simultaneous discretization of space and time variables by using continuous finite element

11. Discontinuous almost automorphic functions and almost automorphic solutions of differential equations with piecewise constant arguments

Directory of Open Access Journals (Sweden)

Alan Chavez

2014-02-01

Full Text Available In this article we introduce a class of discontinuous almost automorphic functions which appears naturally in the study of almost automorphic solutions of differential equations with piecewise constant argument. Their fundamental properties are used to prove the almost automorphicity of bounded solutions of a system of differential equations with piecewise constant argument. Due to the strong discrete character of these equations, the existence of a unique discrete almost automorphic solution of a non-autonomous almost automorphic difference system is obtained, for which conditions of exponential dichotomy and discrete Bi-almost automorphicity are fundamental.

12. Numerical solution of the Neutron Transport Equation using discontinuous nodal methods at X-Y geometry

International Nuclear Information System (INIS)

Delfin L, A.

1996-01-01

The purpose of this work is to solve the neutron transport equation in discrete-ordinates and X-Y geometry by developing and using the strong discontinuous and strong modified discontinuous nodal finite element schemes. The strong discontinuous and modified strong discontinuous nodal finite element schemes go from two to ten interpolation parameters per cell. They are describing giving a set D c and polynomial space S c corresponding for each scheme BDMO, RTO, BL, BDM1, HdV, BDFM1, RT1, BQ and BDM2. The solution is obtained solving the neutron transport equation moments for each nodal scheme by developing the basis functions defined by Pascal triangle and the Legendre moments giving in the polynomial space S c and, finally, looking for the non singularity of the resulting linear system. The linear system is numerically solved using a computer program for each scheme mentioned . It uses the LU method and forward and backward substitution and makes a partition of the domain in cells. The source terms and angular flux are calculated, using the directions and weights associated to the S N approximation and solving the angular flux moments to find the effective multiplication constant. The programs are written in Fortran language, using the dynamic allocation of memory to increase efficiently the available memory of the computing equipment. (Author)

13. OpenACC directive-based GPU acceleration of an implicit reconstructed discontinuous Galerkin method for compressible flows on 3D unstructured grids

Energy Technology Data Exchange (ETDEWEB)

Lou, Jialin [North Carolina State Univ., Raleigh, NC (United States); Xia, Yidong [Idaho National Lab. (INL), Idaho Falls, ID (United States); Luo, Lixiang [North Carolina State Univ., Raleigh, NC (United States); Luo, Hong [North Carolina State Univ., Raleigh, NC (United States); Edwards, Jack [North Carolina State Univ., Raleigh, NC (United States); Mueller, Frank [North Carolina State Univ., Raleigh, NC (United States)

2016-09-01

In this study, we use a combination of modeling techniques to describe the relationship between fracture radius that might be accomplished in a hypothetical enhanced geothermal system (EGS) and drilling distance required to create and access those fractures. We use a combination of commonly applied analytical solutions for heat transport in parallel fractures and 3D finite-element method models of more realistic heat extraction geometries. For a conceptual model involving multiple parallel fractures developed perpendicular to an inclined or horizontal borehole, calculations demonstrate that EGS will likely require very large fractures, of greater than 300 m radius, to keep interfracture drilling distances to ~10 km or less. As drilling distances are generally inversely proportional to the square of fracture radius, drilling costs quickly escalate as the fracture radius decreases. It is important to know, however, whether fracture spacing will be dictated by thermal or mechanical considerations, as the relationship between drilling distance and number of fractures is quite different in each case. Information about the likelihood of hydraulically creating very large fractures comes primarily from petroleum recovery industry data describing hydraulic fractures in shale. Those data suggest that fractures with radii on the order of several hundred meters may, indeed, be possible. The results of this study demonstrate that relatively simple calculations can be used to estimate primary design constraints on a system, particularly regarding the relationship between generated fracture radius and the total length of drilling needed in the fracture creation zone. Comparison of the numerical simulations of more realistic geometries than addressed in the analytical solutions suggest that simple proportionalities can readily be derived to relate a particular flow field.

14. 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

15. General properties of solutions to inhomogeneous Black-Scholes equations with discontinuous maturity payoffs

Science.gov (United States)

O, Hyong-Chol; Jo, Jong-Jun; Kim, Ji-Sok

2016-02-01

We provide representations of solutions to terminal value problems of inhomogeneous Black-Scholes equations and study such general properties as min-max estimates, gradient estimates, monotonicity and convexity of the solutions with respect to the stock price variable, which are important for financial security pricing. In particular, we focus on finding representation of the gradient (with respect to the stock price variable) of solutions to the terminal value problems with discontinuous terminal payoffs or inhomogeneous terms. Such terminal value problems are often encountered in pricing problems of compound-like options such as Bermudan options or defaultable bonds with discrete default barrier, default intensity and endogenous default recovery. Our results can be used in pricing real defaultable bonds under consideration of existence of discrete coupons or taxes on coupons.

16. Modeling Storm Surges Using Discontinuous Galerkin Methods

Science.gov (United States)

2016-06-01

STATEMENT Approved for public release; distribution is unlimited 12b. DISTRIBUTION CODE 13. ABSTRACT (maximum 200 words ) Storm surges have a...model. One of the governing systems of equations used to model storm surges’ effects is the Shallow Water Equations (SWE). In this thesis, we solve the...fundamental truth, we found the error norm of the implicit method to be minimal. This study focuses on the impacts of a simulated storm surge in La Push

17. On the rise velocity discontinuity of a deformable bubble in unbounded viscoelastic solutions

Science.gov (United States)

Tsamopoulos, John; Fraggedakis, Dimitris; Dimakopoulos, Yiannis

2014-11-01

It is well-documented experimentally, but not well-understood that a bubble steadily rising in a viscoelastic solution exhibits a negative wake and a jump discontinuity in its rise velocity, when its radius exceeds a critical value. In all experiments, the bubble shape forms a cusp in its back side and in some experiments it loses axial symmetry forming a wedge. Some authors have related the velocity jump with the existence of the negative wake or even the wedge formation. We have undertaken a computational study to explore the mechanisms behind these phenomena. To this end, we have used the ePTT model and determined its rheological parameters by fitting it to experiments. Then we developed an FE code (using elliptic grid generation and the SUPG and EVSS methods) and calculated the bubble rise and deformation as its radius increases. This simultaneously affects all parameters: Bond, Archimedes and Deborah numbers. Our predictions reproduce very accurately bubble shapes and the results up to the velocity jump or, in certain cases, beyond it using arc-length continuation. The discontinuity is attributed to a hysteresis loop, but does not require the presence of a wedge in the bubble shape and the negative wake is predicted even before this jump. Supported financially by the General Secretariat of Research & Technology of Greece through the program Thalis'' (Grant titled COVISCO'') co-funded by the ESF and National resources.

18. Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid-structure interaction, and free surface flow: Part II

Science.gov (United States)

Saye, Robert

2017-09-01

In this two-part paper, a high-order accurate implicit mesh discontinuous Galerkin (dG) framework is developed for fluid interface dynamics, facilitating precise computation of interfacial fluid flow in evolving geometries. The framework uses implicitly defined meshes-wherein a reference quadtree or octree grid is combined with an implicit representation of evolving interfaces and moving domain boundaries-and allows physically prescribed interfacial jump conditions to be imposed or captured with high-order accuracy. Part one discusses the design of the framework, including: (i) high-order quadrature for implicitly defined elements and faces; (ii) high-order accurate discretisation of scalar and vector-valued elliptic partial differential equations with interfacial jumps in ellipticity coefficient, leading to optimal-order accuracy in the maximum norm and discrete linear systems that are symmetric positive (semi)definite; (iii) the design of incompressible fluid flow projection operators, which except for the influence of small penalty parameters, are discretely idempotent; and (iv) the design of geometric multigrid methods for elliptic interface problems on implicitly defined meshes and their use as preconditioners for the conjugate gradient method. Also discussed is a variety of aspects relating to moving interfaces, including: (v) dG discretisations of the level set method on implicitly defined meshes; (vi) transferring state between evolving implicit meshes; (vii) preserving mesh topology to accurately compute temporal derivatives; (viii) high-order accurate reinitialisation of level set functions; and (ix) the integration of adaptive mesh refinement. In part two, several applications of the implicit mesh dG framework in two and three dimensions are presented, including examples of single phase flow in nontrivial geometry, surface tension-driven two phase flow with phase-dependent fluid density and viscosity, rigid body fluid-structure interaction, and free

19. Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid-structure interaction, and free surface flow: Part I

Science.gov (United States)

Saye, Robert

2017-09-01

In this two-part paper, a high-order accurate implicit mesh discontinuous Galerkin (dG) framework is developed for fluid interface dynamics, facilitating precise computation of interfacial fluid flow in evolving geometries. The framework uses implicitly defined meshes-wherein a reference quadtree or octree grid is combined with an implicit representation of evolving interfaces and moving domain boundaries-and allows physically prescribed interfacial jump conditions to be imposed or captured with high-order accuracy. Part one discusses the design of the framework, including: (i) high-order quadrature for implicitly defined elements and faces; (ii) high-order accurate discretisation of scalar and vector-valued elliptic partial differential equations with interfacial jumps in ellipticity coefficient, leading to optimal-order accuracy in the maximum norm and discrete linear systems that are symmetric positive (semi)definite; (iii) the design of incompressible fluid flow projection operators, which except for the influence of small penalty parameters, are discretely idempotent; and (iv) the design of geometric multigrid methods for elliptic interface problems on implicitly defined meshes and their use as preconditioners for the conjugate gradient method. Also discussed is a variety of aspects relating to moving interfaces, including: (v) dG discretisations of the level set method on implicitly defined meshes; (vi) transferring state between evolving implicit meshes; (vii) preserving mesh topology to accurately compute temporal derivatives; (viii) high-order accurate reinitialisation of level set functions; and (ix) the integration of adaptive mesh refinement. In part two, several applications of the implicit mesh dG framework in two and three dimensions are presented, including examples of single phase flow in nontrivial geometry, surface tension-driven two phase flow with phase-dependent fluid density and viscosity, rigid body fluid-structure interaction, and free

20. Pipe-anchor discontinuity analysis utilizing power series solutions, Bessel functions, and Fourier series

International Nuclear Information System (INIS)

Williams, Dennis K.; Ranson, William F.

2003-01-01

One of the paradigmatic classes of problems that frequently arise in piping stress analysis discipline is the effect of local stresses created by supports and restraints attachments. Over the past 20 years, concerns have been identified by both regulatory agencies in the nuclear power industry and others in the process and chemicals industries concerning the effect of various stiff clamping arrangements on the expected life of the pipe and its various piping components. In many of the commonly utilized geometries and arrangements of pipe clamps, the elasticity problem becomes the axisymmetric stress and deformation determination in a hollow cylinder (pipe) subjected to the appropriate boundary conditions and respective loads per se. One of the geometries that serve as a pipe anchor is comprised of two pipe clamps that are bolted tightly to the pipe and affixed to a modified shoe-type arrangement. The shoe is employed for the purpose of providing an immovable base that can be easily attached either by bolting or welding to a structural steel pipe rack. Over the past 50 years, the computational tools available to the piping analyst have changed dramatically and thereby have caused the implementation of solutions to the basic problems of elasticity to change likewise. The need to obtain closed form elasticity solutions, however, has always been a driving force in engineering. The employment of symbolic calculus that is currently available through numerous software packages makes closed form solutions very economical. This paper briefly traces the solutions over the past 50 years to a variety of axisymmetric stress problems involving hollow circular cylinders employing a Fourier series representation. In the present example, a properly chosen Fourier series represent the mathematical simulation of the imposed axial displacements on the outside diametrical surface. A general solution technique is introduced for the axisymmetric discontinuity stresses resulting from an

1. Stability of Almost Periodic Solution for a General Class of Discontinuous Neural Networks with Mixed Time-Varying Delays

Directory of Open Access Journals (Sweden)

Yingwei Li

2013-01-01

Full Text Available The global exponential stability issues are considered for almost periodic solution of the neural networks with mixed time-varying delays and discontinuous neuron activations. Some sufficient conditions for the existence, uniqueness, and global exponential stability of almost periodic solution are achieved in terms of certain linear matrix inequalities (LMIs, by applying differential inclusions theory, matrix inequality analysis technique, and generalized Lyapunov functional approach. In addition, the existence and asymptotically almost periodic behavior of the solution of the neural networks are also investigated under the framework of the solution in the sense of Filippov. Two simulation examples are given to illustrate the validity of the theoretical results.

2. Continuum damage growth analysis using element free Galerkin ...

using the proposed element free Galerkin method to understand the effect of initial damage and its growth on structural ... Effect of material discontinuity on damage growth analysis is also presented. Keywords. Damage ... 1996), Lagrange multiplier technique (Dolbow & Belytschko 1998), penalty method (Liu. 2002), full ...

3. 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

4. Solution of the Neutron transport equation in hexagonal geometry using strongly discontinuous nodal schemes

International Nuclear Information System (INIS)

Mugica R, C.A.; Valle G, E. del

2005-01-01

In 2002, E. del Valle and Ernest H. Mund developed a technique to solve numerically the Neutron transport equations in discrete ordinates and hexagonal geometry using two nodal schemes type finite element weakly discontinuous denominated WD 5,3 and WD 12,8 (of their initials in english Weakly Discontinuous). The technique consists on representing each hexagon in the union of three rhombuses each one of which it is transformed in a square in the one that the methods WD 5,3 and WD 12,8 were applied. In this work they are solved the mentioned equations of transport using the same discretization technique by hexagon but using two nodal schemes type finite element strongly discontinuous denominated SD 3 and SD 8 (of their initials in english Strongly Discontinuous). The application in each case as well as a reference problem for those that results are provided for the effective multiplication factor is described. It is carried out a comparison with the obtained results by del Valle and Mund for different discretization meshes so much angular as spatial. (Author)

5. 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.

6. A Galerkin formulation of the MIB method for three dimensional elliptic interface problems.

Science.gov (United States)

Xia, Kelin; Wei, Guo-Wei

2014-10-01

We develop a three dimensional (3D) Galerkin formulation of the matched interface and boundary (MIB) method for solving elliptic partial differential equations (PDEs) with discontinuous coefficients, i.e., the elliptic interface problem. The present approach builds up two sets of elements respectively on two extended subdomains which both include the interface. As a result, two sets of elements overlap each other near the interface. Fictitious solutions are defined on the overlapping part of the elements, so that the differentiation operations of the original PDEs can be discretized as if there was no interface. The extra coefficients of polynomial basis functions, which furnish the overlapping elements and solve the fictitious solutions, are determined by interface jump conditions. Consequently, the interface jump conditions are rigorously enforced on the interface. The present method utilizes Cartesian meshes to avoid the mesh generation in conventional finite element methods (FEMs). We implement the proposed MIB Galerkin method with three different elements, namely, rectangular prism element, five-tetrahedron element and six-tetrahedron element, which tile the Cartesian mesh without introducing any new node. The accuracy, stability and robustness of the proposed 3D MIB Galerkin are extensively validated over three types of elliptic interface problems. In the first type, interfaces are analytically defined by level set functions. These interfaces are relatively simple but admit geometric singularities. In the second type, interfaces are defined by protein surfaces, which are truly arbitrarily complex. The last type of interfaces originates from multiprotein complexes, such as molecular motors. Near second order accuracy has been confirmed for all of these problems. To our knowledge, it is the first time for an FEM to show a near second order convergence in solving the Poisson equation with realistic protein surfaces. Additionally, the present work offers the

7. Solution of the transport equation in stationary state and X Y geometry, using continuous and discontinuous hybrid nodal schemes

International Nuclear Information System (INIS)

Xolocostli M, V.; Valle G, E. del; Alonso V, G.

2003-01-01

In this work it is described the development and the application of the NH-FEM schemes, Hybrid Nodal schemes using the Finite Element method in the solution of the neutron transport equation in stationary state and X Y geometry, of which two families of schemes were developed, one of which corresponds to the continuous and the other to the discontinuous ones, inside those first its are had the Bi-Quadratic Bi Q, and to the Bi-cubic BiC, while for the seconds the Discontinuous Bi-lineal DBiL and the Discontinuous Bi-quadratic DBiQ. These schemes were implemented in a program to which was denominated TNHXY, Transport of neutrons with Hybrid Nodal schemes in X Y geometry. One of the immediate applications of the schemes NH-FEM it will be in the analysis of assemblies of nuclear fuel, particularly of the BWR type. The validation of the TNHXY program was made with two test problems or benchmark, already solved by other authors with numerical techniques and to compare results. The first of them consists in an it BWR fuel assemble in an arrangement 7x7 without rod and with control rod providing numerical results. The second is a fuel assemble of mixed oxides (MOX) in an arrangement 10x10. This last problem it is known as the Benchmark problem WPPR of the NEA Data Bank and the results are compared with those of other commercial codes as HELIOS, MCNP-4B and CPM-3. (Author)

8. Existence of solutions for discontinuous hyperbolic partial differential equations in Banach algebras

Directory of Open Access Journals (Sweden)

Bapurao C. Dhage

2006-03-01

Full Text Available In this paper, we prove an existence theorem for hyperbolic differential equations in Banach algebras under Lipschitz and Caratheodory conditions. The existence of extremal solutions is also proved under certain monotonicity conditions.

9. 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

10. Continuous and discontinuous fatigue crack growth of irradiated ultrahigh molecular mass polyethylene in saline solution at 37oC

International Nuclear Information System (INIS)

Zeng, Z.P.; Buggy, M.; Griffin, J.; Little, E.G.

1992-01-01

To provide data for prosthesis design, the fatigue crack growth resistance of irradiated ultrahigh molecular mass polyethylene (UHMMPE) in saline solution at 37 o C was determined from tests performed on compact tension specimens, comparable in size to the components in knee prostheses. The specimens were cyclically loaded by using a sinusoidal wave form at 1 Hz with a minimum-to-maximum load ratio of 0.1. Scanning electron microscopic fractography was used to examine the fracture surfaces. At higher stress levels, the Paris's Law was used to analyse the data, and a striation pattern with each striation corresponding to multi-cycles was observed. At lower stress levels, discontinuous fatigue crack growth was found, a phenomenon which dominated the fatigue life of the material and had not been reported previously in this material. A craze zone ahead of the crack tip was observed, which formed the discontinuous crack growth band with a length relevant to the Dugdale plastic zone length. (author)

11. Continuous and discontinuous fatigue crack growth of irradiated ultrahigh molecular mass polyethylene in saline solution at 37 sup o C

Energy Technology Data Exchange (ETDEWEB)

Zeng, Z.P.; Buggy, M.; Griffin, J.; Little, E.G. (Limerick Univ. (Ireland). Dept. of Mechanical and Production Engineering)

1992-07-01

To provide data for prosthesis design, the fatigue crack growth resistance of irradiated ultrahigh molecular mass polyethylene (UHMMPE) in saline solution at 37{sup o}C was determined from tests performed on compact tension specimens, comparable in size to the components in knee prostheses. The specimens were cyclically loaded by using a sinusoidal wave form at 1 Hz with a minimum-to-maximum load ratio of 0.1. Scanning electron microscopic fractography was used to examine the fracture surfaces. At higher stress levels, the Paris's Law was used to analyse the data, and a striation pattern with each striation corresponding to multi-cycles was observed. At lower stress levels, discontinuous fatigue crack growth was found, a phenomenon which dominated the fatigue life of the material and had not been reported previously in this material. A craze zone ahead of the crack tip was observed, which formed the discontinuous crack growth band with a length relevant to the Dugdale plastic zone length. (author).

12. Discontinuous precipitation in a nickel-free high nitrogen austenitic stainless steel on solution nitriding

DEFF Research Database (Denmark)

2017-01-01

Chromium-rich nitride precipitates in production of nickel-free austenitic stainless steel plates via pressurised solution nitriding of Fe–22.7Cr–2.4Mo ferritic stainless steel at 1473 K (1200 °C) under a nitrogen gas atmosphere was investigated. The microstructure, chemical and phase composition...

13. Experimental evidence for excess entropy discontinuities in glass-forming solutions.

Science.gov (United States)

Lienhard, Daniel M; Zobrist, Bernhard; Zuend, Andreas; Krieger, Ulrich K; Peter, Thomas

2012-02-21

Glass transition temperatures T(g) are investigated in aqueous binary and multi-component solutions consisting of citric acid, calcium nitrate (Ca(NO(3))(2)), malonic acid, raffinose, and ammonium bisulfate (NH(4)HSO(4)) using a differential scanning calorimeter. Based on measured glass transition temperatures of binary aqueous mixtures and fitted binary coefficients, the T(g) of multi-component systems can be predicted using mixing rules. However, the experimentally observed T(g) in multi-component solutions show considerable deviations from two theoretical approaches considered. The deviations from these predictions are explained in terms of the molar excess mixing entropy difference between the supercooled liquid and glassy state at T(g). The multi-component mixtures involve contributions to these excess mixing entropies that the mixing rules do not take into account. © 2012 American Institute of Physics

14. A Runge-Kutta discontinuous finite element method for high speed flows

Science.gov (United States)

Bey, Kim S.; Oden, J. T.

1991-01-01

A Runge-Kutta discontinuous finite element method is developed for hyperbolic systems of conservation laws in two space variables. The discontinuous Galerkin spatial approximation to the conservation laws results in a system of ordinary differential equations which are marched in time using Runge-Kutta methods. Numerical results for the two-dimensional Burger's equation show that the method is (p+1)-order accurate in time and space, where p is the degree of the polynomial approximation of the solution within an element and is capable of capturing shocks over a single element without oscillations. Results for this problem also show that the accuracy of the solution in smooth regions is unaffected by the local projection and that the accuracy in smooth regions increases as p increases. Numerical results for the Euler equations show that the method captures shocks without oscillations and with higher resolution than a first-order scheme.

15. Galerkin finite element methods for wave problems

We compare here the accuracy, stability and wave propagation properties of a few Galerkin methods. The basic Galerkin methods with piecewise linear basis functions (called G1FEM here) and quadratic basis functions (called G2FEM) have been compared with the streamwise-upwind Petrov Galerkin (SUPG) method for ...

16. An Optimal Error Estimates of H1-Galerkin Expanded Mixed Finite Element Methods for Nonlinear Viscoelasticity-Type Equation

Directory of Open Access Journals (Sweden)

Haitao Che

2011-01-01

Full Text Available We investigate a H1-Galerkin mixed finite element method for nonlinear viscoelasticity equations based on H1-Galerkin method and expanded mixed element method. The existence and uniqueness of solutions to the numerical scheme are proved. A priori error estimation is derived for the unknown function, the gradient function, and the flux.

17. Finite element or Galerkin type semidiscrete schemes

Science.gov (United States)

Durgun, K.

1983-01-01

A finite element of Galerkin type semidiscrete method is proposed for numerical solution of a linear hyperbolic partial differential equation. The question of stability is reduced to the stability of a system of ordinary differential equations for which Dahlquist theory applied. Results of separating the part of numerical solution which causes the spurious oscillation near shock-like response of semidiscrete scheme to a step function initial condition are presented. In general all methods produce such oscillatory overshoots on either side of shocks. This overshoot pathology, which displays a behavior similar to Gibb's phenomena of Fourier series, is explained on the basis of dispersion of separated Fourier components which relies on linearized theory to be satisfactory. Expository results represented.

18. 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.

19. Error analysis of a continuous-discontinous Galerkin finite element model for generalized 2D vorticity dynamics

NARCIS (Netherlands)

van der Vegt, Jacobus J.W.; Izsak, F.; Bokhove, Onno

2007-01-01

Abstract. A detailed a priori error estimate is provided for a continuous-discontinuous Galerkin ��?nite element method for the generalized 2D vorticity dynamics equations. These equations describe several types of geophysical ﬂows, including the Euler equations. The algorithm consists of a

20. 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.

1. Early discontinuation

DEFF Research Database (Denmark)

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

2007-01-01

Introduction Discontinuation of medical drug treatment is a serious problem in primary care. The need for a better understanding of the processes, including physician-specific mechanisms, is apparent. The aim of this study was to analyse the association between general practitioners' prescribing....... 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...... of all drugs and drug-specific early discontinuation showed some degree of positive association - strongest for anti-hypertensive drugs (r = 0.62) and antidepressants (r = 0.43). Conclusion This study confirmed our hypothesis that general practitioners with high levels of prescribing attain higher rates...

2. Discontinuous Spectral Difference Method for Conservation Laws on Unstructured Grids

Science.gov (United States)

Liu, Yen; Vinokur, Marcel; Wang, Z. J.

2004-01-01

A new, high-order, conservative, and efficient method for conservation laws on unstructured grids is developed. The concept of discontinuous and high-order local representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) and the Spectral Volume (SV) methods, but while these methods are based on the integrated forms of the equations, the new method is based on the differential form to attain a simpler formulation and higher efficiency. A discussion on the Discontinuous Spectral Difference (SD) Method, locations of the unknowns and flux points and numerical results are also presented.

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

KAUST Repository

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.

4. The application of the Galerkin method to solving PIES for Laplace's equation

Science.gov (United States)

Bołtuć, Agnieszka; Zieniuk, Eugeniusz

2016-06-01

The paper presents the application of the Galerkin method to solving the parametric integral equation system (PIES) on the example of Laplace's equation. The main aim of the paper is the analysis of the effectiveness of two methods for PIES solving: the collocation method and the Galerkin method. Researches were performed on two examples with analytical solutions. Tests concern mainly the accuracy of obtained numerical solutions and their stability. For both analyzed methods calculations were made with the various number of expressions in the approximation series, whilst in the collocation method two variants of the arrangement of collocation points were considered. We also compared the complexity of both methods using the execution time.

5. SWRT: A package for semi-analytical solutions of surface wave propagation, including mode conversion, across transversely aligned vertical discontinuities

Directory of Open Access Journals (Sweden)

A. Datta

2018-03-01

Full Text Available We present a suite of programs that implement decades-old algorithms for computation of seismic surface wave reflection and transmission coefficients at a welded contact between two laterally homogeneous quarter-spaces. For Love as well as Rayleigh waves, the algorithms are shown to be capable of modelling multiple mode conversions at a lateral discontinuity, which was not shown in the original publications or in the subsequent literature. Only normal incidence at a lateral boundary is considered so there is no Love–Rayleigh coupling, but incidence of any mode and coupling to any (other mode can be handled. The code is written in Python and makes use of SciPy's Simpson's rule integrator and NumPy's linear algebra solver for its core functionality. Transmission-side results from this code are found to be in good agreement with those from finite-difference simulations. In today's research environment of extensive computing power, the coded algorithms are arguably redundant but SWRT can be used as a valuable testing tool for the ever evolving numerical solvers of seismic wave propagation. SWRT is available via GitHub (https://github.com/arjundatta23/SWRT.git.

6. SWRT: A package for semi-analytical solutions of surface wave propagation, including mode conversion, across transversely aligned vertical discontinuities

Science.gov (United States)

Datta, Arjun

2018-03-01

We present a suite of programs that implement decades-old algorithms for computation of seismic surface wave reflection and transmission coefficients at a welded contact between two laterally homogeneous quarter-spaces. For Love as well as Rayleigh waves, the algorithms are shown to be capable of modelling multiple mode conversions at a lateral discontinuity, which was not shown in the original publications or in the subsequent literature. Only normal incidence at a lateral boundary is considered so there is no Love-Rayleigh coupling, but incidence of any mode and coupling to any (other) mode can be handled. The code is written in Python and makes use of SciPy's Simpson's rule integrator and NumPy's linear algebra solver for its core functionality. Transmission-side results from this code are found to be in good agreement with those from finite-difference simulations. In today's research environment of extensive computing power, the coded algorithms are arguably redundant but SWRT can be used as a valuable testing tool for the ever evolving numerical solvers of seismic wave propagation. SWRT is available via GitHub (https://github.com/arjundatta23/SWRT.git).

7. 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

8. Nodal DG-FEM solution of high-order Boussinesq-type equations

DEFF Research Database (Denmark)

Engsig-Karup, Allan Peter; Hesthaven, Jan S.; Bingham, Harry B.

2006-01-01

We present a discontinuous Galerkin finite element method (DG-FEM) solution to a set of high-order Boussinesq-type equations for modelling highly nonlinear and dispersive water waves in one and two horizontal dimensions. The continuous equations are discretized using nodal polynomial basis...... functions of arbitrary order in space on each element of an unstructured computational domain. A fourth order explicit Runge-Kutta scheme is used to advance the solution in time. Methods for introducing artificial damping to control mild nonlinear instabilities are also discussed. The accuracy...

9. 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

10. Reproducing Kernel Element Method for Galerkin Solution of Elastostatic Problems Método del elemento reproductor del núcleo para soluciones de problemas elasto-estáticos.

Directory of Open Access Journals (Sweden)

Mario J Juha

2012-12-01

11. Galerkin finite element methods for wave problems

piecewise linear and quadratic basis functions for solving the one-dimensional wave equation. 2. One-dimensional wave equation. First, we briefly discuss the Galerkin method that employs piecewise quadratic polynomials for the basis or interpolating functions. We will call this as G2FEM for ease of reference. Here, one ...

12. Towards Exascale Computing with NUMA: an Element-based Galerkin Nonhydrostatic Global and Mesoscale Atmospheric Modeling

Science.gov (United States)

Giraldo, F.; Mueller, A.; Kopera, M. A.; Abdi, D. S.; Wilcox, L.

2015-12-01

In this talk, we shall describe the NUMA atmospheric model, focusing in particular on its unified continuous/discontinuous (CG and DG) Galerkin numerical methods that are used to represent the spatial derivatives. We shall describe how these two methods are formulated in a unified approach and the advantages that this brings. We will also report on the progress in extending NUMA to using adaptive mesh refinement. Lastly, we will report on the scalability and performance of NUMA on the leadership computing facilities (LCF) of the Department of Energy where we have scaled NUMA to over 3 million MPI threads achieving a 90% efficiency.

13. 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.

14. 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.

15. 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

16. The Space-Time Conservation Element and Solution Element Method-A New High-Resolution and Genuinely Multidimensional Paradigm for Solving Conservation Laws. 2; Numerical Simulation of Shock Waves and Contact Discontinuities

Science.gov (United States)

Wang, Xiao-Yen; Chow, Chuen-Yen; Chang, Sin-Chung

1998-01-01

Without resorting to special treatment for each individual test case, the 1D and 2D CE/SE shock-capturing schemes described previously (in Part I) are used to simulate flows involving phenomena such as shock waves, contact discontinuities, expansion waves and their interactions. Five 1D and six 2D problems are considered to examine the capability and robustness of these schemes. Despite their simple logical structures and low computational cost (for the 2D CE/SE shock-capturing scheme, the CPU time is about 2 micro-secs per mesh point per marching step on a Cray C90 machine), the numerical results, when compared with experimental data, exact solutions or numerical solutions by other methods, indicate that these schemes can accurately resolve shock and contact discontinuities consistently.

17. 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.

18. 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.

19. Enriched Element-Free Galerkin Method for Fracture Analysis of Functionally Graded Piezoelectric Materials

Directory of Open Access Journals (Sweden)

Guang Wei Meng

2015-01-01

Full Text Available A new method using the enriched element-free Galerkin method (EEFGM to model functionally graded piezoelectric materials (FGPMs with cracks was presented. To improve the solution accuracy, extended terms were introduced into the approximation function of the conventional element-free Galerkin method (EFGM to describe the displacement and electric fields near the crack. Compared with the conventional EFGM, the new approach requires smaller domain to describe the crack-tip singular field. Additionally, the domain of the nodes was not affected by the crack. Therefore, the visibility method and the diffraction method were no longer needed. The mechanical response of FGPM was discussed, when its material parameters changed exponentially in a certain direction. The modified J-integrals for FGPM were deduced, whose results were compared with the results of the conventional EFGM and the analytical solution. Numerical example results illustrated that this method is feasible and precise.

20. Time-stepping stability of continuous and discontinuous finite-element methods for 3-D wave propagation

NARCIS (Netherlands)

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

2013-01-01

We analyse the time-stepping stability for the 3-D acoustic wave equation, discretized on tetrahedral meshes. Two types of methods are considered: mass-lumped continuous finite elements and the symmetric interior-penalty discontinuous Galerkin method. Combining the spatial discretization with the

1. 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

2. kantorovich-euler lagrange-galerkin's method for bending analysis ...

African Journals Online (AJOL)

user

Lagrange differential equation is determined for this functional. The Galerkin method is then used to ... Keywords: Kantorovich-Galerkin, thin plate, potential energy functional, Euler-Lagrange differential equation. 1. INTRODUCTION. Plates are .... where R is the two dimensional plate domain., μ is the Poisson's ratio and.

3. Continuum damage growth analysis using element free Galerkin ...

This paper presents an elasto-plastic element free Galerkin formulation based on Newton–Raphson algorithm for damage growth analysis. Isotropic ductile damage evolution law is used. A study has been carried out in this paper using the proposed element free Galerkin method to understand the effect of initial damage ...

4. 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.

5. Numerical Modeling of Stokes Flow in a Circular Cavity by Variational Multiscale Element Free Galerkin Method

Directory of Open Access Journals (Sweden)

Ping Zhang

2014-01-01

Full Text Available The variational multiscale element free Galerkin method is extended to simulate the Stokes flow problems in a circular cavity as an irregular geometry. The method is combined with Hughes’s variational multiscale formulation and element free Galerkin method; thus it inherits the advantages of variational multiscale and meshless methods. Meanwhile, a simple technique is adopted to impose the essential boundary conditions which makes it easy to solve problems with complex area. Finally, two examples are solved and good results are obtained as compared with solutions of analytical and numerical methods, which demonstrates that the proposed method is an attractive approach for solving incompressible fluid flow problems in terms of accuracy and stability, even for complex irregular boundaries.

6. 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.

7. A high-order immersed boundary discontinuous-Galerkin method for Poisson's equation with discontinuous coefficients and singular sources

OpenAIRE

Brandstetter, G; Govindjee, S

2015-01-01

© 2014 John Wiley & Sons, Ltd. We adopt a numerical method to solve Poisson's equation on a fixed grid with embedded boundary conditions, where we put a special focus on the accurate representation of the normal gradient on the boundary. The lack of accuracy in the gradient evaluation on the boundary is a common issue with low-order embedded boundary methods. Whereas a direct evaluation of the gradient is preferable, one typically uses post-processing techniques to improve the quality of th...

8. 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.

9. A cubic subdomain Galerkin method over the geometrically graded mesh to the singularly perturbed problem

Science.gov (United States)

Hepson, Ozlem Ersoy; Daǧ, Idris

2018-01-01

In this paper, a subdomain Galerkin method is set up to find solutions of singularly perturbed boundary value problems which are used widely in many areas such as chemical reactor theory, aerodynamics, quantum mechanics, reaction-diffusion process, optimal control, etc. A combination of the cubic B-spline base functions as an approximation function is used to build up the presented method over the geometrically graded mesh. Thus finer mesh can be established through the end parts of the problem domain where steep solutions exist.

10. 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.

11. 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.

12. Symmetric-Galerkin BEM simulation of fracture with frictional contact

CSIR Research Space (South Africa)

Phan, AV

2003-06-14

Full Text Available A symmetric-Galerkin boundary element framework for fracture analysis with frictional contact (crack friction) on the crack surfaces is presented. The algorithm employs a continuous interpolation on the crack surface (utilizing quadratic boundary...

13. Combined Visibility and Surrounding Triangles Method for Simulation of Crack Discontinuities in Meshless Methods

Directory of Open Access Journals (Sweden)

H. Pirali

2012-01-01

Full Text Available In this paper a combined node searching algorithm for simulation of crack discontinuities in meshless methods called combined visibility and surrounding triangles (CVT is proposed. The element free Galerkin (EFG method is employed for stress analysis of cracked bodies. The proposed node searching algorithm is based on the combination of surrounding triangles and visibility methods; the surrounding triangles method is used for support domains of nodes and quadrature points generated at the vicinity of crack faces and the visibility method is used for points located on the crack faces. In comparison with the conventional methods, such as the visibility, the transparency, and the diffraction method, this method is simpler with reasonable efficiency. To show the performance of this method, linear elastic fracture mechanics analyses are performed on number of standard test specimens and stress intensity factors are calculated. It is shown that the results are in good agreement with the exact solution and with those generated by the finite element method (FEM.

14. 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.

15. Solution of the transport equation in stationary state and X Y geometry, using continuous and discontinuous hybrid nodal schemes; Solucion de la ecuacion de transporte en estado estacionario y geometria X Y, usando esquemas nodales hibridos continuos y discontinuos

Energy Technology Data Exchange (ETDEWEB)

Xolocostli M, V.; Valle G, E. del [IPN-ESFM, 07738 Mexico D.F. (Mexico); Alonso V, G. [ININ, 52045 Ocoyoacac, Estado de Mexico (Mexico)]. e-mail: xvicente@hotmail.com

2003-07-01

In this work it is described the development and the application of the NH-FEM schemes, Hybrid Nodal schemes using the Finite Element method in the solution of the neutron transport equation in stationary state and X Y geometry, of which two families of schemes were developed, one of which corresponds to the continuous and the other to the discontinuous ones, inside those first its are had the Bi-Quadratic Bi Q, and to the Bi-cubic BiC, while for the seconds the Discontinuous Bi-lineal DBiL and the Discontinuous Bi-quadratic DBiQ. These schemes were implemented in a program to which was denominated TNHXY, Transport of neutrons with Hybrid Nodal schemes in X Y geometry. One of the immediate applications of the schemes NH-FEM it will be in the analysis of assemblies of nuclear fuel, particularly of the BWR type. The validation of the TNHXY program was made with two test problems or benchmark, already solved by other authors with numerical techniques and to compare results. The first of them consists in an it BWR fuel assemble in an arrangement 7x7 without rod and with control rod providing numerical results. The second is a fuel assemble of mixed oxides (MOX) in an arrangement 10x10. This last problem it is known as the Benchmark problem WPPR of the NEA Data Bank and the results are compared with those of other commercial codes as HELIOS, MCNP-4B and CPM-3. (Author)

16. Organising medication discontinuation

DEFF Research Database (Denmark)

Nixon, Michael; Kousgaard, Marius Brostrøm

2016-01-01

Background: 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 m...

17. Local derivative post-processing : Challenges for a non-uniform mesh

NARCIS (Netherlands)

Ryan, J.K.

2010-01-01

Previous investigations into accuracy enhancement for the derivatives of a discontinuous Galerkin solution demonstrated that there are many ways to approach obtaining higher order accuracy in the derivatives, each with different advantageous properties. For the discontinuous Galerkin method, the

18. 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

19. Exploiting Superconvergence in Discontinuous Galerkin Methods for Improved Time-Stepping and Visualization

Science.gov (United States)

2016-09-08

ADDRESS(ES) EOARD Unit 4515 APO AE 09421-4515 10.  SPONSOR/MONITOR’S ACRONYM(S) AFRL/AFOSR IOE 11.  SPONSOR/MONITOR’S REPORT       NUMBER(S) AFRL-AFOSR-UK...between the DG mesh and kernel mesh. When the theory was investigated, it was determined that a tensor product filter was not necessary for multi

20. Accuracy, resolution, and computational complexity of a discontinuous Galerkin finite element method

NARCIS (Netherlands)

van der Ven, H.; van der Vegt, Jacobus J.W.; Cockburn, B.; Karniadakis, G.E.; Shu, C.W.

2000-01-01

This series contains monographs of lecture notes type, lecture course material, and high-quality proceedings on topics described by the term "computational science and engineering". This includes theoretical aspects of scientific computing such as mathematical modeling, optimization methods,

1. Localized Artificial Viscosity Stabilization of Discontinuous Galerkin Methods for Nonhydrostatic Mesoscale Atmospheric Modeling

Science.gov (United States)

2014-01-01

modeling 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7...Four resolutions, namely, 400m , 200m, 100m and 50m, are used in the simulations. In Ref. [2], a constant dynamic viscosity is used to ensure a grid...polynomial orders. The effects of on flow field features are studied with P! reconstruction on both 8×2 (i.e., 400m resolution) and 64×16 meshes (i.e

2. High-order discontinuous Galerkin nonlocal transport and energy equations scheme for radiation hydrodynamics

Czech Academy of Sciences Publication Activity Database

Holec, M.; Limpouch, J.; Liska, R.; Weber, Stefan A.

2017-01-01

Roč. 83, č. 10 (2017), s. 779-797 ISSN 0271-2091 R&D Projects: GA MŠk EF15_008/0000162; GA MŠk LQ1606 Grant - others:ELI Beamlines(XE) CZ.02.1.01/0.0/0.0/15_008/0000162 Institutional support: RVO:68378271 Keywords : radiation hydrodynamics * nonlocal transport * Knudsen number * multigroup diffusion * radiation coupling Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders OBOR OECD: Nuclear physics Impact factor: 1.652, year: 2016

3. Application of Parallel Time-Implicit Discontinuous Galerkin Finite Element Methods to Hypersonic Nonequilibrium Flow Problems

Science.gov (United States)

2014-05-01

govindah sarva karana-karanam - Brahma Samhita 5.1 “Krsna who is known as Govinda is the Supreme Godhead. He has an eternal blissful spiritual body. He is...density ablators, for meaningful model comparison. Architecture of the material is chosen such that the material can be easily manufactured but is

4. Towards Next Generation Ocean Models: Novel Discontinuous Galerkin Schemes for 2D Unsteady Biogeochemical Models

Science.gov (United States)

2009-09-01

FVCOM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.7 ICOM ...coastal re- gions featured with complex irregular geometry and steep bottom topography. ICOM Imperial College Ocean Model FEM (CG and DG) using...the ICOM group. This code is written in C. Finel was also developed by the same group, and it is a three-dimensional non- hydrostatic finite element

5. Variational space–time (dis)continuous Galerkin method for nonlinear free surface water waves

NARCIS (Netherlands)

Gagarina, Elena; Ambati, V.R.; van der Vegt, Jacobus J.W.; Bokhove, Onno

2014-01-01

A new variational finite element method is developed for nonlinear free surface gravity water waves using the potential flow approximation. This method also handles waves generated by a wave maker. Its formulation stems from Miles’ variational principle for water waves together with a finite element

6. Variational space-time (dis)continuous Galerkin method for nonlinear free surface waves

NARCIS (Netherlands)

Gagarina, Elena; van der Vegt, Jacobus J.W.; Ambati, V.R.; Bokhove, Onno

A new variational finite element method is developed for nonlinear free surface gravity water waves. This method also handles waves generated by a wave maker. Its formulation stems from Miles' variational principle for water waves together with a space-time finite element discretization that is

7. Large-eddy simulations of a S826 airfoil with the Discontinuous Galerkin Method

DEFF Research Database (Denmark)

Frère, A.; Chivaee, Hamid Sarlak; Mikkelsen, Robert Flemming

2014-01-01

, however, partially explained by the strong sensitivity to the tunnel environment. To overcome this source of error, the ArgoDG LES results are also compared to LES performed with the Finite Volume Method (FVM) code EllipSys3D, a well established wind turbine Computational Fluid Dynamics (CFD) code....... The similarity of the results obtained by these two inherently different methodologies provide strong confidence in the validity of the computations....

8. A discontinuous Galerkin finite element discretization of the Euler equations for compressible and incompressible fluids

NARCIS (Netherlands)

Pesch, L.; van der Vegt, Jacobus J.W.

2008-01-01

Using the generalized variable formulation of the Euler equations of fluid dynamics, we develop a numerical method that is capable of simulating the flow of fluids with widely differing thermodynamic behavior: ideal and real gases can be treated with the same method as an incompressible fluid. The

9. A Study into Discontinuous Galerkin Methods for the Second Order Wave Equation

Science.gov (United States)

2015-06-01

qRw = qn ( Rs , 1 , 1 ) ; 17 dpL = D*qn ( Ls , : , 2 ) ’ ; dpL = dpL ( ngl ) ; 19 dpR = D*qn ( Rs , : , 2 ) ’ ; dpR = dpR ( 1 ) ; 21 wf ( s , : ) = ( 1...2 ) * (qLw + qRw) ; 23 dpf ( s , : ) = ( 1 / 2 ) * ( dpL + dpR) ; end 25 end 1...13 Rs = sidep ( 2 , s ) ; 15 qLw = qn ( Ls , ngl , 1 ) ; qRw = qn ( Rs , 1 , 1 ) ; 17 dpL = D*qn ( Ls , : , 2 ) ’ ; 19 dpL = dpL ( ngl ) ; dpR = D*qn

10. A Moving Discontinuous Galerkin Finite Element Method for Flows with Interfaces

Science.gov (United States)

2017-12-07

cuboid elements. In general, the method works in conjunction with standard local grid operations, including edge collapse, to ensure that degenerate...Shock: Line Plots............................................................................................ 31 iv TABLES 1 Intersecting Oblique...standard local grid operations including edge collapse, cf. [62], while in order to maintain a sufficient level of refinement, remaining cells can be refined

11. Space-time discontinuous Galerkin finite element method for two-fluid flows

NARCIS (Netherlands)

Sollie, W.E.H.

2010-01-01

Multifluid and multiphase flows involve combinations of fluids and interfaces which separate these. These flows are of importance in many natural and industrial processes including fluidized beds and bubble columns. Often the interface is not static but moves with the fluid flow velocity. Also,

12. Discontinuous Galerkin Finite Element Methods for the Navier-Stokes Equations in Entropy Variable Formulation

NARCIS (Netherlands)

Pesch, L.

2007-01-01

Many numerical methods for fluid dynamics are suitable only for a single, idealized type of fluid. Most prominently, algorithms for compressible flow are often tailored to ideal gases and another class of schemes is designed for incompressible media. This dissertation targets a numerical method for

13. Extension of a discontinuous Galerkin finite element method to viscous rotor flow simulations

NARCIS (Netherlands)

van der Ven, H.; Boelens, O.J.; Klaij, C.M.; van der Vegt, Jacobus J.W.

2005-01-01

Heavy vibratory loading of rotorcraft is relevant for many operational aspects of helicopters, such as the structural life span of (rotating) components, op- erational availability, the pilot’s comfort, and the ef- fectiveness of weapon targeting systems. A precise understanding of the source of

14. Extension of a discontinuous Galerkin finite element method to viscous rotor flow simulations

NARCIS (Netherlands)

van der Ven, H.; Boelens, O.J.; Boelens, O.J.; Klaij, C.M.; van der Vegt, Jacobus J.W.

2005-01-01

Heavy vibratory loading of rotorcraft is relevant for many operational aspects of helicopters, such as the structural life span of (rotating) components, operational availability, the pilot's comfort, and the effectiveness of weapon targeting systems. A precise understanding of the source of these

15. A leap-frog discontinuous Galerkin time-domain method of analyzing electromagnetic scattering problems

Science.gov (United States)

Cui, Xue-Wu; Yang, Feng; Zhou, Long-Jian; Gao, Min; Yan, Fei; Liang, Zhi-Peng

2017-09-01

Not Available Project supported by the National Natural Science Foundation of China (Grant Nos. 61301056 and 11176007), the Sichuan Provincial Science and Technology Support Program, China (Grant No. 2013HH0047), the Fok Ying Tung Education Foundation, China (Grant No. 141062), and the “111” Project, China (Grant No. B07046).

16. 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.

17. 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

18. 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

19. Numerical solution of fuzzy boundary value problems using Galerkin ...

point FBVPs. Nonhomogeneous FBVPs using collocation method has been studied by Mohammed and. Fadhel [16]. Jamshidi and Avazpour [17] applied shooting method for second-order fuzzy boundary value problems. (SOFBVPs) under ...

20. Numerical solution of fuzzy boundary value problems using Galerkin ...

, China; Department of Mathematics, Kalinga Institute of Industrial Technology, Bhubaneswar, Odisha 751 024, India; Department of Mathematics, National Institute of Technology, Rourkela, Odisha 769 008, India; Department of Mathematics, ...

1. Numerical solution of fuzzy boundary value problems using Galerkin ...

Home; Journals; Sadhana; Volume 42; Issue 1 ... College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China; Department of Mathematics, Kalinga Institute of Industrial Technology, Bhubaneswar, Odisha 751 024, India; Department of Mathematics, National Institute of Technology, Rourkela, ...

2. A well-posed and stable stochastic Galerkin formulation of the incompressible Navier-Stokes equations with random data

Science.gov (United States)

Pettersson, Per; Nordström, Jan; Doostan, Alireza

2016-02-01

We present a well-posed stochastic Galerkin formulation of the incompressible Navier-Stokes equations with uncertainty in model parameters or the initial and boundary conditions. The stochastic Galerkin method involves representation of the solution through generalized polynomial chaos expansion and projection of the governing equations onto stochastic basis functions, resulting in an extended system of equations. A relatively low-order generalized polynomial chaos expansion is sufficient to capture the stochastic solution for the problem considered. We derive boundary conditions for the continuous form of the stochastic Galerkin formulation of the velocity and pressure equations. The resulting problem formulation leads to an energy estimate for the divergence. With suitable boundary data on the pressure and velocity, the energy estimate implies zero divergence of the velocity field. Based on the analysis of the continuous equations, we present a semi-discretized system where the spatial derivatives are approximated using finite difference operators with a summation-by-parts property. With a suitable choice of dissipative boundary conditions imposed weakly through penalty terms, the semi-discrete scheme is shown to be stable. Numerical experiments in the laminar flow regime corroborate the theoretical results and we obtain high-order accurate results for the solution variables and the velocity divergence converges to zero as the mesh is refined.

3. 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.

4. Application of Galerkin's method for calculating boiling water reactor limit-cycle amplitude using the LAPUR feedback-transfer function and the point-kinetics equations

International Nuclear Information System (INIS)

Damiano, B.; March-Leuba, J.A.; Euler, J.A.

1990-01-01

This paper describes a technique for calculating boiling water reactor (BWR) behavior during steady-state limit-cycle oscillations. An approximate solution is obtained from the application of Galerkin's method to a BWR dynamic model consisting of the point-kinetics equations and the LAPUR-calculated power-to-reactivity feedback-transfer function. The approximate-solution technique is described, and comparisons of approximate solutions with numerical results and measured data are given. 7 refs., 5 figs

5. Galerkin projection methods for solving multiple related linear systems

Energy Technology Data Exchange (ETDEWEB)

Chan, T.F.; Ng, M.; Wan, W.L.

1996-12-31

We consider using Galerkin projection methods for solving multiple related linear systems A{sup (i)}x{sup (i)} = b{sup (i)} for 1 {le} i {le} s, where A{sup (i)} and b{sup (i)} are different in general. We start with the special case where A{sup (i)} = A and A is symmetric positive definite. The method generates a Krylov subspace from a set of direction vectors obtained by solving one of the systems, called the seed system, by the CG method and then projects the residuals of other systems orthogonally onto the generated Krylov subspace to get the approximate solutions. The whole process is repeated with another unsolved system as a seed until all the systems are solved. We observe in practice a super-convergence behaviour of the CG process of the seed system when compared with the usual CG process. We also observe that only a small number of restarts is required to solve all the systems if the right-hand sides are close to each other. These two features together make the method particularly effective. In this talk, we give theoretical proof to justify these observations. Furthermore, we combine the advantages of this method and the block CG method and propose a block extension of this single seed method. The above procedure can actually be modified for solving multiple linear systems A{sup (i)}x{sup (i)} = b{sup (i)}, where A{sup (i)} are now different. We can also extend the previous analytical results to this more general case. Applications of this method to multiple related linear systems arising from image restoration and recursive least squares computations are considered as examples.

6. Problems with Discontinuous Diffusion/Dispersion Coefficients

Directory of Open Access Journals (Sweden)

Stefano Ferraris

2012-01-01

accurate on smooth solutions and based on a special numerical treatment of the diffusion/dispersion coefficients that makes its application possible also when such coefficients are discontinuous. Numerical experiments confirm the convergence of the numerical approximation and show a good behavior on a set of benchmark problems in two space dimensions.

7. Free discontinuity problems

CERN Document Server

Pratelli, Aldo

2016-01-01

This book presents a series of lectures on three of the best known examples of free discontinuity problems: the Mumford-Shah model for image segmentation, a variational model for the epitaxial growth of thin films, and the sharp interface limit of the Ohta-Kawasaki model for pattern formation in dyblock copolymers.

8. Kantorovich-Euler Lagrange-Galerkin's method for bending analysis ...

African Journals Online (AJOL)

The Euler-Lagrange differential equation is determined for this functional. The Galerkin method is then used to obtain the unknown function f(x). Bending moment curvature relations are used to find the bending moments and their extreme values. The results obtained agree remarkably well with literature. The effectiveness ...

9. 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.

10. Convergence of Crank-Nicolson-Galerkin discrete scheme for ...

African Journals Online (AJOL)

We studied the maximum-norm error estimate for the Galerkin finite element discretization in time of a stochastic wave equation by the Crank-Nicolson time stepping finite difference method. The error estimate was obtained by using the notions of rational function and resolvent estimates.

11. Discontinuous finite element and characteristics methods for neutrons transport equation solution in heterogeneous grids; Resolution de l'equation du transport des neutrons par les methodes des elements finis discontinus et des caracteristiques structurees appliquees a des maillages heterogenes

Energy Technology Data Exchange (ETDEWEB)

Masiello, E

2006-07-01

The principal goal of this manuscript is devoted to the investigation of a new type of heterogeneous mesh adapted to the shape of the fuel pins (fuel-clad-moderator). The new heterogeneous mesh guarantees the spatial modelling of the pin-cell with a minimum of regions. Two methods are investigated for the spatial discretization of the transport equation: the discontinuous finite element method and the method of characteristics for structured cells. These methods together with the new representation of the pin-cell result in an appreciable reduction of calculation points. They allow an exact modelling of the fuel pin-cell without spatial homogenization. A new synthetic acceleration technique based on an angular multigrid is also presented for the speed up of the inner iterations. These methods are good candidates for transport calculations for a nuclear reactor core. A second objective of this work is the application of method of characteristics for non-structured geometries to the study of double heterogeneity problem. The letters is characterized by fuel material with a stochastic dispersion of heterogeneous grains, and until now was solved with a model based on collision probabilities. We propose a new statistical model based on renewal-Markovian theory, which makes possible to take into account the stochastic nature of the problem and to avoid the approximations of the collision probability model. The numerical solution of this model is guaranteed by the method of characteristics. (author)

12. Theory and observation of double discontinuities

Directory of Open Access Journals (Sweden)

Y. C. Whang

2004-01-01

Full Text Available Recent research using high-resolution magnetic field data to examine the interior structures of MHD shocks in interplanetary space and in the magnetotail led to a surprising discovery that a slow-mode shock is often followed by an adjoining rotational discontinuity layer on the postshock side. The thickness of each layer is of the order of a few ion inertial lengths. Such a compound structure is known as a double discontinuity. When the magnetic field rotates by several degrees per ion inertial length inside a thin layer, the Hall current term becomes important in the generalized Ohm's law. Steady state solutions based on the Hall-MHD theory have been obtained to show the merging of a rotational layer and a slow shock layer to form a compound structure like the observed double discontinuities.

13. IS DISCONTINUOUS BERGSONISM POSSIBLE?

Directory of Open Access Journals (Sweden)

TERESA CASTELÃO-LAWLESS

2010-11-01

Full Text Available Gaston Bachelard’s position toward the philosophy of Henri Bergson is most interesting. In La Dialectique de la durée (1936, Bachelard claims that “of Bergsonism we accept everything but continuity” and that the rest of his book will be an attempt to show the possibility of a “discontinuous Bergsonism”. In this paper, I focus on the reaction of Bachelard to works of Bergson such as the Essai sur les données immédiates de la conscience (1889, L’Evolution créatrice (1907, and Durée et simultanéité: à propos de la théorie d’Einstein (1922 and demonstrate that even though the conditions necessary for the possibility of a discontinuous Bergsonism are not the same ones which Bachelard had in mind when he accepted most of Bergsonism, their phenomenologies of the scientific spirit were analogous.

14. 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.

15. 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 $\\mathbb{S}^2$.

16. 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

17. Imposition of Dirichlet Boundary Conditions in Element Free Galerkin Method through an Object-Oriented Implementation

Directory of Open Access Journals (Sweden)

Samira Hosseini

Full Text Available Abstract One of the main drawbacks of Element Free Galerkin (EFG method is its dependence on moving least square shape functions which don’t satisfy the Kronecker Delta property, so in this method it’s not possible to apply Dirichlet boundary conditions directly. The aim of the present paper is to discuss different aspects of three widely used methods of applying Dirichlet boundary conditions in EFG method, called Lagrange multipliers, penalty method, and coupling with finite element method. Numerical simulations are presented to compare the results of these methods form the perspective of accuracy, convergence and computational expense. These methods have been implemented in an object oriented programing environment, called INSANE, and the results are presented and compared with the analytical solutions.

18. The use of Galerkin finite-element methods to solve mass-transport equations

Science.gov (United States)

Grove, David B.

1977-01-01

The partial differential equation that describes the transport and reaction of chemical solutes in porous media was solved using the Galerkin finite-element technique. These finite elements were superimposed over finite-difference cells used to solve the flow equation. Both convection and flow due to hydraulic dispersion were considered. Linear and Hermite cubic approximations (basis functions) provided satisfactory results: however, the linear functions were computationally more efficient for two-dimensional problems. Successive over relaxation (SOR) and iteration techniques using Tchebyschef polynomials were used to solve the sparce matrices generated using the linear and Hermite cubic functions, respectively. Comparisons of the finite-element methods to the finite-difference methods, and to analytical results, indicated that a high degree of accuracy may be obtained using the method outlined. The technique was applied to a field problem involving an aquifer contaminated with chloride, tritium, and strontium-90. (Woodard-USGS)

19. A numerical investigation of the GRLW equation using lumped Galerkin approach with cubic B-spline.

Science.gov (United States)

Zeybek, Halil; Karakoç, S Battal Gazi

2016-01-01

In this work, we construct the lumped Galerkin approach based on cubic B-splines to obtain the numerical solution of the generalized regularized long wave equation. Applying the von Neumann approximation, it is shown that the linearized algorithm is unconditionally stable. The presented method is implemented to three test problems including single solitary wave, interaction of two solitary waves and development of an undular bore. To prove the performance of the numerical scheme, the error norms [Formula: see text] and [Formula: see text] and the conservative quantities [Formula: see text], [Formula: see text] and [Formula: see text] are computed and the computational data are compared with the earlier works. In addition, the motion of solitary waves is described at different time levels.

20. Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients⋆⋆⋆

Directory of Open Access Journals (Sweden)

Tempone R.

2011-12-01

Full Text Available 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.

1. The meshless Galerkin method for pressure distribution simulation of horizontal well reservoir

Directory of Open Access Journals (Sweden)

Shuyong Hu

2015-06-01

Full Text Available This paper provides a novel three-dimensional meshless Galerkin for horizontal well reservoir simulation. The pressure function is approached by moving least-square method which consists of weight function, basic function and coefficient. Based on Galerkin principle and use penalty function method, the paper deduces the meshless Galerkin numerical linear equations. Cut off the pressure distribution of the horizontal section from the simulation database of horizontal well reservoir. It demonstrates that meshless Galerkin is a feasible numerical method for the horizontal well reservoir simulation. It is useful to research complex reservoir.

2. Element-Free Galerkin Method Based on Block-Pulse Wavelets Integration for Solving Fourth-Order Obstacle Problem

Directory of Open Access Journals (Sweden)

2013-01-01

Full Text Available We introduce improved element-free Galerkin method based on block pulse wavelet integration for numerical approximations to the solution of a system of fourth-order boundary-value problems associated with obstacle, unilateral, and contact problems. Moving least squares (MLS approach is used to construct shape functions with optimized weight functions and basis. Numerical results for test problems are presented in this article to elaborate the pertinent features for the proposed technique. Comparison with existing techniques shows that our proposed method based on integration technique provides better approximation at reduced computational cost.

3. Extended displacement discontinuity method for analysis of cracks in 2D thermal piezoelectric semiconductors

Science.gov (United States)

Zhao, MingHao; Pan, YiBo; Fan, CuiYing; Xu, GuangTao

2017-08-01

The extended displacement discontinuities method has previously been used for crack analysis of elastic materials, piezoelectric media, magneto-electro-elastic media and piezoelectric semiconductors. Here, this method is extended to study cracks in two-dimensional n-type thermal piezoelectric semiconductors. The extended displacement discontinuities include the conventional displacement discontinuity, electric potential discontinuity, carrier density discontinuity, as well as temperature discontinuity across crack faces; correspondingly, the extended stresses represent conventional stress, electric displacement, electric current, and heat flux. Employing a Fourier transform, the fundamental solutions for a line crack under uniformly distributed extended displacement discontinuities on the crack faces are derived under mechanical, electrical, and heat loading. Based on the obtained fundamental solutions, an extended displacement discontinuity boundary element method is developed. The stress and heat flux intensity factors at the crack tip are calculated under different combined loadings.

4. Discontinious Galerkin formulations for thin bending problems

NARCIS (Netherlands)

Nguyen, T.D.

2008-01-01

A structural thin bending problem is essentially associated with a fourth-order partial differential equation. Within the finite element framework, the numerical solution of thin bending problems demands the use of C^1 continuous shape functions. Elements using these functions are challenging and

5. Solution of the Neutron transport equation in hexagonal geometry using strongly discontinuous nodal schemes; Solucion de la Ecuacion de transporte de neutrones en geometria hexagonal usando esquemas nodales fuertemente discontinuos

Energy Technology Data Exchange (ETDEWEB)

Mugica R, C.A.; Valle G, E. del [IPN, ESFM, Departamento de Ingenieria Nuclear, 07738 Mexico D.F. (Mexico)]. e-mail: cmugica@ipn.mx

2005-07-01

In 2002, E. del Valle and Ernest H. Mund developed a technique to solve numerically the Neutron transport equations in discrete ordinates and hexagonal geometry using two nodal schemes type finite element weakly discontinuous denominated WD{sub 5,3} and WD{sub 12,8} (of their initials in english Weakly Discontinuous). The technique consists on representing each hexagon in the union of three rhombuses each one of which it is transformed in a square in the one that the methods WD{sub 5,3} and WD{sub 12,8} were applied. In this work they are solved the mentioned equations of transport using the same discretization technique by hexagon but using two nodal schemes type finite element strongly discontinuous denominated SD{sub 3} and SD{sub 8} (of their initials in english Strongly Discontinuous). The application in each case as well as a reference problem for those that results are provided for the effective multiplication factor is described. It is carried out a comparison with the obtained results by del Valle and Mund for different discretization meshes so much angular as spatial. (Author)

6. One-dimensional Galerkin methods and superconvergence at interior nodal points

NARCIS (Netherlands)

M. Bakker (Miente)

1984-01-01

htmlabstractIn the case of one-dimensional Galerkin methods the phenomenon of superconvergence at the knots has been known for years [5], [7]. In this paper, a minor kind of superconvergence at specific points inside the segments of the partition is discussed for two classes of Galerkin methods: the

7. 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

8. 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...

9. 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

10. 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

11. 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

12. 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

13. Bearing Capacity Analysis Using Meshless Local Petrov-Galerkin Method

Directory of Open Access Journals (Sweden)

Mužík Juraj

2014-05-01

Full Text Available The paper deals with use of the meshless method for soil bearing capacity analysis. There are many formulations of the meshless methods. The article presents the Meshless Local Petrov-Galerkin method (MLPG - local weak formulation of the equilibrium equations. The main difference between meshless methods and the conventional finite element method (FEM is that meshless shape functions are constructed using randomly scattered set of points without any relation between points. The Heaviside step function is test function used in the meshless implementation presented in the article. Heaviside test function makes weak formulation integral very simple, because only body integral in governing equation is due a body force.

14. 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.

15. Galerkin method for feedback controlled Rayleigh Bénard convection

Science.gov (United States)

Münch, A.; Wagner, B.

2008-11-01

The problem of feedback controlled Rayleigh-Bénard convection is considered. For this problem with the simple flow structure in the vertical direction, a Galerkin method that uses only a few basis functions in this direction is presented. This approximation yields considerable simplification of the problem, explicitly incorporates the non-classical boundary conditions at the horizontal boundaries of the fluid layer resulting from feedback control and reduces the dimension of the original problem by one. This method is in spirit very similar to lubrication theory, where the simple laminar flow in the vertical direction is integrated out across the height of the fluid layer. Using a minimal set of appropriate basis functions to capture the nonlinear behaviour of the flow, we investigate the effects of feedback control on amplitude, wavelength and selection of patterns via weakly nonlinear analysis and numerical simulations of the resulting dimension-reduced problems in two and three dimensions. In the second part of this study we discuss the derivation of the appropriate basis functions and prove convergence of the Galerkin scheme. This paper is published as part of a collection in honour of Todd Dupont's 65th birthday.

16. ODEs with Preisach operator under the derivative and with discontinuous in time right-hand side

International Nuclear Information System (INIS)

Zhezherun, A; Flynn, D

2006-01-01

We consider ordinary Differential equations with a Preisach operator under the derivative. A special case when the right-hand side has discontinuities in time is studied. We present theorems about the existence and uniqueness of solutions. We also prove a theorem which describes the behavior of a solution at the points of discontinuity of the right-hand side

17. 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.

18. Boundary element computations in the forward and inverse problems of electrocardiography: comparison of collocation and Galerkin weightings.

Science.gov (United States)

Stenroos, Matti; Haueisen, Jens

2008-09-01

In electrocardiographic imaging, epicardial potentials are reconstructed computationally from electrocardiographic measurements. The reconstruction is typically done with the help of the boundary element method (BEM), using the point collocation weighting and constant or linear basis functions. In this paper, we evaluated the performance of constant and linear point collocation and Galerkin BEMs in the epicardial potential problem. The integral equations and discretizations were formulated in terms of the single- and double-layer operators. All inner element integrals were calculated analytically. The computational methods were validated against analytical solutions in a simplified geometry. On the basis of the validation, no method was optimal in all testing scenarios. In the forward computation of the epicardial potential, the linear Galerkin (LG) method produced the smallest errors. The LG method also produced the smallest discretization error on the epicardial surface. In the inverse computation of epicardial potential, the electrode-specific transfer matrix performed better than the full transfer matrix. The Tikhonov 2 regularization outperformed the Tikhonov 0. In the optimal modeling conditions, the best BEM technique depended on electrode positions and chosen error measure. When large modeling errors such as omission of the lungs were present, the choice of the basis and weighting functions was not significant.

19. Thermo-mechanical nonlinear vibration analysis of fluid-conveying structures subjected to different boundary conditions using Galerkin-Newton-Harmonic balancing method

Directory of Open Access Journals (Sweden)

Gbeminiyi Sobamowo

2017-04-01

Full Text Available The development of mathematical models for describing the dynamic behaviours of fluid conveying pipes, micro-pipes and nanotubes under the influence of some thermo-mechanical parameters results into nonlinear equations that are very difficult to solve analytically. In cases where the exact analytical solutions are presented either in implicit or explicit forms, high skills and rigorous mathematical analyses were employed. It is noted that such solutions do not provide general exact solutions. Inevitably, comparatively simple, flexible yet accurate and practicable solutions are required for the analyses of these structures. Therefore, in this study, approximate analytical solutions are provided to the nonlinear equations arising in flow-induced vibration of pipes, micro-pipes and nanotubes using Galerkin-Newton-Harmonic Method (GNHM. The developed approximate analytical solutions are shown to be valid for both small and large amplitude oscillations. The accuracies and explicitness of these solutions were examined in limiting cases to establish the suitability of the method.

20. On the optimal polynomial approximation of stochastic PDEs by galerkin and collocation methods

KAUST Repository

Beck, Joakim

2012-09-01

In this work we focus on the numerical approximation of the solution u of a linear elliptic PDE with stochastic coefficients. The problem is rewritten as a parametric PDE and the functional dependence of the solution on the parameters is approximated by multivariate polynomials. We first consider the stochastic Galerkin method, and rely on sharp estimates for the decay of the Fourier coefficients of the spectral expansion of u on an orthogonal polynomial basis to build a sequence of polynomial subspaces that features better convergence properties, in terms of error versus number of degrees of freedom, than standard choices such as Total Degree or Tensor Product subspaces. We consider then the Stochastic Collocation method, and use the previous estimates to introduce a new 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. Numerical results show the effectiveness of the newly introduced polynomial spaces and sparse grids. © 2012 World Scientific Publishing Company.

1. On the sharpness of a superconvergence estimate in connection with one-dimensional Galerkin methods

Directory of Open Access Journals (Sweden)

Goebbels StJ

1999-01-01

Full Text Available The present paper studies some aspects of approximation theory in the context of one-dimensional Galerkin methods. The phenomenon of superconvergence at the knots is well-known. Indeed, for smooth solutions the rate of convergence at these points is instead of , where is the degree of the finite element space. In order to achieve a corresponding result for less smooth functions, we apply K-functional techniques to a Jackson-type inequality and estimate the relevant error by a modulus of continuity. Furthermore, this error estimate requires no additional assumptions on the solution, and it turns out that it is sharp in connection with general Lipschitz classes. The proof of the sharpness is based upon a quantitative extension of the uniform boundedness principle in connection with some ideas of Douglas and Dupont [Numer. Math. 22] (1974 99–109. Here it is crucial to design a sequence of test functions such that a Jackson–Bernstein-type inequality and a resonance condition are satisfied simultaneously.

2. Shock Capturing with PDE-Based Artificial Viscosity for an Adaptive, Higher-Order Discontinuous Galerkin Finite Element Method

National Research Council Canada - National Science Library

Barter, Garrett E

2008-01-01

...), adaptive computational fluid dynamics (CFD). Since these cases involve flow velocities greater than the speed of sound, an appropriate shock capturing for higher-order, adaptive methods is necessary...

3. Implicit filtered P{sub N} for high-energy density thermal radiation transport using discontinuous Galerkin finite elements

Energy Technology Data Exchange (ETDEWEB)

Laboure, Vincent M., E-mail: vincent.laboure@tamu.edu [Nuclear Engineering Department, Texas A& M University, College Station, TX 77843 (United States); McClarren, Ryan G., E-mail: rgm@tamu.edu [Nuclear Engineering Department, Texas A& M University, College Station, TX 77843 (United States); Hauck, Cory D., E-mail: hauckc@ornl.gov [Computational and Applied Mathematics Group, Oak Ridge National Laboratory, Oak Ridge, TN 37831 (United States); Department of Mathematics, University of Tennessee Knoxville, TN 37996-1320 (United States)

2016-09-15

In this work, we provide a fully-implicit implementation of the time-dependent, filtered spherical harmonics (FP{sub N}) equations for non-linear, thermal radiative transfer. We investigate local filtering strategies and analyze the effect of the filter on the conditioning of the system, showing in particular that the filter improves the convergence properties of the iterative solver. We also investigate numerically the rigorous error estimates derived in the linear setting, to determine whether they hold also for the non-linear case. Finally, we simulate a standard test problem on an unstructured mesh and make comparisons with implicit Monte Carlo (IMC) calculations.

4. 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.

5. 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.

6. SOLUTIONING

Directory of Open Access Journals (Sweden)

Maria de Hoyos Guajardo, Ph.D. Candidate, M.Sc., B.Eng.

2004-11-01

Full Text Available The theory that is presented below aims to conceptualise how a group of undergraduate students tackle non-routine mathematical problems during a problem-solving course. The aim of the course is to allow students to experience mathematics as a creative process and to reflect on their own experience. During the course, students are required to produce a written ‘rubric’ of their work, i.e., to document their thoughts as they occur as well as their emotionsduring the process. These ‘rubrics’ were used as the main source of data.Students’ problem-solving processes can be explained as a three-stage process that has been called ‘solutioning’. This process is presented in the six sections below. The first three refer to a common area of concern that can be called‘generating knowledge’. In this way, generating knowledge also includes issues related to ‘key ideas’ and ‘gaining understanding’. The third and the fourth sections refer to ‘generating’ and ‘validating a solution’, respectively. Finally, once solutions are generated and validated, students usually try to improve them further before presenting them as final results. Thus, the last section deals with‘improving a solution’. Although not all students go through all of the stages, it may be said that ‘solutioning’ considers students’ main concerns as they tackle non-routine mathematical problems.

7. Adaptive Wavelet Galerkin Methods on Distorted Domains: Setup of the Algebraic System

Science.gov (United States)

2000-01-01

Lipschitz domain Q C Rn (n > 1), its numerical approximation by a variational method (Galerkin, Petrov-Galerkin, weighted residuals, ... ) requires the...an adaptive approximation di ,of of Remark 2. The construction of A* according to (13) seems to require the explicit knowledge of all the (infinite...Istituto di Analisi Numerica del C.N.R. in Pavia, Italy. References 1. Barinka, A., T. Barsch, P. Charton, A. Cohen, S. Dahlke, W. Dahmen, and K. Urban

8. Occupy the Financial Niche – Saturation and Crisis (discontinuous decisions

Directory of Open Access Journals (Sweden)

Ionut PURICA

2014-09-01

Full Text Available The model presented is proposing an approach that could verify the nonlinear behaviour during a crisis, such that to quantify and predict potential discontinuous behaviour. In this case, the crisis behaviour associated with financial funds reallocation among various credit instruments, described as memes with the sense of Dawkins, is shown to be of discontinuous nature stemming from a logistic penetration in the financial behaviour niche. Actually the logistic penetration is typical in creating cyclic behaviour of economic structures as shown by Marchetti and others from IIASA. A Fokker-Planck equation description results in a stationary solution having a bifurcation like solution with evolution trajectories on a ‘cusp’ type catastrophe that may describe discontinuous decision behaviour

9. Wavelet-based regularization of the Galerkin truncated three-dimensional incompressible Euler flows.

Science.gov (United States)

Farge, Marie; Okamoto, Naoya; Schneider, Kai; Yoshimatsu, Katsunori

2017-12-01

We present numerical simulations of the three-dimensional Galerkin truncated incompressible Euler equations that we integrate in time while regularizing the solution by applying a wavelet-based denoising. For this, at each time step, the vorticity field is decomposed into wavelet coefficients, which are split into strong and weak coefficients, before reconstructing them in physical space to obtain the corresponding coherent and incoherent vorticities. Both components are multiscale and orthogonal to each other. Then, by using the Biot-Savart kernel, one obtains the coherent and incoherent velocities. Advancing the coherent flow in time, while filtering out the noiselike incoherent flow, models turbulent dissipation and corresponds to an adaptive regularization. To track the flow evolution in both space and scale, a safety zone is added in wavelet coefficient space to the coherent wavelet coefficients. It is shown that the coherent flow indeed exhibits an intermittent nonlinear dynamics and a k^{-5/3} energy spectrum, where k is the wave number, characteristic of three-dimensional homogeneous isotropic turbulence. Finally, we compare the dynamical and statistical properties of Euler flows subjected to four kinds of regularizations: dissipative (Navier-Stokes), hyperdissipative (iterated Laplacian), dispersive (Euler-Voigt), and wavelet-based regularizations.

10. Numerical Analysis of an H1-Galerkin Mixed Finite Element Method for Time Fractional Telegraph Equation

Directory of Open Access Journals (Sweden)

Jinfeng Wang

2014-01-01

Full Text Available We discuss and analyze an H1-Galerkin mixed finite element (H1-GMFE method to look for the numerical solution of time fractional telegraph equation. We introduce an auxiliary variable to reduce the original equation into lower-order coupled equations and then formulate an H1-GMFE scheme with two important variables. We discretize the Caputo time fractional derivatives using the finite difference methods and approximate the spatial direction by applying the H1-GMFE method. Based on the discussion on the theoretical error analysis in L2-norm for the scalar unknown and its gradient in one dimensional case, we obtain the optimal order of convergence in space-time direction. Further, we also derive the optimal error results for the scalar unknown in H1-norm. Moreover, we derive and analyze the stability of H1-GMFE scheme and give the results of a priori error estimates in two- or three-dimensional cases. In order to verify our theoretical analysis, we give some results of numerical calculation by using the Matlab procedure.

11. Numerical Analysis of an H 1-Galerkin Mixed Finite Element Method for Time Fractional Telegraph Equation

Science.gov (United States)

Wang, Jinfeng; Zhao, Meng; Zhang, Min; Liu, Yang; Li, Hong

2014-01-01

We discuss and analyze an H 1-Galerkin mixed finite element (H 1-GMFE) method to look for the numerical solution of time fractional telegraph equation. We introduce an auxiliary variable to reduce the original equation into lower-order coupled equations and then formulate an H 1-GMFE scheme with two important variables. We discretize the Caputo time fractional derivatives using the finite difference methods and approximate the spatial direction by applying the H 1-GMFE method. Based on the discussion on the theoretical error analysis in L 2-norm for the scalar unknown and its gradient in one dimensional case, we obtain the optimal order of convergence in space-time direction. Further, we also derive the optimal error results for the scalar unknown in H 1-norm. Moreover, we derive and analyze the stability of H 1-GMFE scheme and give the results of a priori error estimates in two- or three-dimensional cases. In order to verify our theoretical analysis, we give some results of numerical calculation by using the Matlab procedure. PMID:25184148

12. 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.

13. Adaptive Meshless Local Petrov-Galerkin Method with Variable Domain of Influence in 2D Elastostatic Problems

Directory of Open Access Journals (Sweden)

2008-01-01

Full Text Available A meshless local Petrov-Galerkin (MLPG method that employs polygonal sub-domains constructed from several triangular patches rather than the typically used circular sub-domains is presented. Moving least-squares approximation is used to construct the trial displacements and linear, Lagrange interpolation functions are used to construct the test functions. An adaptive technique to improve the accuracy of approximate solutions is developed to minimize the computational cost. Variable domain of influence (VDOI and effective stress gradient indicator (EK for local error assessment are the focus of this study. Several numerical examples are presented to verify the efficiency and accuracy of the proposed adaptive MLPG method. The results show that the proposed adaptive technique performs as expected that is refining the problem domain in area with high stress concentration in which higher accuracy is commonly required.

14. An A Posteriori Error Analysis of Mixed Finite Element Galerkin Approximations to Second Order Linear Parabolic Problems

KAUST Repository

Memon, Sajid

2012-01-01

In this article, a posteriori error estimates are derived for mixed finite element Galerkin approximations to second order linear parabolic initial and boundary value problems. Using mixed elliptic reconstructions, a posteriori error estimates in L∞(L2)- and L2(L2)-norms for the solution as well as its flux are proved for the semidiscrete scheme. Finally, based on a backward Euler method, a completely discrete scheme is analyzed and a posteriori error bounds are derived, which improves upon earlier results on a posteriori estimates of mixed finite element approximations to parabolic problems. Results of numerical experiments verifying the efficiency of the estimators have also been provided. © 2012 Society for Industrial and Applied Mathematics.

15. The Morphosyntax of Discontinuous Exponence

Science.gov (United States)

Campbell, Amy Melissa

2012-01-01

This thesis offers a systematic treatment of discontinuous exponence, a pattern of inflection in which a single feature or a set of features bundled in syntax is expressed by multiple, distinct morphemes. This pattern is interesting and theoretically relevant because it represents a deviation from the expected one-to-one relationship between…

16. Discontinuing Medication: Recurrence Risk Factors

OpenAIRE

J Gordon Millichap

1992-01-01

The results of antiepileptic drug discontinuation in epileptic children who were seizure free for at least 2 years are reported from the Services of Child Neurology and Psychology, Department of Neurology, Clinics Hospital University of Sao Paulo Medical School, Sao Paulo, Brazil.

17. An Elasticity Solution for Simply Supported Rectangular Plates ...

African Journals Online (AJOL)

An Elasticity Solution for Simply Supported Rectangular Plates. VK Sebastian. Abstract. A solution is obtained for simply supported rectangular plates based on the Galerkin vector strain function approach of elasticity. Sinusoidal, uniform and partial loads are studied and detailed numerical results are presented for plates ...

18. A Galerkin, finite-element analysis of steady-state flow and heat transport in the shallow hydrothermal system in the East Mesa area, Imperial Valley, California

Science.gov (United States)

Miller, R.E.

1977-01-01

A steady-state simulation model was applied to the shallow hydrothermal system in the East Mesa area of Imperial Valley, Calif. The steady-state equations of flow and heat transport were solved by use of a Galerkin, finite-element method. A solution was obtained by iterating between the temperature and pressure equations, using updated densities and viscosities. Temperature and pressure were obtained for each node, and corresponding head values were calculated. The simulated temperature and pressure patterns correlated well with the observed patterns. Additional data, mainly from test drilling, would be required for construction of a similar model of the deep hydrothermal system.

19. Two-dimensional linear variation displacement discontinuity method for three-layered elastic media

CSIR Research Space (South Africa)

Shou, KJ

1999-09-01

Full Text Available A new displacement discontinuity method is developed for the analysis of multi-layered elastic media. This approach is based on a novel superposition scheme and the analytical solution to the problem of a displacement discontinuity element within...

20. Continuum damage growth analysis using element free Galerkin ...

various reasons as they avoid burdensome mesh generation, can easily model the evolution of discontinuities such as cracks and interfaces. Among these methods, EFGM is particularly appealing, due to its simplicity, alleviation of numerical difficulties of mesh entanglement, faster rate of convergence, and formulation that ...

1. A novel Galerkin-like weakform and a superconvergent alpha finite element method (S αFEM) for mechanics problems using triangular meshes

Science.gov (United States)

Liu, G. R.; Nguyen-Xuan, H.; Nguyen-Thoi, T.; Xu, X.

2009-06-01

A carefully designed procedure is presented to modify the piecewise constant strain field of linear triangular FEM models, and to reconstruct a strain field with an adjustable parameter α. A novel Galerkin-like weakform derived from the Hellinger-Reissner variational principle is proposed for establishing the discretized system equations. The new weak form is very simple, possesses the same good properties of the standard Galerkin weakform, and works particularly well for strain construction methods. A superconvergent alpha finite element method (S αFEM) is then formulated by using the constructed strain field and the Galerkin-like weakform for solid mechanics problems. The implementation of the S αFEM is straightforward and no additional parameters are used. We prove theoretically and show numerically that the S αFEM always achieves more accurate and higher convergence rate than the standard FEM of triangular elements (T3) and even more accurate than the four-node quadrilateral elements (Q4) when the same sets of nodes are used. The S αFEM can always produce both lower and upper bounds to the exact solution in the energy norm for all elasticity problems by properly choosing an α. In addition, a preferable- α approach has also been devised to produce very accurate solutions for both displacement and energy norms and a superconvergent rate in the energy error norm. Furthermore, a model-based selective scheme is proposed to formulate a combined S αFEM/NS-FEM model that handily overcomes the volumetric locking problems. Intensive numerical studies including singularity problems have been conducted to confirm the theory and properties of the S αFEM.

2. Final Technical Report 'Double discontinuities in space plasma'

International Nuclear Information System (INIS)

Yun Chow Whang

2004-01-01

This research used high-resolution magnetic field data to examine the interior structures of MHD shocks in interplanetary space and in the magnetotail; we discovered that a slow-mode shock is often followed by an adjoining rotational discontinuity layer on the postshock side. The thickness of each layer is of the order of a few ion inertial lengths. Such a compound structure is known as a double discontinuity. When the magnetic field rotates by several degrees per ion inertial length inside a thin layer, the Hall current term becomes important in the generalized Ohm's law. Steady state solutions based on the Hall-MHD theory have been obtained to show the merging of a rotational layer and a slow shock layer to form a compound structure like the observed double discontinuities

3. 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...

4. Discontinuity minimization for omnidirectional video projections

Science.gov (United States)

2017-09-01

Advances in display technologies both for head mounted devices and television panels demand resolution increase beyond 4K for source signal in virtual reality video streaming applications. This poses a problem of content delivery trough a bandwidth limited distribution networks. Considering a fact that source signal covers entire surrounding space investigation reviled that compression efficiency may fluctuate 40% in average depending on origin selection at the conversion stage from 3D space to 2D projection. Based on these knowledge the origin selection algorithm for video compression applications has been proposed. Using discontinuity entropy minimization function projection origin rotation may be defined to provide optimal compression results. Outcome of this research may be applied across various video compression solutions for omnidirectional content.

5. Model for vortex turbulence with discontinuities in the solar wind

Directory of Open Access Journals (Sweden)

2003-01-01

Full Text Available A model of vortex with embedded discontinuities in plasma flow is developed in the framework of ideal MHD in a low b plasma. Vortex structures are considered as a result of 2-D evolution of nonlinear shear Alfvén waves in the heliosphere. Physical properties of the solutions and vector fields are analyzed and the observational aspects of the model are discussed. The ratio of normal components to the discontinuity Br /Vr can be close to -2. The alignment between velocity and magnetic field vectors takes place. Spacecraft crossing such vortices will typically observe a pair of discontinuities, but with dissimilar properties. Occurrence rate for different discontinuity types is estimated and agrees with observations in high-speed solar wind stream. Discontinuity crossing provides a backward rotation of magnetic field vector and can be observed as part of a backward arc. The Ulysses magnetometer data obtained in the fast solar wind are compared with the results of theoretical modelling.

6. Stabilization of the solution of a doubly nonlinear parabolic equation

International Nuclear Information System (INIS)

Andriyanova, È R; Mukminov, F Kh

2013-01-01

The method of Galerkin approximations is employed to prove the existence of a strong global (in time) solution of a doubly nonlinear parabolic equation in an unbounded domain. The second integral identity is established for Galerkin approximations, and passing to the limit in it an estimate for the decay rate of the norm of the solution from below is obtained. The estimates characterizing the decay rate of the solution as x→∞ obtained here are used to derive an upper bound for the decay rate of the solution with respect to time; the resulting estimate is pretty close to the lower one. Bibliography: 17 titles

7. Farmers\\' Discontinuance Decision Behaviours Of Yam Minisett ...

African Journals Online (AJOL)

Farmers' discontinuance decision behaviours of technologies is attributed to certain reasons and it is governed by certain socio-economic variables. This study identified and analyzed the rate of discontinuance of yam minisett technology, reasons for discontinuance and the socio-economic determinants of the ...

8. Crack edge collocation for the direct computation of stress intensity factors using the displacement discontinuity method

CSIR Research Space (South Africa)

Napier, JAL

2002-09-01

Full Text Available The numerical solution of problems relating to crack fracture and failure can be accomplished using the displacement discontinuity boundary element method. This paper presents an extension to the normal formulation of this method to enable stress...

9. 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

10. Mechanical hemolysis in blood flow: user-independent predictions with the solution of a partial differential equation.

Science.gov (United States)

Lacasse, David; Garon, Andre; Pelletier, Dominique

2007-02-01

This paper presents for the first time numerical predictions of mechanical blood hemolysis obtained by solving a hyperbolic partial differential equation (PDE) modelling the hemolysis in a Eulerian frame of reference. This provides hemolysis predictions over the entire computational domain as an alternative to the Lagrangian approach consisting in evaluating cell hemolysis along their trajectories. The solution of a PDE over a computational domain, such as in the approach presented herein, yields a unique solution. This is a clear advantage over the Lagrangian approach, which requires the human-made choice of a limited number of trajectories for integration and inevitably results in the incomplete coverage of the computational domain. The hyperbolic hemolysis model is solved with a Discontinuous Galerkin finite element method. The solution algorithm also includes adaptive remeshing to provide high accuracy simulations. Predictions of the modified index of hemolysis (MIH) are presented for flows in dialysis cannulae and sudden contractions. MIH predictions for cannulae differ significantly from those obtained by other authors using the Lagrangian approach. The predictions for flows in sudden contractions are used, along with our own experimental measurements, to assess the value of the threshold shear stress required for hemolysis that is included in the hemolysis model.

11. Analysis of a finite-difference and a Galerkin technique applied to the simulation of advection and diffusion of air pollutants from a line source

International Nuclear Information System (INIS)

Runca, E.; Melli, P.; Sardei, F.

1985-01-01

A finite-difference scheme and a Galerkin scheme are compared with respect to a very accurate solution describing time-dependent advection and diffusion of air pollutants from a line source in an atmosphere vertically stratified and limited by an inversion layer. The accurate solution was achieved by applying the finite-difference scheme on a very refined grid with a very small time step. The grid size and time step were defined according to stability and accuracy criteria discussed in the text. It is found that for the problem considered the two methods can be considered equally accurate. However, the Galerkin method gives a better approximation in the vicinity of the source. This was assumed to be partly due to the different way the source term is taken into account in the two methods. Improvement of the accuracy of the finite-difference scheme was achieved by approximating, at every step, the contribution of the source term by a Gaussian puff moving and diffusing with the velocity and diffusivity of the source location, instead of utilizing a stepwise function for the numerical approximation of the delta function representing the source term

12. 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

13. 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.

14. Calculation of BWR [Boiling Water Reactor] limit cycle amplitude using Galerkin's method

International Nuclear Information System (INIS)

Damiano, B.; March-Leuba, J.; Euler, J.A.

1990-01-01

This paper describes the application of Galerkin's method to estimate the amplitude of boiling water reactor (BWR) limit cycle oscillations. It will be shown that Galerkin's method can be applied to a model of BWR dynamics consisting of the point kinetics equations and the LAPUR generated feedback transfer function to calculate the time history of small amplitude limit cycles. This allows results from the linear frequency domain code LAPUR to be used to calculate nonlinear time domain information. 2 refs., 2 figs., 1 tab

15. Rotational discontinuities in anisotropic plasmas

International Nuclear Information System (INIS)

Omidi, N.

1992-01-01

The kinetic structure of rotational discontinuities (RDs) in anisotropic plasmas with T perpendicular /T parallel > 1 is investigated by using a one-dimensional electromagnetic hybrid code. To form the RD, a new approach is used where the plasma is injected from one boundary and reflected from the other, resulting in the generation of a traveling fast shock and an RD. Unlike the previously used methods, no a priori assumptions are made regarding the initial structure (i.e. width or sense of rotation) of the rotational discontinuity. The results show that across the RD both the magnetic field strength and direction, as well as the plasma density change. Given that such a change can also be associated with an intermediate shock, the Rankine-Hugoniot relations are used to confirm that the observed structures are indeed RDs. It is found that the thickness of RDs is a few ion inertial lengths and is independent of the rotation angle. Also, the preferred sense of rotation is in the electron sense; however, RDs with a rotation angle larger than 180 degree are found to be unstable, changing their rotation to a stable ion sense

16. 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

17. Approximate solutions of some problems of scattering of surface ...

A Choudhary

reflection coefficients are compared to the known results obtained by utilizing a Galerkin type of approximate method after reducing the bvps to integral equations whose complete solutions are difficult to be determined. Various combinations of discretization of the resulting dual series relations obtained in the present ...

18. Construction of energy-stable Galerkin reduced order models.

Energy Technology Data Exchange (ETDEWEB)

Kalashnikova, Irina; Barone, Matthew Franklin; Arunajatesan, Srinivasan; van Bloemen Waanders, Bart Gustaaf

2013-05-01

This report aims to unify several approaches for building stable projection-based reduced order models (ROMs). Attention is focused on linear time-invariant (LTI) systems. The model reduction procedure consists of two steps: the computation of a reduced basis, and the projection of the governing partial differential equations (PDEs) onto this reduced basis. Two kinds of reduced bases are considered: the proper orthogonal decomposition (POD) basis and the balanced truncation basis. The projection step of the model reduction can be done in two ways: via continuous projection or via discrete projection. First, an approach for building energy-stable Galerkin ROMs for linear hyperbolic or incompletely parabolic systems of PDEs using continuous projection is proposed. The idea is to apply to the set of PDEs a transformation induced by the Lyapunov function for the system, and to build the ROM in the transformed variables. The resulting ROM will be energy-stable for any choice of reduced basis. It is shown that, for many PDE systems, the desired transformation is induced by a special weighted L2 inner product, termed the %E2%80%9Csymmetry inner product%E2%80%9D. Attention is then turned to building energy-stable ROMs via discrete projection. A discrete counterpart of the continuous symmetry inner product, a weighted L2 inner product termed the %E2%80%9CLyapunov inner product%E2%80%9D, is derived. The weighting matrix that defines the Lyapunov inner product can be computed in a black-box fashion for a stable LTI system arising from the discretization of a system of PDEs in space. It is shown that a ROM constructed via discrete projection using the Lyapunov inner product will be energy-stable for any choice of reduced basis. Connections between the Lyapunov inner product and the inner product induced by the balanced truncation algorithm are made. Comparisons are also made between the symmetry inner product and the Lyapunov inner product. The performance of ROMs constructed

19. Tracking discontinuities in hyperbolic conservation laws with spectral accuracy

Science.gov (United States)

Touil, H.; Hussaini, M. Y.; Sussman, M.

2007-08-01

It is well known that the spectral solutions of conservation laws have the attractive distinguishing property of infinite-order convergence (also called spectral accuracy) when they are smooth (e.g., [C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, Spectral Methods for Fluid Dynamics, Springer-Verlag, Heidelberg, 1988; J.P. Boyd, Chebyshev and Fourier Spectral Methods, second ed., Dover, New York, 2001; C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, Spectral Methods: Fundamentals in Single Domains, Springer-Verlag, Berlin Heidelberg, 2006]). If a discontinuity or a shock is present in the solution, this advantage is lost. There have been attempts to recover exponential convergence in such cases with rather limited success. The aim of this paper is to propose a discontinuous spectral element method coupled with a level set procedure, which tracks discontinuities in the solution of nonlinear hyperbolic conservation laws with spectral convergence in space. Spectral convergence is demonstrated in the case of the inviscid Burgers equation and the one-dimensional Euler equations.

20. Applications of Taylor-Galerkin finite element method to compressible internal flow problems

Science.gov (United States)

Sohn, Jeong L.; Kim, Yongmo; Chung, T. J.

1989-01-01

A two-step Taylor-Galerkin finite element method with Lapidus' artificial viscosity scheme is applied to several test cases for internal compressible inviscid flow problems. Investigations for the effect of supersonic/subsonic inlet and outlet boundary conditions on computational results are particularly emphasized.

1. 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

2. The artificial compression method for computation of shocks and contact discontinuities. I - Single conservation laws

Science.gov (United States)

Harten, A.

1977-01-01

The paper discusses the use of the artificial compression method for the computation of discontinuous solutions of a single conservation law by finite difference methods. The single conservation law has either a shock or a contact discontinuity. Any monotone finite difference scheme applied to the original equation smears the discontinuity, while the same scheme applied to the equation modified by an artificial compression flux produces steady progressing profiles. If L is any finite difference scheme in conservation form and C is an artificial compressor, the split flux artificial compression method CL is a corrective scheme: L smears the discontinuity while propagating it; C compresses the smeared transition toward a sharp discontinuity. Numerical implementation of artificial compression is described.

3. Nano-particle drag prediction at low Reynolds number using a direct Boltzmann-BGK solution approach

Science.gov (United States)

Evans, B.

2018-01-01

This paper outlines a novel approach for solution of the Boltzmann-BGK equation describing molecular gas dynamics applied to the challenging problem of drag prediction of a 2D circular nano-particle at transitional Knudsen number (0.0214) and low Reynolds number (0.25-2.0). The numerical scheme utilises a discontinuous-Galerkin finite element discretisation for the physical space representing the problem particle geometry and a high order discretisation for molecular velocity space describing the molecular distribution function. The paper shows that this method produces drag predictions that are aligned well with the range of drag predictions for this problem generated from the alternative numerical approaches of molecular dynamics codes and a modified continuum scheme. It also demonstrates the sensitivity of flow-field solutions and therefore drag predictions to the wall absorption parameter used to construct the solid wall boundary condition used in the solver algorithm. The results from this work has applications in fields ranging from diagnostics and therapeutics in medicine to the fields of semiconductors and xerographics.

4. Space-time adaptive solution of inverse problems with the discrete adjoint method

Science.gov (United States)

2014-08-01

5. 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).

6. Multigrid technique and Optimized Schwarz method on block-structured grids with discontinuous interfaces

DEFF Research Database (Denmark)

Kolmogorov, Dmitry; Sørensen, Niels N.; Shen, Wen Zhong

2013-01-01

An Optimized Schwarz method using Robin boundary conditions for relaxation scheme is presented in the frame of Multigrid method on discontinuous grids. At each iteration the relaxation scheme is performed in two steps: one step with Dirichlet and another step with Robin boundary conditions at inner...... block boundaries. A Robin parameter that depends on grid geometry and grid discontinuity at block interfaces is introduced. The general solution algorithm is based on SIMPLE method and a conservative _nite-volume scheme on block-structured grids with discontinuous interfaces. The multigrid method...

7. Discontinuation of Preventive Drugs in General Practice

DEFF Research Database (Denmark)

Andersen, John Sahl; Lindberg, Laura Maria Glahder; Nixon, Michael Simon

of death in the United States. The public expenses to drug treatment are constantly increasing. The possibility to withdraw the medication must be taken into account but the decision to discontinue drugs is complex and poorly understood. Planned studies: 1. Patients’ views upon discontinuation...

8. 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....

9. Characterization of discontinuity systems in gneiss formation

International Nuclear Information System (INIS)

Kim, Jhin Wung; Kang, Byoung Moo; Rhee, Chan Goo

1990-05-01

Suitability evaluation for the site of radioactive waste disposal includes the consideration on rock mass stability and groundwater flow condition, which reflects the attitude of discontinuities present in rock. The research work was done to develop the objective descriptive method and analysing techniques for the discontinuity system and to enhance techniques for predicting the extent of the system in subsurface. A descriptive method for evaluating discontinuities in gneissic rock mass was established. The distribution of discontinuities were analysed based on geometric, mechanical, and hydrogeological parameters. The various parameters of discontinuties were collected based on rock type, discontinuites were collection and plunge, trace length, roughness, aperture type. The three dimensional distribution and orientation of the system were synthesized. The results indicate that the discontinuities are composed of 3 major sets. The frequency, concentrations, spacings, trace lengths, and the interconnectivity index were estimated for the three sets. The frequency depends on depth but abnormal high frequency zone also exists. (author)

10. Vertebral Fractures After Discontinuation of Denosumab

DEFF Research Database (Denmark)

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

2018-01-01

Denosumab reduces bone resorption and vertebral and nonvertebral fracture risk. Denosumab discontinuation increases bone turnover markers 3 months after a scheduled dose is omitted, reaching above-baseline levels by 6 months, and decreases bone mineral density (BMD) to baseline levels by 12 months....... 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...

11. Green's function approach to neutron flux discontinuities

International Nuclear Information System (INIS)

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)

12. Historical transformation and epistemological discontinuity

Directory of Open Access Journals (Sweden)

Močnik Rastko

2013-01-01

Full Text Available Starting from recent formulas of EU bureaucracy for subordinating scientific and educational apparatuses to the needs of the capital and to the requests of its political representatives, the article analyses the interconnection between the historical transformation of the ideological state apparatuses (universities, higher education institutions, research institutes etc. and the epistemological discontinuity provoked by the triumph of technosciences. The hypothesis to be tested is the following: While the crisis of West European-North American capitalism requires an ever tighter submission of ideological state apparatuses, and especially of scientific and academic apparatuses to the needs of the capital, theoretical practices in the humanities and social sciences have come to the point where they entered into an open conflict with the domination of the capital and have, as a consequence, started to subvert their own institutional supports in the ideological apparatuses of the capitalist state. For this purpose, the article reconsiders social sciences as a compromise formation and, eventually, reassesses the historical materialism as a non-Cartesian modern science.

13. The shallow water equations on the sphere and their Lagrange- Galerkin-solution

CERN Document Server

Heinze, T

2002-01-01

The shallow water equations are formulated on the sphere in a three- dimensional coordinate system with the aid of tangential velocity components and differential operators. We introduce a modified semi- Lagrangian scheme for the discretization in time. The discretization in space is solved by linear finite elements. The grids we use are regular refinements of a macro triangulation which itself is derived from a highly symmetric polyeder also known as a bucky or soccer ball. The good numerical results show that this combination is a promising approach. The numerical algorithm is stable and its strength is the conservation of mass and energy. (16 refs).

14. Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations

KAUST Repository

Carlberg, Kevin

2010-10-28

A Petrov-Galerkin projection method is proposed for reducing the dimension of a discrete non-linear static or dynamic computational model in view of enabling its processing in real time. The right reduced-order basis is chosen to be invariant and is constructed using the Proper Orthogonal Decomposition method. The left reduced-order basis is selected to minimize the two-norm of the residual arising at each Newton iteration. Thus, this basis is iteration-dependent, enables capturing of non-linearities, and leads to the globally convergent Gauss-Newton method. To avoid the significant computational cost of assembling the reduced-order operators, the residual and action of the Jacobian on the right reduced-order basis are each approximated by the product of an invariant, large-scale matrix, and an iteration-dependent, smaller one. The invariant matrix is computed using a data compression procedure that meets proposed consistency requirements. The iteration-dependent matrix is computed to enable the least-squares reconstruction of some entries of the approximated quantities. The results obtained for the solution of a turbulent flow problem and several non-linear structural dynamics problems highlight the merit of the proposed consistency requirements. They also demonstrate the potential of this method to significantly reduce the computational cost associated with high-dimensional non-linear models while retaining their accuracy. © 2010 John Wiley & Sons, Ltd.

15. 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.

16. A subgrid viscosity Lagrance-Galerkin method for convection-diffusion problems

OpenAIRE

Bermejo Bermejo, Rodolfo; Galan Del Sastre, Pedro; Saavedra Lago, Laura

2014-01-01

We present and analyze a subgrid viscosity Lagrange-Galerk in method that combines the subgrid eddy viscosity method proposed in W. Layton, A connection between subgrid scale eddy viscosity and mixed methods. Appl. Math. Comp., 133: 14 7-157, 2002, and a conventional Lagrange-Galerkin method in the framework of P1⊕ cubic bubble finite elements. This results in an efficient and easy to implement stabilized method for convection dominated convection diffusion reaction problems. Numeric...

17. 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

18. 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...

19. Development of Galerkin Method for Solving the Generalized Burger's-Huxley Equation

Directory of Open Access Journals (Sweden)

2013-01-01

Full Text Available Numerical treatments for the generalized Burger's—Huxley GBH equation are presented. The treatments are based on cardinal Chebyshev and Legendre basis functions with Galerkin method. Gauss quadrature formula and El-gendi method are used to convert the problem into a system of ordinary differential equations. The numerical results are compared with the literatures to show efficiency of the proposed methods.

20. Numerical Solution of the Modified Equal Width Wave Equation

Directory of Open Access Journals (Sweden)

Seydi Battal Gazi Karakoç

2012-01-01

Full Text Available Numerical solution of the modified equal width wave equation is obtained by using lumped Galerkin method based on cubic B-spline finite element method. Solitary wave motion and interaction of two solitary waves are studied using the proposed method. Accuracy of the proposed method is discussed by computing the numerical conserved laws 2 and ∞ error norms. The numerical results are found in good agreement with exact solution. A linear stability analysis of the scheme is also investigated.

1. Discontinuity Detection for Analysis of Telerobot Trajectories

Science.gov (United States)

Yeom, Kiwon; Ellis, Stephen R.; Adelstein, Bernard D.

2013-01-01

To identify spatial and temporal discontinuities in telerobot movement in order to describe the shift in operators control and error correction strategies from continuous control to move-and-wait strategies. This shift was studied under conditions of simulated increasingly time-delayed teleoperation. The ultimate goal is to determine if the time delay associated with the shift is invariant with independently imposed control difficulty. We expect this shift to manifest itself as changes in the number of discontinuity of movement path. We proposed an approach to spatial and temporal discontinuity detection algorithm for analysis of teleoperated trajectory in three dimensional space. The algorithm provides a simple and potentially objective method for detecting the discontinuity during telerobot operation and evaluating the difficulty of rotational coordinate condition in teleoperation.

2. 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...

Directory of Open Access Journals (Sweden)

J Gordon Millichap

2009-04-01

Full Text Available Prevalence of ADHD drug discontinuance in adolescents and young adults was studied in the UK by using the General Practice Database for patients aged 15-21 years from 1999 to 2006.

4. Discontinuous modelling of masonry failure

OpenAIRE

VANDOREN, Bram

2013-01-01

A robust and efficient numerical model is a valuable engineering tool for predicting the load-bearing capacity and failure mode of masonry structures. Such a computational model consists of three key ingredients: a constitutive law which incorporates the non-linear material responses, a kinematic framework for describing failure mechanisms, and a solution algorithm which is capable of modelling the complete loading behaviour of a structure up to total failure. This work focuses on the latter ...

5. FABRIC TENSOR FOR DISCONTINUOUS GEOLOGICAL MATERIALS

OpenAIRE

小田, 匡寛

1982-01-01

Geometrical property (fabric) of discontinuity in geological materials is discussed in terms of (1) position and density, (2) shape and dimension and (3) orientation of related discontinuities such as joint, fault and discrete particle. By taking into account these geometrical elements, a unique measure called fabric tensor F_ is definitely introduced to embody the fabric concept without loss of generality.The first invariant of F_ is important as an index measure to evaluate the crack intens...

6. Analysis of Direct Extrusion Operation Using The Bubnov-Galerkin ...

African Journals Online (AJOL)

... was obtained in a matrix form from the weighted residual, boundary condition were now applied to obtain the pressure distribution across the cross-section of the blank. Finite element results were obtained for a particular values of coefficient of friction and blank diameter and compared with the exact solution on a graph.

7. On the Strong Solution for the 3D Stochastic Leray-Alpha Model

Directory of Open Access Journals (Sweden)

Gabriel Deugoue

2010-01-01

Full Text Available We prove the existence and uniqueness of strong solution to the stochastic Leray-α equations under appropriate conditions on the data. This is achieved by means of the Galerkin approximation scheme. We also study the asymptotic behaviour of the strong solution as alpha goes to zero. We show that a sequence of strong solutions converges in appropriate topologies to weak solutions of the 3D stochastic Navier-Stokes equations.

8. On the Strong Solution for the 3D Stochastic Leray-Alpha Model

Directory of Open Access Journals (Sweden)

Deugoue Gabriel

2010-01-01

Full Text Available Abstract We prove the existence and uniqueness of strong solution to the stochastic Leray- equations under appropriate conditions on the data. This is achieved by means of the Galerkin approximation scheme. We also study the asymptotic behaviour of the strong solution as alpha goes to zero. We show that a sequence of strong solutions converges in appropriate topologies to weak solutions of the 3D stochastic Navier-Stokes equations.

9. 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

10. A Semilinear Wave Equation with a Boundary Condition of Many-Point Type: Global Existence and Stability of Weak Solutions

Directory of Open Access Journals (Sweden)

Giai Giang Vo

2015-01-01

Full Text Available This paper is devoted to the study of a wave equation with a boundary condition of many-point type. The existence of weak solutions is proved by using the Galerkin method. Also, the uniqueness and the stability of solutions are established.

11. 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.

12. A New Iterative Scheme for the Solution of Tenth Order Boundary ...

African Journals Online (AJOL)

Tonistar

Nigerian Journal of Basic and Applied Science (June, 2016), 24(1): 76-81 ... ABSTRACT. A new iterative scheme for the solution of tenth order boundary value problems has been implemented ... tenth order boundary value problems as compared with the results generated from the Galerkin method available in literature.

13. 27 CFR 478.127 - 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... Records § 478.127 Discontinuance of business. Where a licensed business is discontinued and succeeded by a... be delivered to the successor. Where discontinuance of the business is absolute, the records shall be...

14. 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...

15. 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...

16. Exponential discontinuous numerical scheme for electron transport in the continuous slowing down approximation

International Nuclear Information System (INIS)

Prinja, A.K.

1997-01-01

A nonlinear discretization scheme in space and energy, based on the recently developed exponential discontinuous method, is applied to continuous slowing down dominated electron transport (i.e., in the absence of scattering.) Numerical results for dose and charge deposition are obtained and compared against results from the ONELD and ONEBFP codes, and against exact results from an adjoint Monte Carlo code. It is found that although the exponential discontinuous scheme yields strictly positive and monotonic solutions, the dose profile is considerably straggled when compared to results from the linear codes. On the other hand, the linear schemes produce negative results which, furthermore, do not damp effectively in some cases. A general conclusion is that while yielding strictly positive solutions, the exponential discontinuous method does not show the crude cell accuracy for charged particle transport as was apparent for neutral particle transport problems

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

Science.gov (United States)

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

18. 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.

19. Vibration of quadrilateral embedded multilayered graphene sheets based on nonlocal continuum models using the Galerkin method

Science.gov (United States)

Babaei, H.; Shahidi, A. R.

2011-12-01

Free vibration analysis of quadrilateral multilayered graphene sheets (MLGS) embedded in polymer matrix is carried out employing nonlocal continuum mechanics. The principle of virtual work is employed to derive the equations of motion. The Galerkin method in conjunction with the natural coordinates of the nanoplate is used as a basis for the analysis. The dependence of small scale effect on thickness, elastic modulus, polymer matrix stiffness and interaction coefficient between two adjacent sheets is illustrated. The non-dimensional natural frequencies of skew, rhombic, trapezoidal and rectangular MLGS are obtained with various geometrical parameters and mode numbers taken into account, and for each case the effects of the small length scale are investigated.

20. 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.

1. 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.

2. A new benchmark reference solution for double-diffusive convection in a heterogeneous porous medium

OpenAIRE

Shao, Q.; Fahs, M.; Younes, Anis; Makradi, A.; Mara, T.

2016-01-01

A new benchmark with a high accurate solution is proposed for the verification of numerical codes dealing with double-diffusive convection in a heterogeneous porous medium. The new benchmark is inspired by the popular problem of square porous cavity by assuming a stratified porous medium. A high accurate steady state solution is developed using the Fourier-Galerkin method. To this aim, the unknowns are expanded in double infinite Fourier series. The accuracy of the developed solution is asses...

3. Direct solution of the Chemical Master Equation using quantized tensor trains.

Directory of Open Access Journals (Sweden)

2014-03-01

Full Text Available The Chemical Master Equation (CME is a cornerstone of stochastic analysis and simulation of models of biochemical reaction networks. Yet direct solutions of the CME have remained elusive. Although several approaches overcome the infinite dimensional nature of the CME through projections or other means, a common feature of proposed approaches is their susceptibility to the curse of dimensionality, i.e. the exponential growth in memory and computational requirements in the number of problem dimensions. We present a novel approach that has the potential to "lift" this curse of dimensionality. The approach is based on the use of the recently proposed Quantized Tensor Train (QTT formatted numerical linear algebra for the low parametric, numerical representation of tensors. The QTT decomposition admits both, algorithms for basic tensor arithmetics with complexity scaling linearly in the dimension (number of species and sub-linearly in the mode size (maximum copy number, and a numerical tensor rounding procedure which is stable and quasi-optimal. We show how the CME can be represented in QTT format, then use the exponentially-converging hp-discontinuous Galerkin discretization in time to reduce the CME evolution problem to a set of QTT-structured linear equations to be solved at each time step using an algorithm based on Density Matrix Renormalization Group (DMRG methods from quantum chemistry. Our method automatically adapts the "basis" of the solution at every time step guaranteeing that it is large enough to capture the dynamics of interest but no larger than necessary, as this would increase the computational complexity. Our approach is demonstrated by applying it to three different examples from systems biology: independent birth-death process, an example of enzymatic futile cycle, and a stochastic switch model. The numerical results on these examples demonstrate that the proposed QTT method achieves dramatic speedups and several orders of

4. Three-Dimensional Numerical Simulation of a 30-GHz Gyrotron Resonator With an Explicit High-Order Discontinuous-Galerkin-Based Parallel Particle-In-Cell Method

DEFF Research Database (Denmark)

Stock, Andreas; Neudorfer, Jonathan; Riedlinger, Marc

2012-01-01

reductions. This is a computational expensive endeavor, which requires today's high-performance computing capacity. However, this enables a detailed analysis of the EM field, the excited TE2,3 mode, the frequencies, and the azimuthal particle bunching in the beam. Therefrom, we present new insights...

5. Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework II: Force, vibration, and molecular dynamics calculations

Science.gov (United States)

Zhang, Gaigong; Lin, Lin; Hu, Wei; Yang, Chao; Pask, John E.

2017-04-01

Recently, we have proposed the adaptive local basis set for electronic structure calculations based on Kohn-Sham density functional theory in a pseudopotential framework. The adaptive local basis set is efficient and systematically improvable for total energy calculations. In this paper, we present the calculation of atomic forces, which can be used for a range of applications such as geometry optimization and molecular dynamics simulation. We demonstrate that, under mild assumptions, the computation of atomic forces can scale nearly linearly with the number of atoms in the system using the adaptive local basis set. We quantify the accuracy of the Hellmann-Feynman forces for a range of physical systems, benchmarked against converged planewave calculations, and find that the adaptive local basis set is efficient for both force and energy calculations, requiring at most a few tens of basis functions per atom to attain accuracies required in practice. Since the adaptive local basis set has implicit dependence on atomic positions, Pulay forces are in general nonzero. However, we find that the Pulay force is numerically small and systematically decreasing with increasing basis completeness, so that the Hellmann-Feynman force is sufficient for basis sizes of a few tens of basis functions per atom. We verify the accuracy of the computed forces in static calculations of quasi-1D and 3D disordered Si systems, vibration calculation of a quasi-1D Si system, and molecular dynamics calculations of H2 and liquid Al-Si alloy systems, where we show systematic convergence to benchmark planewave results and results from the literature.

6. Time-independent reaction-diffusion equation with a discontinuous reactive term

Science.gov (United States)

Levashova, N. T.; Nefedov, N. N.; Orlov, A. O.

2017-05-01

A two-dimensional singularly perturbed elliptic equation referred to in applications as the reaction-diffusion equation is considered. The nonlinearity describing the reaction is assumed to be discontinuous on a certain closed curve. On the basis of the generalized asymptotic comparison principle, the existence of smooth solution is proven and the accuracy of the asymptotic approximation is estimated.

7. Discontinuous precipitation in copper base alloys

Discontinuous precipitation (DP) is associated with grain boundary migration in the wake of which alternate plates of the precipitate and the depleted matrix form. Some copper base alloys show ... 100 > ± 0.1, DP is observed. This criterion points to diffusional coherency strain theory to be the operative mechanism for DP.

8. Intrauterine Contraceptive Device Discontinuation Among Women in ...

African Journals Online (AJOL)

In conclusion, more effort should be directed to counseling for adherence to the IUD use to ensure longer duration of use. Provision of the levonorgestrel intrauterine system which reduces bleeding and dysmenorrhoea, in our clinic may increase the continuation rate of IUD. Key words; IUD, duration of use, discontinuation, ...

9. Discontinuous precipitation in copper base alloys

Discontinuous precipitation (DP) is associated with grain boundary migration in the wake of which alternate plates of the precipitate and the ... force, the fundamental problem for the driving force for grain boundary (GB) migration, exists. .... systems (Germany: Springer Verlag). Kashyap K T, Ramachandra C, Sujatha M and ...

10. General practitioners’ decisions about discontinuation of medication

DEFF Research Database (Denmark)

Nixon, Michael Simon; Vendelø, Morten Thanning

2016-01-01

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...

11. Multiple discontinuities for 2-to-4 processes

International Nuclear Information System (INIS)

Cahill, Kevin; Stapp, H.P.

1976-01-01

Formulas that express the multiple normal-threshold discontinuities of scattering functions for 2-to-4 processes as sums of products of scattering amplitudes for related processes are derived from a combination field-theory and S-matrix principles [fr

12. Forecasting Technological Discontinuities in the ICT Industry

DEFF Research Database (Denmark)

Hoisl, Karin; Stelzer, Tobias; Biala, Stefanie

2015-01-01

in the ICT industry. The conjoint approach allows for a simulation of the forecasting process and considers utility trade-offs. The results show that for both types of experts the perceived benefit of users most highly contributes to predicting technological discontinuities. Internal experts assign more...

13. An equilibrium closure result for discontinuous games

NARCIS (Netherlands)

Balder, E.J.

2011-01-01

For games with discontinuous payoffs Simon and Zame (1990) introduced payoff indeterminacy, in the form of endogenous sharing rules, which are measurable selections of a certain payoff correspondence. Their main result concerns the existence of a mixed Nash equilibrium and an associated sharing

14. 38 CFR 21.7135 - Discontinuance dates.

Science.gov (United States)

2010-07-01

... education, the discontinuance date of educational assistance shall be the last date of attendance. (b) Death... veteran is receiving additional educational assistance based on a child's school attendance between the..., withdraws from all courses or receives all nonpunitive grades, and in either case there are no mitigating...

15. Discontinuous precipitation in copper base alloys

Discontinuous precipitation (DP) is associated with grain boundary migration in the wake of which alternate plates of the precipitate and the depleted matrix form. Some copper base alloys show DP while others do not. In this paper the misfit strain parameter, , has been calculated and predicted that if 100 > ± 0.1, DP is ...

16. 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.

17. 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.

18. On unified theory for scalar conservation laws with fluxes and sources discontinuous with respect to the unknown

Science.gov (United States)

Bulíček, Miroslav; Gwiazda, Piotr; Świerczewska-Gwiazda, Agnieszka

2017-01-01

We deal with the Cauchy problem for multi-dimensional scalar conservation laws, where the fluxes and the source terms can be discontinuous functions of the unknown. The main novelty of the paper is the introduction of a kinetic formulation for the considered problem. To handle the discontinuities we work in the framework of re-parametrization of the flux and the source functions, which was previously used for Kružkov entropy solutions. Within this approach we obtain a fairly complete picture: existence of entropy measure valued solutions, entropy weak solutions and their equivalence to the kinetic solution. The results of existence and uniqueness follow under the assumption of Hölder continuity at zero of the flux. The source term, what is another novelty for the studies on problems with discontinuous flux, is only assumed to be one-side Lipschitz, not necessarily monotone function.

19. Management of pelvic discontinuity in revision total hip arthroplasty: a review of the literature.

Science.gov (United States)

Abdelnasser, Mohammad K; Klenke, Frank M; Whitlock, Patrick; Khalil, Aly M; Khalifa, Yaser E; Ali, Hassan M; Siebenrock, Klaus A

2015-01-01

Pelvic discontinuity is a complex problem in revision total hip arthroplasty. Although rare, the incidence is likely to increase due to the ageing population and the increasing number of total hip arthroplasties being performed. The various surgical options available to solve this problem include plating, massive allografts, reconstruction rings, custom triflanged components and tantalum implants. However, the optimal solution remains controversial. None of the known methods completely solves the major obstacles associated with this problem, such as restoration of massive bone loss, implant failure in the short- and long-term and high complication rates. This review discusses the diagnosis, decision making, and treatment options of pelvic discontinuity in revision total hip arthroplasty.

20. Discontinuous finite element treatment of duct problems in transport calculations

International Nuclear Information System (INIS)

Mirza, A. M.; Qamar, S.

1998-01-01

A discontinuous finite element approach is presented to solve the even-parity Boltzmann transport equation for duct problems. Presence of ducts in a system results in the streaming of particles and hence requires the employment of higher order angular approximations to model the angular flux. Conventional schemes based on the use of continuous trial functions require the same order of angular approximations to be used everywhere in the system, resulting in wastage of computational resources. Numerical investigations for the test problems presented in this paper indicate that the discontinuous finite elements eliminate the above problems and leads to computationally efficient and economical methods. They are also found to be more suitable for treating the sharp changes in the angular flux at duct-observer interfaces. The new approach provides a single-pass alternate to extrapolation and interactive schemes which need multiple passes of the solution strategy to acquire convergence. The method has been tested with the help of two case studies, namely straight and dog-leg duct problems. All results have been verified against those obtained from Monte Carlo simulations and K/sup +/ continuous finite element method. (author)

1. Bifurcation in autonomous and nonautonomous differential equations with discontinuities

CERN Document Server

Akhmet, Marat

2017-01-01

This book is devoted to bifurcation theory for autonomous and nonautonomous differential equations with discontinuities of different types. That is, those with jumps present either in the right-hand-side or in trajectories or in the arguments of solutions of equations. The results obtained in this book can be applied to various fields such as neural networks, brain dynamics, mechanical systems, weather phenomena, population dynamics, etc. Without any doubt, bifurcation theory should be further developed to different types of differential equations. In this sense, the present book will be a leading one in this field. The reader will benefit from the recent results of the theory and will learn in the very concrete way how to apply this theory to differential equations with various types of discontinuity. Moreover, the reader will learn new ways to analyze nonautonomous bifurcation scenarios in these equations. The book will be of a big interest both for beginners and experts in the field. For the former group o...

2. Ionic Diffusion and Kinetic Homogeneous Chemical Reactions in the Pore Solution of Porous Materials with Moisture Transport

DEFF Research Database (Denmark)

Johannesson, Björn

2009-01-01

’s law of diffusion and the generalized Darcy’s law will be used together with derived constitutive equations for chemical reactions within phases. The mass balance equations for the constituents and the phases together with the constitutive equations gives the coupled set of non-linear differential...... general description of chemical reactions among constituents is described. The Petrov – Galerkin approach are used in favour of the standard Galerkin weighting in order to improve the solution when the convective part of the problem is dominant. A modified type of Newton – Raphson scheme is derived...

3. Galerkin finite element scheme with Bayliss-Gunzburger-Turkel-like boundary conditions for vectorial optical mode solver

NARCIS (Netherlands)

Uranus, H.P.; Hoekstra, Hugo; van Groesen, Embrecht W.C.

A Galerkin finite element scheme furnished with 1st-order Bayliss-Gunzburger-Turkel-like boundary conditions is formulated to compute both the guided and leaky modes of anisotropic channel waveguides of non-magnetic materials with diagonal permittivity tensor. The scheme is formulated using

4. Galerkin finite element scheme with Bayliss-Gunzburger-Turkel-like boundary conditions for vectorial optical mode solver

NARCIS (Netherlands)

Uranus, H.P.; Hoekstra, Hugo; van Groesen, Embrecht W.C.

2003-01-01

A Galerkin finite element scheme furnished with 1st-order Bayliss-Gunzberger-Turkel-like boundary conditions is formulated to compute both the guided and leaky modes of anisotropic channel waveguides of non-magnetic material with diagonal permitivity tensor. The scheme is formulated using

5. Scalability of Semi-Implicit Time Integrators for Nonhydrostatic Galerkin-based Atmospheric Models on Large Scale Cluster

Science.gov (United States)

2011-01-01

Scalability of Semi-Implicit Time Integrators for Nonhydrostatic Galerkin-based Atmospheric Models on Large Scale Cluster James F. Kelly and Francis...present performance statistics to explain the scalability behavior. Keywords- atmospheric models , time intergrators, MPI, scal- ability, performance; I...moving toward the nonhy- drostatic regime. The nonhydrostatic atmospheric models , which run at resolutions finer than 10 km, possess fast- moving

6. 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

7. A discontinuous control volume finite element method for multi-phase flow in heterogeneous porous media

Science.gov (United States)

Salinas, P.; Pavlidis, D.; Xie, Z.; Osman, H.; Pain, C. C.; Jackson, M. D.

2018-01-01

We present a new, high-order, control-volume-finite-element (CVFE) method for multiphase porous media flow with discontinuous 1st-order representation for pressure and discontinuous 2nd-order representation for velocity. The method has been implemented using unstructured tetrahedral meshes to discretize space. The method locally and globally conserves mass. However, unlike conventional CVFE formulations, the method presented here does not require the use of control volumes (CVs) that span the boundaries between domains with differing material properties. We demonstrate that the approach accurately preserves discontinuous saturation changes caused by permeability variations across such boundaries, allowing efficient simulation of flow in highly heterogeneous models. Moreover, accurate solutions are obtained at significantly lower computational cost than using conventional CVFE methods. We resolve a long-standing problem associated with the use of classical CVFE methods to model flow in highly heterogeneous porous media.

8. Discontinuity Preserving Image Registration through Motion Segmentation: A Primal-Dual Approach

Directory of Open Access Journals (Sweden)

Silja Kiriyanthan

2016-01-01

Full Text Available Image registration is a powerful tool in medical image analysis and facilitates the clinical routine in several aspects. There are many well established elastic registration methods, but none of them can so far preserve discontinuities in the displacement field. These discontinuities appear in particular at organ boundaries during the breathing induced organ motion. In this paper, we exploit the fact that motion segmentation could play a guiding role during discontinuity preserving registration. The motion segmentation is embedded in a continuous cut framework guaranteeing convexity for motion segmentation. Furthermore we show that a primal-dual method can be used to estimate a solution to this challenging variational problem. Experimental results are presented for MR images with apparent breathing induced sliding motion of the liver along the abdominal wall.

9. Discontinuation of Preventive Drugs in General Practice

DEFF Research Database (Denmark)

Andersen, John Sahl; Lindberg, Laura Maria Glahder; Nixon, Michael Simon

Introduction: In Denmark about 600,000 persons are treated for hypertension and more than 300,000 people are receiving cholesterol lowering drugs. The prevalence of hypertension in people aged 80 years is 70%. For antidepressants the defined daily doses/1000 aged >80 years/day exceed 200. By far...... the most preventive drugs are prescribed in general practice. Special considerations exist in relation to medication of elderly patients. The prevalence of polypharmacy and the subsequent increased risk of side effects and drug interactions is high. Drug-related problems represent the fifth leading cause...... of death in the United States. The public expenses to drug treatment are constantly increasing. The possibility to withdraw the medication must be taken into account but the decision to discontinue drugs is complex and poorly understood. Planned studies: 1. Patients’ views upon discontinuation...

10. SERVING TIMES OF DISCONTINUOUS MATERIALS HANDLING MACHINES

OpenAIRE

PÉTER TELEK

2014-01-01

The performance of production systems highly depend on the effectiveness of the serving process, which consist of different materials handling operations depend on the applied machines. During the design process of serving systems there are key role of the characterisations of the handling equipment: they determine the applicability of the given machines. In my paper, I analyse the serving operations of discontinuous materials handling machines and define the time requirements of them. After ...

11. The performance of proper orthogonal decomposition in discontinuous flows

Directory of Open Access Journals (Sweden)

Jing Li

2016-09-01

Full Text Available In this paper, flow reconstruction accuracy and flow prediction capability of discontinuous transonic flow field by means of proper orthogonal decomposition (POD method is studied. Although linear superposition of “high frequency waves” in different POD modes can achieve the reconstruction of the shock wave, the smoothness of the solution near the shock wave cannot be guaranteed. The modal coefficients are interpolated or extrapolated and different modal components are superposed to realize the prediction of the flow field beyond the snapshot sets. Results show that compared with the subsonic flow, the transonic flow with shock wave requires more POD modes to reach a comparative reconstruction accuracy. When a shock wave exists, the interpolation prediction ability is acceptable. However, large errors exist in extrapolation, and increasing the number of POD modes cannot effectively improve the prediction accuracy of the flow field.

12. A study on thermal damage during hyperthermia treatment based on DPL model for multilayer tissues using finite element Legendre wavelet Galerkin approach.

Science.gov (United States)

Kumar, Dinesh; Rai, K N

2016-12-01

Hyperthermia is a process that uses heat from the spatial heat source to kill cancerous cells without damaging the surrounding healthy tissues. Efficacy of hyperthermia technique is related to achieve temperature at the infected cells during the treatment process. A mathematical model on heat transfer in multilayer tissues in finite domain is proposed to predict the control temperature profile at hyperthermia position. The treatment technique uses dual-phase-lag model of heat transfer in multilayer tissues with modified Gaussian distribution heat source subjected to the most generalized boundary condition and interface at the adjacent layers. The complete dual-phase-lag model of bioheat transfer is solved using finite element Legendre wavelet Galerkin approach. The present solution has been verified with exact solution in a specific case and provides a good accuracy. The effect of the variability of different parameters such as lagging times, external heat source, metabolic heat source and the most generalized boundary condition on temperature profile in multilayer tissues is analyzed and also discussed the effective approach of hyperthermia treatment. Furthermore, we studied the modified thermal damage model with regeneration of healthy tissues as well. For viewpoint of thermal damage, the least thermal damage has been observed in boundary condition of second kind. The article concludes with a discussion of better opportunities for future clinical application of hyperthermia treatment. Copyright Â© 2016 Elsevier Ltd. All rights reserved.

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....

14. 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

15. 25 CFR 175.21 - Discontinuance of service.

Science.gov (United States)

2010-04-01

... Utility Service Administration § 175.21 Discontinuance of service. Failure of customer(s) to comply with... 25 Indians 1 2010-04-01 2010-04-01 false Discontinuance of service. 175.21 Section 175.21 Indians... service. The procedure(s) for discontinuance of service shall be set forth in the operations manual. ...

16. 27 CFR 555.61 - Discontinuance of business or operations.

Science.gov (United States)

2010-04-01

... 27 Alcohol, Tobacco Products and Firearms 3 2010-04-01 2010-04-01 false Discontinuance of business... Permits § 555.61 Discontinuance of business or operations. Where an explosive materials business or operations is either discontinued or succeeded by a new owner, the owner of the business or operations...

17. Finite element solution algorithm for incompressible fluid dynamics

Science.gov (United States)

Baker, A. J.

1974-01-01

A finite element solution algorithm is established for the two-dimensional Navier-Stokes equations governing the transient motion of a viscous incompressible fluid, i.e., hydrodynamics. Dependent variable transformation renders the differential equation description uniformly elliptic. The finite element algorithm is established using the Galerkin criterion on a local basis within the Method of Weighted Residuals. It is unconstrained with respect to system linearity, computational mesh uniformity or solution domain closure regularity. The finite element matrices are established using a linear 'natural coordinate function' description. Computational solutions using the COMOC computer program illustrate the various features of the algorithm including recirculating flows.

18. galerkin's methods

African Journals Online (AJOL)

user

in spacecrafts, vehicle systems, nuclear reactors, etc. Most of the applications subject the composite ... weak wind pressures could be the excitor to facilities and indirectly make unpleasant noises and vibrations [1]. .... Equation (26) is a 25 terms equation to maximum power of 8 with several unknowns. The coefficients Am ...

19. Laminar-turbulent patterning in wall-bounded shear flows: a Galerkin model

Energy Technology Data Exchange (ETDEWEB)

Seshasayanan, K [Laboratoire de Physique Statistique, CNRS UMR 8550, École Normale Supérieure, F-75005 Paris (France); Manneville, P, E-mail: paul.manneville@polytechnique.edu [Laboratoire d’Hydrodynamique, CNRS UMR7646, École Polytechnique, F-91128, Palaiseau (France)

2015-06-15

On its way to turbulence, plane Couette flow–the flow between counter-translating parallel plates–displays a puzzling steady oblique laminar-turbulent pattern. We approach this problem via Galerkin modelling of the Navier–Stokes equations. The wall-normal dependence of the hydrodynamic field is treated by means of expansions on functional bases fitting the boundary conditions exactly. This yields a set of partial differential equations for spatiotemporal dynamics in the plane of the flow. Truncating this set beyond the lowest nontrivial order is numerically shown to produce the expected pattern, therefore improving over what was obtained at the cruder effective wall-normal resolution. Perspectives opened by this approach are discussed. (paper)

20. Modeling the mechanics of HMX detonation using a Taylor–Galerkin scheme

Directory of Open Access Journals (Sweden)

2016-05-01

Full Text Available Design of energetic materials is an exciting area in mechanics and materials science. Energetic composite materials are used as propellants, explosives, and fuel cell components. Energy release in these materials are accompanied by extreme events: shock waves travel at typical speeds of several thousand meters per second and the peak pressures can reach hundreds of gigapascals. In this paper, we develop a reactive dynamics code for modeling detonation wave features in one such material. The key contribution in this paper is an integrated algorithm to incorporate equations of state, Arrhenius kinetics, and mixing rules for particle detonation in a Taylor–Galerkin finite element simulation. We show that the scheme captures the distinct features of detonation waves, and the detonation velocity compares well with experiments reported in literature.

1. 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.

2. Lagrange–Galerkin methods for the incompressible Navier-Stokes equations: a review

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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.

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

KAUST Repository

Bäck, Joakim

2010-09-17

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. By introducing a suitable generalization of the classical sparse grid SC method, we are able to compare SG and SC on the same underlying multivariate polynomial space in terms of accuracy vs. computational work. The approximation spaces considered here include isotropic and anisotropic versions of Tensor Product (TP), Total Degree (TD), Hyperbolic Cross (HC) and Smolyak (SM) polynomials. Numerical results for linear elliptic SPDEs indicate a slight computational work advantage of isotropic SC over SG, with SC-SM and SG-TD being the best choices of approximation spaces for each method. Finally, numerical results corroborate the optimality of the theoretical estimate of anisotropy ratios introduced by the authors in a previous work for the construction of anisotropic approximation spaces. © 2011 Springer.

4. A High Order Filter with Galerkin Finite Element Method for the Spherical Local domain Model

Science.gov (United States)

Lee, C. H.; Cheong, H. B.; Kang, H. G.

2017-12-01

A High Order Filter with Galerkin Finite Element Method for the Spherical Local domain ModelChung-Hui Lee1 and Hyeong-Bin Cheong and Hyun-Gyu KangDepartment of Environmental Atmospheric Sciences, Pukyong National University, Busan, Korea (1 chlee@pukyong.ac.kr) A high-order filter with Galerkin finite element method is constructed by applying a two dimensional finite element method with quadrilateral basis functions to the spherical limited area domain. The quadrilateral basis function is defined as four shape-functions on separate four grid-boxes which share the same gridpoint. A first-order derivative is represented with an algebraic equation consisting of nine point stencil. Helmholtz equation on a sphere is the basic component of the high order filter and the filtering is performed by solving this equation with two dimensional finite element method. As the theory describes, for spherical Laplacian operator and first-order derivative, the convergence rates of the error were revealed to be second-order and fourth-order, respectively. In addition, since the convergence rate of errors for the filter in this study was the same as the filter with Fourier finite element method, the accuracy of the filter is comparable to the filter based on the Fourier finite element method. The high-order filter was applied to the WRF (Weather Research and Forecasting) as hyper-viscosity and its performance was compared with those of the built-in viscosity scheme of the WRF model. As a result of the tropical cyclone simulation, the forecast error for the high-order filter and the built-in viscosity were similar for the minimum pressure and track prediction. However, for the precipitation and rainfall distribution, the prediction with high-order filter appeared closer to observations than those with built-in viscosity.

5. Periodic synchronization control of discontinuous delayed networks by using extended Filippov-framework.

Science.gov (United States)

Cai, Zuowei; Huang, Lihong; Guo, Zhenyuan; Zhang, Lingling; Wan, Xuting

2015-08-01

This paper is concerned with the periodic synchronization problem for a general class of delayed neural networks (DNNs) with discontinuous neuron activation. One of the purposes is to analyze the problem of periodic orbits. To do so, we introduce new tools including inequality techniques and Kakutani's fixed point theorem of set-valued maps to derive the existence of periodic solution. Another purpose is to design a switching state-feedback control for realizing global exponential synchronization of the drive-response network system with periodic coefficients. Unlike the previous works on periodic synchronization of neural network, both the neuron activations and controllers in this paper are allowed to be discontinuous. Moreover, owing to the occurrence of delays in neuron signal, the neural network model is described by the functional differential equation. So we introduce extended Filippov-framework to deal with the basic issues of solutions for discontinuous DNNs. Finally, two examples and simulation experiments are given to illustrate the proposed method and main results which have an important instructional significance in the design of periodic synchronized DNNs circuits involving discontinuous or switching factors. Copyright © 2015 Elsevier Ltd. All rights reserved.

6. Singularity and dynamics on discontinuous vector fields

CERN Document Server

Luo, Albert CJ

2006-01-01

This book discussed fundamental problems in dynamics, which extensively exist in engineering, natural and social sciences. The book presented a basic theory for the interactions among many dynamical systems and for a system whose motions are constrained naturally or artificially. The methodology and techniques presented in this book are applicable to discontinuous dynamical systems in physics, engineering and control. In addition, they may provide useful tools to solve non-traditional dynamics in biology, stock market and internet network et al, which cannot be easily solved by the traditional

7. Boundary discontinuous Fourier analysis of thick beams with clamped and simply supported edges via CUF

Directory of Open Access Journals (Sweden)

F.G. CANALES

2017-10-01

Full Text Available This paper presents an analytical solution for static analysis of thick rectangular beams with different boundary conditions. Carrera’s Unified Formulation (CUF is used in order to consider shear deformation theories of arbitrary order. The novelty of the present work is that a boundary discontinuous Fourier approach is used to consider clamped boundary conditions in the analytical solution, unlike Navier-type solutions which are restricted to simply supported beams. Governing equations are obtained by employing the principle of virtual work. The numerical accuracy of results is ascertained by studying the convergence of the solution and comparing the results to those of a 3D finite element solution. Beams subjected to bending due to a uniform pressure load and subjected to torsion due to opposite linear forces are considered. Overall, accurate results close to those of 3D finite element solutions are obtained, which can be used to validate finite element results or other approximate methods.

8. Rock discontinuity surface roughness variation with scale

Science.gov (United States)

Bitenc, Maja; Kieffer, D. Scott; Khoshelham, Kourosh

2017-04-01

ABSTRACT: Rock discontinuity surface roughness refers to local departures of the discontinuity surface from planarity and is an important factor influencing the shear resistance. In practice, the Joint Roughness Coefficient (JRC) roughness parameter is commonly relied upon and input to a shear strength criterion such as developed by Barton and Choubey [1977]. The estimation of roughness by JRC is hindered firstly by the subjective nature of visually comparing the joint profile to the ten standard profiles. Secondly, when correlating the standard JRC values and other objective measures of roughness, the roughness idealization is limited to a 2D profile of 10 cm length. With the advance of measuring technologies that provide accurate and high resolution 3D data of surface topography on different scales, new 3D roughness parameters have been developed. A desirable parameter is one that describes rock surface geometry as well as the direction and scale dependency of roughness. In this research a 3D roughness parameter developed by Grasselli [2001] and adapted by Tatone and Grasselli [2009] is adopted. It characterizes surface topography as the cumulative distribution of local apparent inclination of asperities with respect to the shear strength (analysis) direction. Thus, the 3D roughness parameter describes the roughness amplitude and anisotropy (direction dependency), but does not capture the scale properties. In different studies the roughness scale-dependency has been attributed to data resolution or size of the surface joint (see a summary of researches in [Tatone and Grasselli, 2012]). Clearly, the lower resolution results in lower roughness. On the other hand, have the investigations of surface size effect produced conflicting results. While some studies have shown a decrease in roughness with increasing discontinuity size (negative scale effect), others have shown the existence of positive scale effects, or both positive and negative scale effects. We

9. The meshless local Petrov-Galerkin method based on moving Kriging interpolation for solving the time fractional Navier-Stokes equations.

Science.gov (United States)

Thamareerat, N; Luadsong, A; Aschariyaphotha, N

2016-01-01

In this paper, we present a numerical scheme used to solve the nonlinear time fractional Navier-Stokes equations in two dimensions. We first employ the meshless local Petrov-Galerkin (MLPG) method based on a local weak formulation to form the system of discretized equations and then we will approximate the time fractional derivative interpreted in the sense of Caputo by a simple quadrature formula. The moving Kriging interpolation which possesses the Kronecker delta property is applied to construct shape functions. This research aims to extend and develop further the applicability of the truly MLPG method to the generalized incompressible Navier-Stokes equations. Two numerical examples are provided to illustrate the accuracy and efficiency of the proposed algorithm. Very good agreement between the numerically and analytically computed solutions can be observed in the verification. The present MLPG method has proved its efficiency and reliability for solving the two-dimensional time fractional Navier-Stokes equations arising in fluid dynamics as well as several other problems in science and engineering.

10. Vibration analysis of orthotropic circular and elliptical nano-plates embedded in elastic medium based on nonlocal Mindlin plate theory and using Galerkin method

International Nuclear Information System (INIS)

Anjomshoa, Amin; Tahani, Masoud

2016-01-01

In the present study a continuum model based on the nonlocal elasticity theory is developed for free vibration analysis of embedded ortho tropic thick circular and elliptical nano-plates rested on an elastic foundation. The elastic foundation is considered to behave like a Pasternak type of foundations. Governing equations for vibrating nano-plate are derived according to the Mindlin plate theory in which the effects of shear deformations of nano-plate are also included. The Galerkin method is then employed to obtain the size dependent natural frequencies of nano-plate. The solution procedure considers the entire nano-plate as a single super-continuum element. Effect of nonlocal parameter, lengths of nano-plate, aspect ratio, mode number, material properties, thickness and foundation on circular frequencies are investigated. It is seen that the nonlocal frequencies of the nano-plate are smaller in comparison to those from the classical theory and this is more pronounced for small lengths and higher vibration modes. It is also found that as the aspect ratio increases or the nanoplate becomes more elliptical, the small scale effect on natural frequencies increases. Further, it is observed that the elastic foundation decreases the influence of nonlocal parameter on the results. Since the effect of shear deformations plays an important role in vibration analysis and design of nano-plates, by predicting smaller values for fundamental frequencies, the study of these nano-structures using thick plate theories such as Mindlin plate theory is essential.

11. Development of Galerkin Finite Element Method Three-dimensional Computational Code for the Multigroup Neutron Diffusion Equation with Unstructured Tetrahedron Elements

Directory of Open Access Journals (Sweden)

Seyed Abolfazl Hosseini

2016-02-01

Full Text Available In the present paper, development of the three-dimensional (3D computational code based on Galerkin finite element method (GFEM for solving the multigroup forward/adjoint diffusion equation in both rectangular and hexagonal geometries is reported. Linear approximation of shape functions in the GFEM with unstructured tetrahedron elements is used in the calculation. Both criticality and fixed source calculations may be performed using the developed GFEM-3D computational code. An acceptable level of accuracy at a low computational cost is the main advantage of applying the unstructured tetrahedron elements. The unstructured tetrahedron elements generated with Gambit software are used in the GFEM-3D computational code through a developed interface. The forward/adjoint multiplication factor, forward/adjoint flux distribution, and power distribution in the reactor core are calculated using the power iteration method. Criticality calculations are benchmarked against the valid solution of the neutron diffusion equation for International Atomic Energy Agency (IAEA-3D and Water-Water Energetic Reactor (VVER-1000 reactor cores. In addition, validation of the calculations against the P1 approximation of the transport theory is investigated in relation to the liquid metal fast breeder reactor benchmark problem. The neutron fixed source calculations are benchmarked through a comparison with the results obtained from similar computational codes. Finally, an analysis of the sensitivity of calculations to the number of elements is performed.

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

KAUST Repository

Jin, Bangti

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.

13. 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

14. Puncture black hole initial data: A single domain Galerkin-collocation method for trumpet and wormhole data sets

Science.gov (United States)

Clemente, P. C. M.; de Oliveira, H. P.

2017-07-01

We present a single-domain Galerkin-collocation method to calculate puncture initial data sets for single and binary black holes, either in the trumpet or wormhole geometries. The combination of aspects belonging to the Galerkin and the collocation methods together with the adoption of spherical coordinates in all cases are shown to be very effective. We propose a unified expression for the conformal factor to describe trumpet and spinning black holes. In particular, for the spinning trumpet black holes, we exhibit the deformation of the limit surface due to the spin from a sphere to an oblate spheroid. We also revisit the energy content in the trumpet and wormhole puncture data sets. The algorithm can be extended to describe binary black holes.

15. 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.

16. 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.

17. A transient, Hex-Z nodal code corrected by discontinuity factors

International Nuclear Information System (INIS)

Shatilla, Y.A.M.; Henry, A.F.

1993-01-01

This document constitutes Volume 1 of the Final Report of a three-year study supported by the special Research Grant Program for Nuclear Energy Research set up by the US Department of Energy. The original motivation for the work was to provide a fast and accurate computer program for the analysis of transients in heavy water or graphite-moderated reactors being considered as candidates for the New Production Reactor. Thus, part of the funding was by way of pass-through money from the Savannah River Laboratory. With this intent in mind, a three-dimensional (Hex-Z), general-energy-group transient, nodal code was created, programmed, and tested. In order to improve accuracy, correction terms, called open-quotes discontinuity factors,close quotes were incorporated into the nodal equations. Ideal values of these factors force the nodal equations to provide node-integrated reaction rates and leakage rates across nodal surfaces that match exactly those edited from a more exact reference calculation. Since the exact reference solution is needed to compute the ideal discontinuity factors, the fact that they result in exact nodal equations would be of little practical interest were it not that approximate discontinuity factors, found at a greatly reduced cost, often yield very accurate results. For example, for light-water reactors, discontinuity factors found from two-dimensional, fine-mesh, multigroup transport solutions for two-dimensional cuts of a fuel assembly provide very accurate predictions of three-dimensional, full-core power distributions. The present document (volume 1) deals primarily with the specification, programming and testing of the three-dimensional, Hex-Z computer program. The program solves both the static (eigenvalue) and transient, general-energy-group, nodal equations corrected by user-supplied discontinuity factors

18. Oscillations of a Class of Forced Second-Order Differential Equations with Possible Discontinuous Coefficients

Directory of Open Access Journals (Sweden)

Siniša Miličić

2013-01-01

Full Text Available We study the oscillation of all solutions of a general class of forced second-order differential equations, where their second derivative is not necessarily a continuous function and the coefficients of the main equation may be discontinuous. Our main results are not included in the previously published known oscillation criteria of interval type. Many examples and consequences are presented illustrating the main results.

19. On nonlinear boundary value problems with deviating arguments and discontinuous right hand side

Directory of Open Access Journals (Sweden)

B. C. Dhage

1993-01-01

Full Text Available In this paper we shall study the existence of the extremal solutions of a nonlinear boundary value problem of a second order differential equation with general Dirichlet/Neumann form boundary conditions. The right hand side of the differential equation is assumed to contain a deviating argument, and it is allowed to possess discontinuities in all the variables. The proof is based on a generalized iteration method.

20. Discrete Mixed Petrov-Galerkin Finite Element Method for a Fourth-Order Two-Point Boundary Value Problem

Directory of Open Access Journals (Sweden)

L. Jones Tarcius Doss

2012-01-01

Full Text Available A quadrature-based mixed Petrov-Galerkin finite element method is applied to a fourth-order linear ordinary differential equation. After employing a splitting technique, a cubic spline trial space and a piecewise linear test space are considered in the method. The integrals are then replaced by the Gauss quadrature rule in the formulation itself. Optimal order a priori error estimates are obtained without any restriction on the mesh.

1. 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.

2. Discontinuation of Opiate Treatment: A Retrospective Review of 49 Patients

OpenAIRE

Alen J Salerian

2015-01-01

This retrospective study reviews 49 patients- one year with opiate and one year post treatment discontinuation - treated at a private outpatient psychopharmacology center. This retrospective study reviews the health status of 398 patients with two distinct subgroups, 17 local and 32 out-of-town patients. Results revealed significant rise in fatalities after opiate discontinuation. The review results are consistent with increased risk of premature death following opiate discontinuation. It may...

3. Regression Discontinuity Designs Based on Population Thresholds

DEFF Research Database (Denmark)

Eggers, Andrew C.; Freier, Ronny; Grembi, Veronica

) to measure the effects of these threshold-based policies on political and economic outcomes. Using evidence from France, Germany, and Italy, we highlight two common pitfalls that arise in exploiting population-based policies (confounded treatment and sorting) and we provide guidance for detecting......In many countries, important features of municipal government (such as the electoral system, mayors' salaries, and the number of councillors) depend on whether the municipality is above or below arbitrary population thresholds. Several papers have used a regression discontinuity design (RDD...... and addressing these pitfalls. Even when these problems are present, population-threshold RDD may be the best available research design for studying the effects of certain policies and political institutions....

4. Discontinuity and complexity in nonlinear physical systems

CERN Document Server

Baleanu, Dumitru; Luo, Albert

2014-01-01

This unique book explores recent developments in experimental research in this broad field, organized in four distinct sections. Part I introduces the reader to the fractional dynamics and Lie group analysis for nonlinear partial differential equations. Part II covers chaos and complexity in nonlinear Hamiltonian systems, important to understand the resonance interactions in nonlinear dynamical systems, such as Tsunami waves and wildfire propagations; as well as Lev flights in chaotic trajectories, dynamical system synchronization and DNA information complexity analysis. Part III examines chaos and periodic motions in discontinuous dynamical systems, extensively present in a range of systems, including piecewise linear systems, vibro-impact systems and drilling systems in engineering. And in Part IV, engineering and financial nonlinearity are discussed. The mechanism of shock wave with saddle-node bifurcation and rotating disk stability will be presented, and the financial nonlinear models will be discussed....

5. RURAL TOURISM IN ROMANIA - EVOLUTIONS AND DISCONTINUITIES

Directory of Open Access Journals (Sweden)

Ionica SOARE

2011-12-01

Full Text Available This paper analyzes the evolution of rural tourism since the early '70s, the time of onset, and indicates the discontinuity recorded especially after 1989 until the brink of the preparation for Romania's joining the European Union and the present state, one far behind the countries with extremely high degree of urbanization and industrialization, probably as a result of a lack of strategy for this form of tourism in which the beneficiary is the Ministry of Tourism, as the health tourism and ecotourism have recently had. The location of many villages in areas of outstanding natural landscapes, the richness and variety of cultural heritage that endows them, are issues related to an increased tourism potential that can be capitalized and those unique tourism products that can not be seen, admired and offered by other countries.

6. Management of severe periacetabular bone loss combined with pelvic discontinuity in revision hip arthroplasty.

Science.gov (United States)

Friedrich, Max J; Schmolders, Jan; Michel, Robert D; Randau, Thomas M; Wimmer, Matthias D; Kohlhof, Hendrik; Wirtz, Dieter C; Gravius, Sascha

2014-12-01

7. Factors related to continuous and discontinuous attendance at memory clinics.

Science.gov (United States)

Hishikawa, N; Fukui, Y; Nakano, Y; Morihara, R; Takemoto, M; Sato, K; Yamashita, T; Ohta, Y; Abe, K

2017-05-01

Few studies have examined why some patients with dementia stop attending medical consultations. We conducted a retrospective study to investigate factors associated with discontinuous clinic attendance. Participants were 988 patients with dementia from university hospital (UH) clinics and affiliated local hospital (LH) clinics. We compared continuous and discontinuous attenders on cognitive and affective functions and activities of daily living (ADL), and also compared UH and LH patients (UH: continuous, n = 176; discontinuous, n = 207; LH: continuous, n = 418; discontinuous, n = 187). The total annual rate of discontinuation was 8.0%, and the mean period of attendance before discontinuation was 2.2 ± 2.4 years (UH, 2.8 ± 3.0; LH, 1.5 ± 1.3, P attendance at their own discretion (35.3% for LH). We identified the main reasons for discontinuation of attendance as returning to the family doctor and cessation of hospital attendance at their own discretion. The best predictors of discontinuation were ADL decline and worsening BPSD. There were significant differences in discontinuation between UH and LH patients with dementia. © 2017 EAN.

8. Robust Finite-Time Stabilization of Fractional-Order Neural Networks With Discontinuous and Continuous Activation Functions Under Uncertainty.

Science.gov (United States)

Ding, Zhixia; Zeng, Zhigang; Wang, Leimin

2017-03-10

This paper is concerned with robust finite-time stabilization for a class of fractional-order neural networks (FNNs) with two types of activation functions (i.e., discontinuous and continuous activation function) under uncertainty. It is worth noting that there exist few results about FNNs with discontinuous activation functions, which is mainly because classical solutions and theories of differential equations cannot be applied in this case. Especially, there is no relevant finite-time stabilization research for such system, and this paper makes up for the gap. The existence of global solution under the framework of Filippov for such system is guaranteed by limiting discontinuous activation functions. According to set-valued analysis and Kakutani's fixed point theorem, we obtain the existence of equilibrium point. In particular, based on differential inclusion theory and fractional Lyapunov stability theory, several new sufficient conditions are given to ensure finite-time stabilization via a novel discontinuous controller, and the upper bound of the settling time for stabilization is estimated. In addition, we analyze the finite-time stabilization of FNNs with Lipschitz-continuous activation functions under uncertainty. The results of this paper improve corresponding ones of integer-order neural networks with discontinuous and continuous activation functions. Finally, three numerical examples are given to show the effectiveness of the theoretical results.

9. Local bounds preserving stabilization for continuous Galerkin discretization of hyperbolic systems

Science.gov (United States)

Mabuza, Sibusiso; Shadid, John N.; Kuzmin, Dmitri

2018-05-01

The objective of this paper is to present a local bounds preserving stabilized finite element scheme for hyperbolic systems on unstructured meshes based on continuous Galerkin (CG) discretization in space. A CG semi-discrete scheme with low order artificial dissipation that satisfies the local extremum diminishing (LED) condition for systems is used to discretize a system of conservation equations in space. The low order artificial diffusion is based on approximate Riemann solvers for hyperbolic conservation laws. In this case we consider both Rusanov and Roe artificial diffusion operators. In the Rusanov case, two designs are considered, a nodal based diffusion operator and a local projection stabilization operator. The result is a discretization that is LED and has first order convergence behavior. To achieve high resolution, limited antidiffusion is added back to the semi-discrete form where the limiter is constructed from a linearity preserving local projection stabilization operator. The procedure follows the algebraic flux correction procedure usually used in flux corrected transport algorithms. To further deal with phase errors (or terracing) common in FCT type methods, high order background dissipation is added to the antidiffusive correction. The resulting stabilized semi-discrete scheme can be discretized in time using a wide variety of time integrators. Numerical examples involving nonlinear scalar Burgers equation, and several shock hydrodynamics simulations for the Euler system are considered to demonstrate the performance of the method. For time discretization, Crank-Nicolson scheme and backward Euler scheme are utilized.

10. Discontinuation of Buprenorphine Maintenance Therapy: Perspectives and Outcomes

Science.gov (United States)

Bentzley, Brandon S.; Barth, Kelly S.; Back, Sudie E.; Book, Sarah W.

2015-01-01

Buprenorphine maintenance therapy (BMT) is increasingly the preferred opioid maintenance agent due to its reduced toxicity and availability in an office-based setting in the United States. Although BMT has been shown to be highly efficacious, it is often discontinued soon after initiation. No current systematic review has yet investigated providers’ or patients’ reasons for BMT discontinuation or the outcomes that follow. Hence, provider and patient perspectives associated with BMT discontinuation after a period of stable buprenorphine maintenance and the resultant outcomes were systematically reviewed with specific emphasis on pre-buprenorphine-taper parameters predictive of relapse following BMT discontinuation. Few identified studies address provider or patient perspectives associated with buprenorphine discontinuation. Within the studies reviewed providers with residency training in BMT were more likely to favor long term BMT instead of detoxification, and providers were likely to consider BMT discontinuation in the face of medication misuse. Patients often desired to remain on BMT because of fear of relapse to illicit opioid use if they were to discontinue BMT. The majority of patients who discontinued BMT did so involuntarily, often due to failure to follow strict program requirements, and 1 month following discontinuation, rates of relapse to illicit opioid use exceeded 50% in every study reviewed. Only lower buprenorphine maintenance dose, which may be a marker for attenuated addiction severity, predicted better outcomes across studies. Relaxed BMT program requirements and frequent counsel on the high probability of relapse if BMT is discontinued may improve retention in treatment and prevent the relapse to illicit opioid use that is likely to follow BMT discontinuation. PMID:25601365

11. Discontinuities in Early Development of the Understanding of Physical Causality

Science.gov (United States)

Aschersleben, Gisa; Henning, Anne; Daum, Moritz M.

2013-01-01

Research on early physical reasoning has shown surprising discontinuities in developmental trajectories. Infants possess some skills that seem to disappear and then re-emerge in childhood. It has been suggested that prediction skills required in search tasks might cause these discontinuities (Keen, 2003). We tested 3.5- to 5-year-olds'…

12. Enacting discontinuity-what's useful and what's cumbersome

NARCIS (Netherlands)

Stegmaier, Peter

2015-01-01

In this paper, I will review various empirical and theoretical sets of conditions and strategies under which active and purposeful discontinuity appears accomplishable. More abrupt and more incremental processes of discontinuation will be distinguished, as well as how they are linked to different

13. Qualitative study of reasons for discontinuation of injectable ...

African Journals Online (AJOL)

Discontinuation of contraception is a major problem in Kenya. Even though they want to space or limit their births, over a quarter of contraceptive injectable users discontinue use of the method within 12 months of beginning use. Fourteen focus group discussions were conducted in Nyando District, Kenya among current ...

14. 27 CFR 25.277 - Discontinuance of operations.

Science.gov (United States)

2010-04-01

... BUREAU, DEPARTMENT OF THE TREASURY LIQUORS BEER Pilot Brewing Plants § 25.277 Discontinuance of operations. When operations of a pilot brewing plant are to be discontinued, the operator shall notify the... operations have been completed and all beer at the premises has been disposed of and accounted for, the...

15. Discontinuous pn-heterojunction for organic thin film transistors

NARCIS (Netherlands)

Cho, B.; Yu, S.H.; Kim, M.; Lee, M.H.; Huh, W.; Lee, J.; Kim, J.; Cho, J.H.; Lee, J.Y.; Song, Y.J.; Kang, M.S.

2014-01-01

Utilization of discontinuous pn-oragnic heterojunction is introduced as a versatile method to improve charge transport in organic thin film transistors (OTFTs). The method is demonstrated by depositing n-type dioctyl perylene tetracarboxylic diimide (PTCDI-C8) discontinuously onto base p-type

16. 27 CFR 21.3 - Stocks of discontinued formulas.

Science.gov (United States)

2010-04-01

... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Stocks of discontinued..., DEPARTMENT OF THE TREASURY LIQUORS FORMULAS FOR DENATURED ALCOHOL AND RUM General Provisions § 21.3 Stocks of discontinued formulas. Denaturers, or specially denatured spirits dealers or users, having on hand stocks of...

17. Effect of Boron Doping on Cellular Discontinuous Precipitation for Age-Hardenable Cu–Ti Alloys

Directory of Open Access Journals (Sweden)

Satoshi Semboshi

2015-06-01

Full Text Available The effects of boron doping on the microstructural evolution and mechanical and electrical properties of age-hardenable Cu–4Ti (at.% alloys are investigated. In the quenched Cu–4Ti–0.03B (at.% alloy, elemental B (boron is preferentially segregated at the grain boundaries of the supersaturated solid-solution phase. The aging behavior of the B-doped alloy is mostly similar to that of conventional age-hardenable Cu–Ti alloys. In the early stage of aging at 450 °C, metastable β′-Cu4Ti with fine needle-shaped precipitates continuously form in the matrix phase. Cellular discontinuous precipitates composed of the stable β-Cu4Ti and solid-solution laminates are then formed and grown at the grain boundaries. However, the volume fraction of the discontinuous precipitates is lower in the Cu–4Ti–0.03B alloy than the Cu–4Ti alloy, particularly in the over-aging period of 72–120 h. The suppression of the formation of discontinuous precipitates eventually results in improvement of the hardness and tensile strength. It should be noted that minor B doping of Cu–Ti alloys also effectively enhances the elongation to fracture, which should be attributed to segregation of B at the grain boundaries.

18. Green’s Function Approach to Solution of Transient Temperature for Thermal Stresses of Functionally Graded Material

Science.gov (United States)

Kim, Kui-Seob; Noda, Naotake

The transient temperature solution for a functionally graded material (FGM) is formulated by Green’s function based on the Galerkin method. An approximate solution that satisfies the homogeneous boundary condition is substituted into the governing equation to yield an eigenvalue problem. To solve the eigenvalue problem, the eigenfunctions are approximated by a series of polynomials satisfying the homogeneous boundary condition. The Galerkin method is used to determine the coefficients of eigenfunctions. The transient temperature solution for a general heat conduction equation with a source and nonhomogeneous boundary conditions is obtained by using Green’s function, which is expressed by eigenvalues and corresponding eigenfunctions. Transient thermal stresses in a FGM plate and a FGM hollow circular cylinder are discussed.

19. A Convergence Result for the Euler-Maruyama Method for a Simple Stochastic Differential Equation with Discontinuous Drift

DEFF Research Database (Denmark)

Simonsen, Maria; Schiøler, Henrik; Leth, John-Josef

2014-01-01

The Euler-Maruyama method is applied to a simple stochastic differential equation (SDE) with discontinuous drift. Convergence aspects are investigated in the case, where the Euler-Maruyama method is simulated in dyadic points. A strong rate of convergence is presented for the numerical simulations...... and it is shown that the produced sequences converge almost surely. This is an improvement of the general result for SDEs with discontinuous drift, i.e. that the Euler-Maruyama approximations converge in probability to a strong solution of the SDE. A numerical example is presented together with a confidence...

20. Discontinuities in a damped quantum harmonic oscillator

International Nuclear Information System (INIS)

Giraldi, Filippo; Petruccione, Francesco

2012-01-01

The quantum model for a damped harmonic oscillator linearly coupled to a reservoir of continuous frequency modes has been exactly diagonalized either with or without the rotating wave approximation. The exact dynamics, formally described in terms of the coupling function, is analyzed for the Drude model. In this scenario, we focus on a class of couplings recovering the Drude form as a limiting case. The exact time evolution of the expectation values of the position, momentum and number operators are described through Fox H-functions, as well as the correlation function of the reservoir. In correspondence with the critical values of the frequency, discontinuities appear in the long time scale dynamics, arbitrarily slowing down the relaxations of the above observables. This effect allows one to enhance arbitrarily the lifetime of the excitations, giving relevant applications in the study of the quantum domain of opto-mechanical and nano-mechanical resonators. The critical frequency approach constitutes a further method of control in the scenario of environment-induced decoherence via reservoir engineering. (paper)

1. 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.

2. A Piecewise Bi-Linear Discontinuous Finite Element Spatial Discretization of the Sn Transport Equation

Energy Technology Data Exchange (ETDEWEB)

Bailey, T S; Chang, J H; Warsa, J S; Adams, M L

2010-12-22

We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretizations that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems.

3. Unique solution to periodic boundary value problems

Directory of Open Access Journals (Sweden)

Yong Sun

1991-01-01

Full Text Available Existence of unique solution to periodic boundary value problems of differential equations with continuous or discontinuous right-hand side is considered by utilizing the method of lower and upper solutions and the monotone properties of the operator. This is subject to discussion in the present paper.

4. How Condom Discontinuation Occurs: Interviews With Emerging Adult Women.

Science.gov (United States)

Mullinax, Margo; Sanders, Stephanie; Dennis, Barbara; Higgins, Jenny; Fortenberry, J Dennis; Reece, Michael

We have almost no data on how and when couples stop using condoms. This qualitative study investigated the process of condom discontinuation. From November 2013 to April 2014, a total of 25 women living in a college town in the Midwest, ages 18 to 25, participated in semistructured interviews centered around three domains: partner interactions, contraceptive use, and sexually transmitted infection (STI) prevention. Analysis followed a critical qualitative research orientation. Participants described actively seeking the best options to prevent pregnancy, perceiving condom discontinuation in favor of hormonal methods as a smart decision, and reported wanting to discontinue using condoms due to physical discomfort. Oftentimes, nonverbal communication around contextual instances of condom unavailability paved the way for discontinuation. Participants indicated the decision to stop using condoms was neither deliberate nor planned. Condom discontinuation rarely occurred at one point in time; instead, it was preceded by a period of occasional use. Even after participants described themselves as not using condoms, sporadic condom use was normal (typically related to fertility cycles). This study provides a more detailed understanding of how and why emerging adults negotiate condom discontinuation, thereby enhancing our ability to design effective condom continuation messages. Attention should be paid to helping emerging adults think more concretely about condom discontinuation.

5. Adaptive Finite Element Methods for Elliptic Problems with Discontinuous Coefficients

KAUST Repository

Bonito, Andrea

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.

6. Predictors of premature discontinuation of treatment in multiple disease states

Directory of Open Access Journals (Sweden)

Eric Nantz

2009-01-01

Full Text Available Eric Nantz1, Hong Liu-Seifert2, Vladimir Skljarevski21Department of Statistics, Western Michigan University, Kalamazoo, MI, USA; 2Lilly Research Laboratories, Eli Lilly and Company, Indianapolis, IN, USABackground: Premature discontinuation of treatment impacts outcomes of clinical practice. The traditional perception has been patient discontinuation is mainly driven by unwanted side effects. Systematic analysis of data from clinical trials across several disease states was performed to identify predictors of premature discontinuation during clinical interventions.Methods: A post hoc analysis was conducted on 22 randomized, double-blind, placebo-controlled clinical trials for treatment of fibromyalgia, diabetic peripheral neuropathic pain, major depressive disorder, and generalized anxiety disorder. Analyses were conducted on pooled data within each disease state.Results: Lack of early therapeutic response was a significant predictor of patient discontinuation in each disease state. Visit-wise changes in therapeutic response and severity of adverse events were also significant risk factors, with change in therapeutic response having a higher significance level in three disease states. Patients who discontinued due to adverse events had similar therapeutic responses as patients completing treatment.Conclusion: Contrary to the conventional belief that premature treatment discontinuation is primarily related to adverse events, our findings suggest lack of therapeutic response also plays a significant role in patient attrition. This research highlights the importance of systematic monitoring of therapeutic response in clinical practice as a measure to prevent patients’ discontinuation from pharmacological treatments.Keywords: attrition, depression, generalized anxiety disorder, fibromyalgia, therapeutic response, adverse event

7. Galerkin method for unsplit 3-D Dirac equation using atomically/kinetically balanced B-spline basis

Energy Technology Data Exchange (ETDEWEB)

Fillion-Gourdeau, F., E-mail: filliong@CRM.UMontreal.ca [Université du Québec, INRS – Énergie, Matériaux et Télécommunications, Varennes, J3X 1S2 (Canada); Centre de Recherches Mathématiques, Université de Montréal, Montréal, H3T 1J4 (Canada); Lorin, E., E-mail: elorin@math.carleton.ca [School of Mathematics and Statistics, Carleton University, Ottawa, K1S 5B6 (Canada); Centre de Recherches Mathématiques, Université de Montréal, Montréal, H3T 1J4 (Canada); Bandrauk, A.D., E-mail: andre.bandrauk@usherbrooke.ca [Laboratoire de Chimie Théorique, Faculté des Sciences, Université de Sherbrooke, Sherbrooke, J1K 2R1 (Canada); Centre de Recherches Mathématiques, Université de Montréal, Montréal, H3T 1J4 (Canada)

2016-02-15

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.

8. OPTIMAL ESTIMATES FOR THE SEMIDISCRETE GALERKIN METHOD APPLIED TO PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS WITH NONSMOOTH DATA

KAUST Repository

GOSWAMI, DEEPJYOTI

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.

9. 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.

10. 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)

11. Stacking by electroinjection with discontinuous buffers in capillary zone electrophoresis.

Science.gov (United States)

Shihabi, Zak K

2002-08-01

The work presented here demonstrates that electroinjection can be performed using discontinuous buffers, which can result in better stacking than that obtained by hydrodynamic injection. The sample can be concentrated at the tip of the capillary leaving practically the whole capillary for sample separation. This results in several advantages, such as better sample concentration, higher plate number and shorter time of stacking. However, sample introduction by electromigration is suited for samples free or low in salt content. Samples, which are high in salt content, are better introduced by the hydrodynamic injection for stacking by the discontinuous buffers. Different simple methods to introduce the discontinuity in the buffer for electroinjection are discussed.

12. 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

13. Discontinuation of continuous renal replacement therapy: A post hoc analysis of a prospective multicenter observational study

NARCIS (Netherlands)

Uchino, Shigehiko; Bellomo, Rinaldo; Morimatsu, Hiroshi; Morgera, Stanislao; Schetz, Miet; Tan, Ian; Bouman, Catherine; Macedo, Ettiene; Gibney, Noel; Tolwani, Ashita; Oudemans-van Straaten, Heleen; Ronco, Claudio; Kellum, John A.

2009-01-01

Objectives: To describe current practice for the discontinuation of continuous renal replacement therapy in a multinational setting and to identify variables associated with successful discontinuation. The approach to discontinue continuous renal replacement therapy may affect patient outcomes.

14. Steady-state solution of the PTC thermistor problem using a quadratic spline finite element method

Directory of Open Access Journals (Sweden)

2002-01-01

Full Text Available The problem of heat transfer in a Positive Temperature Coefficient (PTC thermistor, which may form one element of an electric circuit, is solved numerically by a finite element method. The approach used is based on Galerkin finite element using quadratic splines as shape functions. The resulting system of ordinary differential equations is solved by the finite difference method. Comparison is made with numerical and analytical solutions and the accuracy of the computed solutions indicates that the method is well suited for the solution of the PTC thermistor problem.

15. Linear Approximation and Asymptotic Expansion of Solutions for a Nonlinear Carrier Wave Equation in an Annular Membrane with Robin-Dirichlet Conditions

Directory of Open Access Journals (Sweden)

Le Thi Phuong Ngoc

2016-01-01

Full Text Available This paper is devoted to the study of a nonlinear Carrier wave equation in an annular membrane associated with Robin-Dirichlet conditions. Existence and uniqueness of a weak solution are proved by using the linearization method for nonlinear terms combined with the Faedo-Galerkin method and the weak compact method. Furthermore, an asymptotic expansion of a weak solution of high order in a small parameter is established.

16. Modelling discontinuous well log signal to identify lithological ...

Identification of sharp and discontinuous lithological boundaries from well log signal stemming fromheterogeneous subsurface structures assumes a special significance in geo-exploration studies. Well logdata acquired from various geological settings generally display nonstationary/nonlinear characteristicswith varying ...

17. Actor Bonds in Situations of Discontinuous Business Activities

DEFF Research Database (Denmark)

Skaates, Maria Anne

2000-01-01

in situations of discontinuity. Therefore an analysis and comparison of relevant concepts that capture the key generative features of actor bonds in both socially constructed networks and socially constructed markets is undertaken. These concepts include the "milieu" of project marketing (Cova et al., 1996......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......) and the institutional concept of the "field". Finally this paper introduces the concept of "social capital" (Bourdieu, 1983) and discusses whether it can be used to conceptualize the dynamic features of actor bonds in situations of discontinuity....

18. Clopidogrel discontinuation after myocardial infarction and risk of thrombosis

DEFF Research Database (Denmark)

Charlot, Mette; Nielsen, Lars Hougaard; Lindhardsen, Jesper

2012-01-01

The benefit of extending clopidogrel treatment beyond the 12-month period recommended in current guidelines after myocardial infarction (MI) is debated. We analysed the risk of adverse cardiovascular outcomes after discontinuation of 12 months of clopidogrel treatment....

19. Reasons for discontinuation of implanon among users in Buffalo City ...

African Journals Online (AJOL)

Reasons for discontinuation of implanon among users in Buffalo City Metropolitan Municipality, South Africa: a cross-sectional study. Khungelwa Patricia Mrwebi, Daniel Ter Goon, Eyitayo Omolara Owolabi, Oladele Vincent Adeniyi, Eunice Seekoe, Anthony Idowu Ajayi ...

20. Robust state estimation for neural networks with discontinuous activations.

Science.gov (United States)

Liu, Xiaoyang; Cao, Jinde

2010-12-01

Discontinuous dynamical systems, particularly neural networks with discontinuous activation functions, arise in a number of applications and have received considerable research attention in recent years. In this paper, the robust state estimation problem is investigated for uncertain neural networks with discontinuous activations and time-varying delays, where the neuron-dependent nonlinear disturbance on the network outputs are only assumed to satisfy the local Lipschitz condition. Based on the theory of differential inclusions and nonsmooth analysis, several criteria are presented to guarantee the existence of the desired robust state estimator for the discontinuous neural networks. It is shown that the design of the state estimator for such networks can be achieved by solving some linear matrix inequalities, which are dependent on the size of the time derivative of the time-varying delays. Finally, numerical examples are given to illustrate the theoretical results.