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.
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.
Numerical solution of fuzzy boundary value problems using Galerkin ...
Indian Academy of Sciences (India)
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.
EXPLICIT LEAST-DEGREE BOUNDARY FILTERS FOR DISCONTINUOUS GALERKIN*
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
Numerical solution of fuzzy boundary value problems using Galerkin ...
Indian Academy of Sciences (India)
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 ...
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.
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.
Directory of Open Access Journals (Sweden)
Muhammad Azam
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.
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
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
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.
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.
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.
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.
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.
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.
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
A higher order space-time Galerkin scheme for time domain integral equations
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.
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.
Integrability and boundary conditions of supersymmetric systems
International Nuclear Information System (INIS)
Yue Ruihong; Liang Hong
1996-01-01
By studying the solutions of the reflection equations, we find out a series of integrable supersymmetric systems with different boundary conditions. The Hamiltonian contains four free parameters which describe the contribution of the boundary terms
Second-Order Boundary Value Problem with Integral Boundary Conditions
Directory of Open Access Journals (Sweden)
Nieto JuanJ
2011-01-01
Full Text Available The nonlinear alternative of the Leray Schauder type and the Banach contraction principle are used to investigate the existence of solutions for second-order differential equations with integral boundary conditions. The compactness of solutions set is also investigated.
Retarded potentials and time domain boundary integral equations a road map
Sayas, Francisco-Javier
2016-01-01
This book offers a thorough and self-contained exposition of the mathematics of time-domain boundary integral equations associated to the wave equation, including applications to scattering of acoustic and elastic waves. The book offers two different approaches for the analysis of these integral equations, including a systematic treatment of their numerical discretization using Galerkin (Boundary Element) methods in the space variables and Convolution Quadrature in the time variable. The first approach follows classical work started in the late eighties, based on Laplace transforms estimates. This approach has been refined and made more accessible by tailoring the necessary mathematical tools, avoiding an excess of generality. A second approach contains a novel point of view that the author and some of his collaborators have been developing in recent years, using the semigroup theory of evolution equations to obtain improved results. The extension to electromagnetic waves is explained in one of the appendices...
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...
International Nuclear Information System (INIS)
Ackroyd, R.T.
1982-01-01
Some minimum and maximum variational principles for even-parity neutron transport are reviewed and the corresponding principles for odd-parity transport are derived by a simple method to show why the essential boundary conditions associated with these maximum principles have to be imposed. The method also shows why both the essential and some of the natural boundary conditions associated with these minimum principles have to be imposed. These imposed boundary conditions for trial functions in the variational principles limit the choice of the finite element used to represent trial functions. The reasons for the boundary conditions imposed on the principles for even- and odd-parity transport point the way to a treatment of composite neutron transport, for which completely boundary-free maximum and minimum principles are derived from a functional identity. In general a trial function is used for each parity in the composite neutron transport, but this can be reduced to one without any boundary conditions having to be imposed. (author)
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.
Beghein, Yves
2013-03-01
The time domain combined field integral equation (TD-CFIE), which is constructed from a weighted sum of the time domain electric and magnetic field integral equations (TD-EFIE and TD-MFIE) for analyzing transient scattering from closed perfect electrically conducting bodies, is free from spurious resonances. The standard marching-on-in-time technique for discretizing the TD-CFIE uses Galerkin and collocation schemes in space and time, respectively. Unfortunately, the standard scheme is theoretically not well understood: stability and convergence have been proven for only one class of space-time Galerkin discretizations. Moreover, existing discretization schemes are nonconforming, i.e., the TD-MFIE contribution is tested with divergence conforming functions instead of curl conforming functions. We therefore introduce a novel space-time mixed Galerkin discretization for the TD-CFIE. A family of temporal basis and testing functions with arbitrary order is introduced. It is explained how the corresponding interactions can be computed efficiently by existing collocation-in-time codes. The spatial mixed discretization is made fully conforming and consistent by leveraging both Rao-Wilton-Glisson and Buffa-Christiansen basis functions and by applying the appropriate bi-orthogonalization procedures. The combination of both techniques is essential when high accuracy over a broad frequency band is required. © 2012 IEEE.
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...
Singularity Preserving Numerical Methods for Boundary Integral Equations
Kaneko, Hideaki (Principal Investigator)
1996-01-01
In the past twelve months (May 8, 1995 - May 8, 1996), under the cooperative agreement with Division of Multidisciplinary Optimization at NASA Langley, we have accomplished the following five projects: a note on the finite element method with singular basis functions; numerical quadrature for weakly singular integrals; superconvergence of degenerate kernel method; superconvergence of the iterated collocation method for Hammersteion equations; and singularity preserving Galerkin method for Hammerstein equations with logarithmic kernel. This final report consists of five papers describing these projects. Each project is preceeded by a brief abstract.
Regularized boundary integral representations for dislocations and cracks in smart media
International Nuclear Information System (INIS)
Rungamornrat, J; Senjuntichai, T
2009-01-01
This paper presents a complete set of singularity-reduced boundary integral relations for isolated discontinuities embedded in three-dimensional infinite media. The development is carried out within a broad context that allows the treatment of a well-known class of smart media such as linear piezoelectric, linear piezomagnetic and linear piezoelectromagnetic materials. In addition, resulting boundary integral representations are applicable to general discontinuities of arbitrary geometry and possessing a general jump distribution. The latter aspect allows the treatment of two special kinds of discontinuities: dislocations and cracks. The most attractive feature of the current development is that all integral relations for field quantities such as state variables and their gradients, the body flux, and the generalized interaction energy produced by dislocations are expressed only in terms of line integrals over the dislocation loops and, for cracks, the key governing boundary integral equation is established in a symmetric weak form and contains only weakly singular kernels of O(1/r). Results for the former case are fundamental and useful in the context of dislocation mechanics and modeling while the resulting weakly singular, weak form integral equation constitutes a basis for the development of a well-known numerical technique, called a symmetric Galerkin boundary element method (SGBEM), for analysis of cracked bodies. The weakly singular nature of such an integral equation allows low order interpolations to be used in the numerical approximation. The key ingredient for achieving such development of integral representations is the use of certain special decompositions in the derivative-transferring process via Stokes's theorem. Existence of such decompositions is ensured by a careful consideration of the singularity nature of the kernels, and a particular solution of the weakly singular functions involved is obtained by solving a system of partial differential
Surface free energy for systems with integrable boundary conditions
International Nuclear Information System (INIS)
Goehmann, Frank; Bortz, Michael; Frahm, Holger
2005-01-01
The surface free energy is the difference between the free energies for a system with open boundary conditions and the same system with periodic boundary conditions. We use the quantum transfer matrix formalism to express the surface free energy in the thermodynamic limit of systems with integrable boundary conditions as a matrix element of certain projection operators. Specializing to the XXZ spin-1/2 chain we introduce a novel 'finite temperature boundary operator' which characterizes the thermodynamical properties of surfaces related to integrable boundary conditions
Boundary integral methods for unsaturated flow
International Nuclear Information System (INIS)
Martinez, M.J.; McTigue, D.F.
1990-01-01
Many large simulations may be required to assess the performance of Yucca Mountain as a possible site for the nations first high level nuclear waste repository. A boundary integral equation method (BIEM) is described for numerical analysis of quasilinear steady unsaturated flow in homogeneous material. The applicability of the exponential model for the dependence of hydraulic conductivity on pressure head is discussed briefly. This constitutive assumption is at the heart of the quasilinear transformation. Materials which display a wide distribution in pore-size are described reasonably well by the exponential. For materials with a narrow range in pore-size, the exponential is suitable over more limited ranges in pressure head. The numerical implementation of the BIEM is used to investigate the infiltration from a strip source to a water table. The net infiltration of moisture into a finite-depth layer is well-described by results for a semi-infinite layer if αD > 4, where α is the sorptive number and D is the depth to the water table. the distribution of moisture exhibits a similar dependence on αD. 11 refs., 4 figs.,
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.
Galerkin method for feedback controlled Rayleigh Bénard convection
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.
Existence results for nonlinear boundary-value problems with integral boundary conditions
Directory of Open Access Journals (Sweden)
Mouffak Benchohra
2005-01-01
Full Text Available In this paper, we investigate the existence of solutions for a second order nonlinear boundary-value problem with integral boundary conditions. By using suitable fixed point theorems, we study the cases when the right hand side has convex and nonconvex values.
APPLICATION OF BOUNDARY INTEGRAL EQUATION METHOD FOR THERMOELASTICITY PROBLEMS
Directory of Open Access Journals (Sweden)
Vorona Yu.V.
2015-12-01
Full Text Available Boundary Integral Equation Method is used for solving analytically the problems of coupled thermoelastic spherical wave propagation. The resulting mathematical expressions coincide with the solutions obtained in a conventional manner.
Boundary integral formulation for cracks at imperfect interfaces
Mishuris, G.; Piccolroaz, A.; Vellender, A.
2013-01-01
We consider an infinite bi-material plane containing a semi-infinite crack situated on a soft imperfect interface. The crack is loaded by a general asymmetrical system of forces distributed along the crack faces. On the basis of the weight function approach and the fundamental reciprocal identity, we derive the corresponding boundary integral formulation, relating physical quantities. The boundary integral equations derived in this paper in the imperfect interface setting show a weak singular...
Boundary conditions in conformal and integrable theories
Petkova, V B
2000-01-01
The study of boundary conditions in rational conformal field theories is not only physically important. It also reveals a lot on the structure of the theory ``in the bulk''. The same graphs classify both the torus and the cylinder partition functions and provide data on their hidden ``quantum symmetry''. The Ocneanu triangular cells -- the 3j-symbols of these symmetries, admit various interpretations and make a link between different problems.
Panafricanism, African Boundaries and Regional Integration ...
African Journals Online (AJOL)
The Pan African idea of closer unity is examined. Regional economic integration as a Pan African perspective is presented as a major way out of the deep and worsening economic crises bedeviling African economics. Attempts have been made since the 1960s to create and re-create institutions for regional economic ...
An integral equation method to boundary value problems in elastostatics
International Nuclear Information System (INIS)
Gospodinov, G.K.
1987-01-01
The boundary element method (BEM) is already a well established numerical technique for solving some boundary value problems in elastostatics - Brebbia and Walker (1980). The main feature of this approach is the use of fundamental solutions which reduces the dimension of the problem by one and results in finding some unknown functions on the boundary only. So if we want to use the BEM we need: First - the fundamental solutions, and second - the boundary integral equations which are usually constructed by means of Betti's law or Green's second identity. In many cases of practical importance however, the fundamental solutions are not known, or they are so complicated that the effective implementation of the BEM is under question. On the other hand, if the thickness of the domain in the two dimensional case is not constant, or the material is orthotropic the solution with boundary element method is complicated in a similar way. (orig./GL)
A spectral-element discontinuous Galerkin lattice Boltzmann method for nearly incompressible flows
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.
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
Optimal control problems for impulsive systems with integral boundary conditions
Directory of Open Access Journals (Sweden)
Allaberen Ashyralyev
2013-03-01
Full Text Available In this article, the optimal control problem is considered when the state of the system is described by the impulsive differential equations with integral boundary conditions. Applying the Banach contraction principle the existence and uniqueness of the solution is proved for the corresponding boundary problem by the fixed admissible control. The first and second variation of the functional is calculated. Various necessary conditions of optimality of the first and second order are obtained by the help of the variation of the controls.
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
Integrated care in the daily work: coordination beyond organisational boundaries.
Petrakou, Alexandra
2009-07-09
In this paper, integrated care in an inter-organisational cooperative setting of in-home elderly care is studied. The aim is to explore how home care workers coordinate their daily work, identify coordination issues in situ and discuss possible actions for supporting seamless and integrated elderly care at home. The empirical findings are drawn from an ethnographic workplace study of the cooperation and coordination taking place between home care workers in a Swedish county. Data were collected through observational studies, interviews and group discussions. The paper identifies a need to support two core issues. Firstly, it must be made clear how the care interventions that are currently defined as 'self-treatment' by the home health care should be divided. Secondly, the distributed and asynchronous coordination between all care workers involved, regardless of organisational belonging must be better supported. Integrated care needs to be developed between organisations as well as within each organisation. As a matter of fact, integrated care needs to be built up beyond organisational boundaries. Organisational boundaries affect the planning of the division of care interventions, but not the coordination during the home care process. During the home care process, the main challenge is the coordination difficulties that arise from the fact that workers are distributed in time and/or space, regardless of organisational belonging. A core subject for future practice and research is to develop IT tools that reach beyond formal organisational boundaries and processes while remaining adaptable in view of future structure changes.
Integrated care in the daily work: coordination beyond organisational boundaries
Directory of Open Access Journals (Sweden)
Alexandra Petrakou
2009-07-01
Full Text Available Objectives: In this paper, integrated care in an inter-organisational cooperative setting of in-home elderly care is studied. The aim is to explore how home care workers coordinate their daily work, identify coordination issues in situ and discuss possible actions for supporting seamless and integrated elderly care at home. Method: The empirical findings are drawn from an ethnographic workplace study of the cooperation and coordination taking place between home care workers in a Swedish county. Data were collected through observational studies, interviews and group discussions. Findings: The paper identifies a need to support two core issues. Firstly, it must be made clear how the care interventions that are currently defined as ‘self-treatment’ by the home health care should be divided. Secondly, the distributed and asynchronous coordination between all care workers involved, regardless of organisational belonging must be better supported. Conclusion: Integrated care needs to be developed between organisations as well as within each organisation. As a matter of fact, integrated care needs to be built up beyond organisational boundaries. Organisational boundaries affect the planning of the division of care interventions, but not the coordination during the home care process. During the home care process, the main challenge is the coordination difficulties that arise from the fact that workers are distributed in time and/or space, regardless of organisational belonging. A core subject for future practice and research is to develop IT tools that reach beyond formal organisational boundaries and processes while remaining adaptable in view of future structure changes.
Methods for assessing NPP containment pressure boundary integrity
International Nuclear Information System (INIS)
Naus, D.J.; Ellingwood, B.R.; Graves, H.L.
2004-01-01
Research is being conducted to address aging of the containment pressure boundary in light-water reactor plants. Objectives of this research are to (1) understand the significant factors relating to corrosion occurrence, efficacy of inspection, and structural capacity reduction of steel containments and of liners of concrete containments; (2) provide the U.S. Nuclear Regulatory Commission (USNRC) reviewers a means of establishing current structural capacity margins or estimating future residual structural capacity margins for steel containments and concrete containments as limited by liner integrity; and (3) provide recommendations, as appropriate, on information to be requested of licensees for guidance that could be utilized by USNRC reviewers in assessing the seriousness of reported incidences of containment degradation. Activities include development of a degradation assessment methodology; reviews of techniques and methods for inspection and repair of containment metallic pressure boundaries; evaluation of candidate techniques for inspection of inaccessible regions of containment metallic pressure boundaries; establishment of a methodology for reliability-based condition assessments of steel containments and liners; and fragility assessments of steel containments with localized corrosion
MIB Galerkin method for elliptic interface problems.
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
A boundary integral formalism for stochastic ray tracing in billiards
International Nuclear Information System (INIS)
Chappell, David J.; Tanner, Gregor
2014-01-01
Determining the flow of rays or non-interacting particles driven by a force or velocity field is fundamental to modelling many physical processes. These include particle flows arising in fluid mechanics and ray flows arising in the geometrical optics limit of linear wave equations. In many practical applications, the driving field is not known exactly and the dynamics are determined only up to a degree of uncertainty. This paper presents a boundary integral framework for propagating flows including uncertainties, which is shown to systematically interpolate between a deterministic and a completely random description of the trajectory propagation. A simple but efficient discretisation approach is applied to model uncertain billiard dynamics in an integrable rectangular domain
The Boundary/Pedestal Integrated Science Application for FSP
Energy Technology Data Exchange (ETDEWEB)
Rognlien, T. D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Snyder, P. B. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2011-06-17
This Integrated Science Application (ISA) represents a combination of the former Integrated Boundary and Pedestal Science Drivers carried out over the last year as part of the Fusion Simulation Program’s planning phase. Those Science Driver plans, as well as four others, can be viewed on the website (http://fspscidri.web.lehigh.edu/index.php/Main_Page). The Boundary Science Driver report is also available as LLNL document LLNL-TR-471260. The plans described in those documents assumed ample resources would be available. This document represents a plan of vital importance for developing powerful simulation tools for magnetic fusion energy devices, but is of substantially less scope than the original Science Drivers because of budget limitations and the fact that here two Science Drivers are merged owing to the close proximity of the two regions that they model: (1) the warm plasma region known as the scrapeoff layer (SOL) where magnetic field lines directly contact material structures together with the associate plasma-wall interactions and (2) the adjacent hotter plasma region know as the pedestal, which is the beginning of the confining closed magnetic field line core.
Cavity RF mode analysis using a boundary-integral method
International Nuclear Information System (INIS)
Jong, M.S. de; Adams, F.P.
1993-01-01
A 3-dimensional boundary-integral method has been developed for rf cavity mode analysis. A frequency-dependent, homogeneous linear matrix equation is generated from a variant of the magnetic field integral equation (MFIE) where the domain of integration is a closed surface specifying the rf envelope of the cavity. Frequencies at which the MFIE has non-zero solutions are mode frequencies of the cavity, and the solutions are the corresponding surface magnetic field distributions. The MFIE can then be used to calculate the electric and magnetic field at any other point inside the cavity. Forward iteration is used to find the largest complex eigenvalue of the matrix at a specific frequency. This eigenvalue is 1 when the frequency corresponds to a cavity rf resonance. The matrix equivalent of the MFIE is produced by approximating the cavity surface by a set of perfectly conducting surface elements, and assuming that the surface magnetic field has constant amplitude on each element. The method can handle cavities with complex symmetries, and be easily integrated with finite-element heat-transfer and stress analysis codes
An implicit discontinuous Galerkin finite element model for water waves
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
Galerkin finite element methods for wave problems
Indian Academy of Sciences (India)
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 ...
Advanced applications of boundary-integral equation methods
International Nuclear Information System (INIS)
Cruse, T.A.; Wilson, R.B.
1978-01-01
Numerical analysis has become the basic tool for both design and research problems in solid mechanics. The need for accuracy and detail, plus the availablity of the high speed computer has led to the development of many new modeling methods ranging from general purpose structural analysis finite element programs to special purpose research programs. The boundary-integral equation (BIE) method is based on classical mathematical techniques but is finding new life as a basic stress analysis tool for engineering applications. The paper summarizes some advanced elastic applications of fracture mechanics and three-dimensional stress analysis, while referencing some of the much broader developmental effort. Future emphasis is needed to exploit the BIE method in conjunction with other techniques such as the finite element method through the creation of hybrid stress analysis methods. (Auth.)
Directory of Open Access Journals (Sweden)
Nahed S. Hussein
2014-01-01
Full Text Available A numerical boundary integral scheme is proposed for the solution to the system of eld equations of plane. The stresses are prescribed on one-half of the circle, while the displacements are given. The considered problem with mixed boundary conditions in the circle is replaced by two problems with homogeneous boundary conditions, one of each type, having a common solution. The equations are reduced to a system of boundary integral equations, which is then discretized in the usual way, and the problem at this stage is reduced to the solution to a rectangular linear system of algebraic equations. The unknowns in this system of equations are the boundary values of four harmonic functions which define the full elastic solution and the unknown boundary values of stresses or displacements on proper parts of the boundary. On the basis of the obtained results, it is inferred that a stress component has a singularity at each of the two separation points, thought to be of logarithmic type. The results are discussed and boundary plots are given. We have also calculated the unknown functions in the bulk directly from the given boundary conditions using the boundary collocation method. The obtained results in the bulk are discussed and three-dimensional plots are given. A tentative form for the singular solution is proposed and the corresponding singular stresses and displacements are plotted in the bulk. The form of the singular tangential stress is seen to be compatible with the boundary values obtained earlier. The efficiency of the used numerical schemes is discussed.
Integrable systems on so(4) related to XXX spin chains with boundaries
International Nuclear Information System (INIS)
Tsiganov, A V; Goremykin, O V
2004-01-01
We consider two-site XXX Heisenberg magnets with different boundary conditions, which are integrable systems on so(4) possessing additional cubic and quartic integrals of motion. The separated variables for these models are constructed using the Sklyanin method
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.
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 $\\mathbb{S}^2$.
Piloting and Path Integration within and across Boundaries
Mou, Weimin; Wang, Lin
2015-01-01
Three experiments investigated whether navigation is less efficient across boundaries than within boundaries. In an immersive virtual environment, participants learned objects' locations in a large room or a small room. Participants then pointed to the objects' original locations after physically walking a circuitous path without vision.…
Boundary integral equations of time harmonic wave scattering at complex structures
Claeys, Xavier
2016-01-01
The first chapter will be a brief recapitulation of well known results concerning layer potentials in the context of wave propagation in harmonic regime. In Chapter 2, we give an overview of the Rumsey reaction principle that is the most popular boundary integral formulation for multi-subdomain scattering, and we present a new alternative integral formulation that seems to be the first boundary integral formulation of the second kind for multi-subdomain scattering in geometrical configuration...
Inviscid/Boundary-Layer Aeroheating Approach for Integrated Vehicle Design
Lee, Esther; Wurster, Kathryn E.
2017-01-01
A typical entry vehicle design depends on the synthesis of many essential subsystems, including thermal protection system (TPS), structures, payload, avionics, and propulsion, among others. The ability to incorporate aerothermodynamic considerations and TPS design into the early design phase is crucial, as both are closely coupled to the vehicle's aerodynamics, shape and mass. In the preliminary design stage, reasonably accurate results with rapid turn-representative entry envelope was explored. Initial results suggest that for Mach numbers ranging from 9-20, a few inviscid solutions could reasonably sup- port surface heating predictions at Mach numbers variation of +/-2, altitudes variation of +/-10 to 20 kft, and angle-of-attack variation of +/- 5. Agreement with Navier-Stokes solutions was generally found to be within 10-15% for Mach number and altitude, and 20% for angle of attack. A smaller angle-of-attack increment than the 5 deg around times for parametric studies and quickly evolving configurations are necessary to steer design decisions. This investigation considers the use of an unstructured 3D inviscid code in conjunction with an integral boundary-layer method; the former providing the flow field solution and the latter the surface heating. Sensitivity studies for Mach number, angle of attack, and altitude, examine the feasibility of using this approach to populate a representative entry flight envelope based on a limited set of inviscid solutions. Each inviscid solution is used to generate surface heating over the nearby trajectory space. A subset of a considered in this study is recommended. Results of the angle-of-attack sensitivity studies show that smaller increments may be needed for better heating predictions. The approach is well suited for application to conceptual multidisciplinary design and analysis studies where transient aeroheating environments are critical for vehicle TPS and thermal design. Concurrent prediction of aeroheating
Signatures of chaos and non-integrability in two-dimensional gravity with dynamical boundary
Directory of Open Access Journals (Sweden)
Fitkevich Maxim
2016-01-01
Full Text Available We propose a model of two-dimensional dilaton gravity with a boundary. In the bulk our model coincides with the classically integrable CGHS model; the dynamical boundary cuts of the CGHS strong-coupling region. As a result, classical dynamics in our model reminds that in the spherically-symmetric gravity: wave packets of matter fields either reflect from the boundary or form black holes. We find large integrable sector of multisoliton solutions in this model. At the same time, we argue that the model is globally non-integrable because solutions at the verge of black hole formation display chaotic properties.
Boundary element methods for dielectric cavity construction and integration
Chen, Feiwu; Chipman, Daniel M.
2003-11-01
Improvements in boundary element methods are described for solution of reaction field equations that incorporate important dielectric effects of solvation, including influences of volume polarization, into electronic structure calculations on solute properties. Most current implementations assume constant boundary elements on the cavity surface separating solvent from solute, often employing an empirical parameter to enhance slow convergence associated with the treatment of singularities. In this work we describe a scheme for the linear interpolation of boundary elements and the analytic treatment of singularities that improves convergence without the need for any empirical parameter. Another advance is described for isodensity surface triangulation that succeeds even with molecular surfaces having prominent pockets, which cause the failure of previous simpler methods. Numerical examples are presented to demonstrate the efficacy of these new procedures in practice.
Galerkin finite element methods for wave problems
Indian Academy of Sciences (India)
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,.
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.
One out of many? Boundary negotiation and identity formation in postmerger integration
Drori, Israel; Wrzesniewski, Amy; Ellis, Shmuel
2013-01-01
This research investigates how boundaries are utilized during the postmerger integration process to influence the postmerger identity of the firm. We suggest that the boundaries that define the structures, practices, and values of firms prior to a merger become reinforced, contested, or revised in
Applications of Taylor-Galerkin finite element method to compressible internal flow problems
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.
Space-time discontinuous Galerkin finite element method for inviscid gas dynamics
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
Upper and lower solutions method for differential inclusions with integral boundary conditions
Directory of Open Access Journals (Sweden)
Abdelghani Ouahab
2006-03-01
Full Text Available A nonlinear alternative of the Leray-Schauder type for multivalued maps combined with upper and lower solutions is used to investigate the existence of solutions for second-order differential inclusions with integral boundary conditions.
Integrating Observations of the Boundary Current Flow around Sri Lanka
2015-09-30
around Sri Lanka Uwe Send and Matthias Lankhorst Scripps Institution of Oceanography 9500 Gilman Drive, Mail Code 0230 La Jolla, CA 92093-0230...of Bengal. For this, the flow around Sri Lanka is critical since it exchanges salt and freshwater between the Bay of Bengal and the Arabian Sea...OBJECTIVES In-situ continuous observations of the boundary current flow around Sri Lanka will be collected over a period of several years. In order
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.
De La Rosa Gomez, Alejandro; MacKay, Niall; Regelskis, Vidas
2017-04-01
We present a general method of folding an integrable spin chain, defined on a line, to obtain an integrable open spin chain, defined on a half-line. We illustrate our method through two fundamental models with sl2 Lie algebra symmetry: the Heisenberg XXX and the Inozemtsev hyperbolic spin chains. We obtain new long-range boundary Hamiltonians and demonstrate that they exhibit Yangian symmetries, thus ensuring integrability of the models we obtain. The method presented provides a ;bottom-up; approach for constructing integrable boundaries and can be applied to any spin chain model.
Three-dimensional analysis of chevron-notched specimens by boundary integral method
Mendelson, A.; Ghosn, L.
1983-01-01
The chevron-notched short bar and short rod specimens was analyzed by the boundary integral equations method. This method makes use of boundary surface elements in obtaining the solution. The boundary integral models were composed of linear triangular and rectangular surface segments. Results were obtained for two specimens with width to thickness ratios of 1.45 and 2.00 and for different crack length to width ratios ranging from 0.4 to 0.7. Crack opening displacement and stress intensity factors determined from displacement calculations along the crack front and compliance calculations were compared with experimental values and with finite element analysis.
Kot, V. A.
2017-11-01
The modern state of approximate integral methods used in applications, where the processes of heat conduction and heat and mass transfer are of first importance, is considered. Integral methods have found a wide utility in different fields of knowledge: problems of heat conduction with different heat-exchange conditions, simulation of thermal protection, Stefantype problems, microwave heating of a substance, problems on a boundary layer, simulation of a fluid flow in a channel, thermal explosion, laser and plasma treatment of materials, simulation of the formation and melting of ice, inverse heat problems, temperature and thermal definition of nanoparticles and nanoliquids, and others. Moreover, polynomial solutions are of interest because the determination of a temperature (concentration) field is an intermediate stage in the mathematical description of any other process. The following main methods were investigated on the basis of the error norms: the Tsoi and Postol’nik methods, the method of integral relations, the Gudman integral method of heat balance, the improved Volkov integral method, the matched integral method, the modified Hristov method, the Mayer integral method, the Kudinov method of additional boundary conditions, the Fedorov boundary method, the method of weighted temperature function, the integral method of boundary characteristics. It was established that the two last-mentioned methods are characterized by high convergence and frequently give solutions whose accuracy is not worse that the accuracy of numerical solutions.
McCullough, Jeffrey S; Snir, Eli M
2010-05-01
We study the relationship between physician-hospital integration and its relation to monitoring IT utilization. We develop a theoretical model in which monitoring IT may complement or substitute for integration and test these relationships using a novel data source. Physician labor market heterogeneity identifies the empirical model. We find that monitoring IT utilization is increasing in integration, implying that expanded firm boundaries complement monitoring IT adoption. We argue that the relationship between monitoring IT and firm boundaries depends upon the contractibility of the monitored information.
Second-order domain derivative of normal-dependent boundary integrals
Balzer, Jonathan
2010-03-17
Numerous reconstruction tasks in (optical) surface metrology allow for a variational formulation. The occurring boundary integrals may be interpreted as shape functions. The paper is concerned with the second-order analysis of such functions. Shape Hessians of boundary integrals are considered difficult to find analytically because they correspond to third-order derivatives of an, in a sense equivalent, domain integral. We complement previous results by considering cost functions depending explicitly on the surface normal. The correctness and practicability of our calculations are verified in the context of a Newton-type shape reconstruction method. © 2010 Birkhäuser / Springer Basel AG.
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.
Discontinuous Galerkin for the Radiative Transport Equation
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.
OhioLINK: Implementing Integrated Library Services across Institutional Boundaries.
Hawks, Carol Pitts
1995-01-01
Discusses the implementation of the OhioLINK (Ohio Library and Information Network) system, an integrated library system linking 23 public and private academic institutions and the Ohio State Library. Topics include a history of OhioLINK; organizational structure; decision-making procedures; public relations strategies; cooperative circulation;…
Behavior of boundary string field theory associated with integrable massless flow.
Fujii, A; Itoyama, H
2001-06-04
We put forward an idea that the boundary entropy associated with integrable massless flow of thermodynamic Bethe ansatz (TBA) is identified with tachyon action of boundary string field theory. We show that the temperature parametrizing a massless flow in the TBA formalism can be identified with tachyon energy for the classical action at least near the ultraviolet fixed point, i.e., the open string vacuum.
Zieniuk, Eugeniusz; Kapturczak, Marta
2017-07-01
In recent studies of parametric integral equations system (PIES), the input data, necessary to define the shape of boundary, was defined in precise way. However, it is just assumption for further calculations. In practice even the most accurate measurement instruments generate errors. Therefore, in this paper we decide to propose the method for modelling and solving the boundary value problems with uncertainly defined shape of boundary. In view of advantages in precisely defined problems, we decide to generalize PIES method. To define the uncertainty of the input data we propose the modification of directed interval arithmetic.
Galerkin and weighted Galerkin methods for a forward-backward heat equation
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
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
Discontinuous Galerkin algorithms for fully kinetic plasmas
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.
[Boundaries and integrity in the "Social Contract for Spanish Science", 1907-1939].
Gómez, Amparo
2014-01-01
This article analyzes the relationship between science and politics in Spain in the early 20th century from the perspective of the Social Contract for Science. The article shows that a genuine social contract for science was instituted in Spain during this period, although some boundary and integrity problems emerged. These problems are analyzed, showing that the boundary problems were a product of the conservative viewpoint on the relationship between science and politics, while the integrity problems involved the activation of networks of influence in the awarding of scholarships to study abroad. Finally, the analysis reveals that these problems did not invalidate the Spanish social contract for science.
A spectral hybridizable discontinuous Galerkin method for elastic-acoustic wave propagation
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
Integrating Sustainability into the Curriculum: Crossing Disciplinary Boundaries
Pushnik, J.
2012-12-01
The next generation will confront an increased number of global issues that interface the complexities of socioeconomic perspectives, environmental stability, poverty and development. Recently California State University Chico undertook a general education reform, providing a unique opportunity to craft a general education pathway to prepare students for these challenges by focusing a curriculum on sustainability. The Sustainability Pathway emphasizes a system thinking approach to help students understand and be able to address a set of problems involving the biosphere processes, human institutions and the economic vitality. The curriculum intentionally integrates courses from across the disciplines of natural sciences, social sciences, agriculture, engineering, economics, arts and humanities into a central focused theme of sustainability. The diverse backgrounds and academic focus of the participating faculty has necessitate the development of a common language and a cohesion within the curriculum. To address these needs a faculty learning community (FLC) was established to build on a common set of case studies. Three regional environmental water related issues were selected that had demonstrable socioeconomic, equity/ethical dimensions and environmental consequences. These case studies are Klamath River basin in northern California, the Bay-Delta project in the central part of the state and the Sultan Sea in southern California. Members of the FLC has contributed a perspective from their academic discipline which includes proposed reading lists, web based resources and PowerPoint presentations which are housed in common web- based resource repository. The pedagogical rational is to create linkages and cohesion among the courses in the curriculum by iteratively examining these case studies as basis for development of a multidisciplinary perspective as students progress through their general education.
The application of the Galerkin method to solving PIES for Laplace's equation
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.
Energy Technology Data Exchange (ETDEWEB)
Chen, Ke [Univ. of Liverpool (United Kingdom)
1996-12-31
We study various preconditioning techniques for the iterative solution of boundary integral equations, and aim to provide a theory for a class of sparse preconditioners. Two related ideas are explored here: singularity separation and inverse approximation. Our preliminary conclusion is that singularity separation based preconditioners perform better than approximate inverse based while it is desirable to have both features.
Directory of Open Access Journals (Sweden)
A. Guezane-Lakoud
2012-01-01
Full Text Available This work is devoted to the existence of positive solutions for a fractional boundary value problem with fractional integral deviating argument. The proofs of the main results are based on Guo-Krasnoselskii fixed point theorem and Avery and Peterson fixed point theorem. Two examples are given to illustrate the obtained results, ending the paper.
A Von Karman integral approach to a two phase boundary layer problem
Henry, R.; Pasamehmetoglu, P.; Eno, B.; Anderson, L.
1987-01-01
A Von Karman integral approximation of a two phase boundary layer is developed for bodies of arbitrary shape. The flow field considered is that of the injection of water through a porous airfoil. A solution for the special case of a flat plate is presented. The equations for the airfoil solution are developed and possible effects on airflow separation are discussed.
Directory of Open Access Journals (Sweden)
Samira Hamani
2010-01-01
Full Text Available In this article, the authors establish sufficient conditions for the existence of solutions for a class of boundary value problem for fractional differential inclusions involving the Caputo fractional derivative and nonlinear integral conditions. Both cases of convex and nonconvex valued right hand sides are considered. The topological structure of the set of solutions also examined.
Directory of Open Access Journals (Sweden)
Mouffak Benchohra
2012-01-01
Full Text Available The aim of this paper is to investigate a class of boundary value problems for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of weak noncompactness.
Directory of Open Access Journals (Sweden)
Archana Chauhan
2012-12-01
Full Text Available In this article, we establish a general framework for finding solutions for impulsive fractional integral boundary-value problems. Then, we prove the existence and uniqueness of solutions by applying well known fixed point theorems. The obtained results are illustrated with an example for their feasibility.
Sareni , Bruno; Krähenbühl , Laurent; Beroual , Abderrahmane; Nicolas , Alain; Brosseau , C.
1997-01-01
We present a numerical method based upon the resolution of boundary integral equations for the calculation of the effective permittivity of a lossless composite structure consisting of a two component mixture, each with its own dielectric anti shape characteristics. The topological arrangements considered are periodic lattices inhomogeneities. Our numerical simulations are compared to the effective medium approach and with results of previous works.
A formulation with boundary integrals and solution optimization for a heat transfer inverse problem
International Nuclear Information System (INIS)
Honorio, Mario C.F.; Bezerra, Luciano M.
1997-01-01
This paper presents a boundary integral formulation in conjunction with optimization techniques for the solution of inverse thermal design problems. In this type of problems, sometimes it is necessary to determine the appropriate position and shape of an internal cooling/heating channel inside an object so that reference thermal boundary values could be obtained on the outer surface. An initial feasible position of the channel is first guessed by the user. The channel is defined in terms of design variables. The formulation tries to minimize an objective function which measures the difference between model and reference data. The program attempts to minimize the objective function in order to meet the over specified thermal boundary conditions on the outer surface. This minimization or optimization problem is a constrained problem since the cooling/heating channel must be inside the object. In the optimization process, the holes position is iteratively changed. Although more complex in terms of mathematical formulation. the boundary element method is particularly suited for this type of problem involving constant mesh updates. The Boundary Element Method formulation calculates the thermal response which is compared with reference data. The quasi-Newton search algorithm used for objective function optimization needs the response sensitivities with respect to the design variables. The sensitivities are calculated by finite differences and by implicit differentiation of the boundary element equations. Some numerical results are presented and discussed. (author). 10 refs., 8 figs., 2 tabs
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.
Lakin, W. D.
1986-01-01
Integrating and differentiating matrices allow the numerical integration and differential of functions whose values are known at points of a discrete grid. Previous derivations of these matrices were restricted to one dimensional grids or to rectangular grids with uniform spacing in at least one direction. Integrating and differentiating matrices were developed for grids with nonuniform spacing in both directions. The use of these matrices as operators to reformulate boundary value problems on rectangular domains as matrix problems for a finite dimensional solution vector is considered. The method requires nonuniform grids which include near boundary points. An eigenvalue problem for the transverse vibrations of a simply supported rectangular plate is solved to illustrate the method.
Lakin, W. D.
1986-01-01
Integrating and differentiating matrices allow the numerical integration and differential of functions whose values are known at points of a discrete grid. Previous derivations of these matrices were restricted to one dimensional grids or to rectangular grids with uniform spacing in at least one direction. Integrating and differentiating matrices were developed for grids with nonuniform spacing in both directions. The use of these matrices as operators to reformulate boundary value problems on rectangular domains as matrix problems for a finite dimensional solution vector is considered. The method requires nonuniform grids which include near boundary points. An eigenvalue problem for the transverse vibrations of a simply supported rectangular plate is solved to illustrate the method.
On the elastostatic significance of four boundary integrals involving biharmonic functions
DEFF Research Database (Denmark)
Christiansen, Søren
1998-01-01
For a biharmonic function U, depending upon two space variables, it is known that four curve integrals, which involve U and some derivatives of U evaluated at a closed boundary, must be equal to zero. When U plays the role of an Airy stress function, we investigate the elastostatic significance...... of the four integrals and we find that it is related to the displacements of the elastic material: Single valued displacements are obtained provided that three of the integrals are zero. (The fourth integral does not provide further information.) It is already known from the classical literature that two...... of the integrals are related to single valued displacements, but the elastostatical significance of the third integral seems to be a new result. The method of investigation is unconventional: For "all possible" biharmonic functions, in polar coordinates, we determine stresses, strains, displacements etc. together...
POSITIVE SOLUTIONS OF A NONLINEAR THREE-POINT EIGENVALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS
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FAOUZI HADDOUCHI
2015-11-01
Full Text Available In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP for the following second-order differential equation u''(t + \\lambda a(tf(u(t = 0; 0 0 is a parameter, 0 <\\eta < 1, 0 <\\alpha < 1/{\\eta}. . By using the properties of the Green's function and Krasnoselskii's fixed point theorem on cones, the eigenvalue intervals of the nonlinear boundary value problem are considered, some sufficient conditions for the existence of at least one positive solutions are established.
Boundary integral equation methods in eigenvalue problems of elastodynamics and thin plates
Kitahara, M
1985-01-01
The boundary integral equation (BIE) method has been used more and more in the last 20 years for solving various engineering problems. It has important advantages over other techniques for numerical treatment of a wide class of boundary value problems and is now regarded as an indispensable tool for potential problems, electromagnetism problems, heat transfer, fluid flow, elastostatics, stress concentration and fracture problems, geomechanical problems, and steady-state and transient electrodynamics.In this book, the author gives a complete, thorough and detailed survey of the method. It pro
Directory of Open Access Journals (Sweden)
Daniel Williams
2018-04-01
Full Text Available Most scholarship on integration and assimilation in Europe has examined laws, policies and quantitative data to understand the integration of immigrants. Fewer studies have looked at the meaning of integration for immigrants and host societies. This article helps to fill this gap in scholarship by examining the construction of immigrants and Germany in mandatory integration courses in contemporary Germany. Using ethnographic observations of integration courses and discourse analysis of curricular materials, I analyze these constructions using a boundary-construction approach, where both the content of what separates immigrants from host society members, and the brightness of the boundary are used as a basis for viewing immigrants as outsiders versus citizens. I use the terms suspect outsiders and prospective citizens to describe the nature of the immigrant/German boundary based on these constructions. The findings show that three themes—gender and family norms, democracy and rights, and religious freedom—form the content of the immigrant/German boundary. Within these themes, Germany’s civic integration courses generally construct immigrants as prospective citizens by blurring the immigrant/German boundary. The nature of the immigrant/German boundary is crucial for both the integration of immigrants and for Germany. A bright boundary that invokes the notion of immigrants as fundamentally different places the burden of integration on them to change, while a blurred boundary potentially redefines what it means to be German.
The Galerkin Finite Element Method for A Multi-term Time-Fractional Diffusion equation
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...
López-Martínez, Rafael; Barragán, Ricardo; Bernal, Juan Pablo; Reháková, Daniela; Gómez-Tuena, Arturo; Martini, Michelangelo; Ortega, Carlos
2017-04-01
The integration of calpionellid biostratigraphy, microfacies analysis, Usbnd Pb geochronology, and strontium chemostratigraphy improves the definition of the Berriasian-Valanginian boundary in the Tlatlauquitepec area and validates the age of calpionellid zones from eastern Mexico in this interval. An age of 139.85 Ma derived from 87Sr/86Sr ratio within the base of Calpionellites Zone defines the Berriasian-Valanginian boundary. Additionally, the 134.0 ± 0.5 Ma Usbnd Pb age returned by zircon grains from a tuff level exposed at the top of the succession confirms the Valanginian age of the whole analyzed section. Microfacies analysis reveals sea level variations that can be coincident with the KVa1-KVa4 eustatic cycles. These new data suggest that calpionellid biostratigraphy represents the most useful tool for the definition of the Berriasian-Valanginian time boundary in central Mexico and its correlation with the rest of the Tethyan domain.
Adaptive discontinuous Galerkin methods for non-linear reactive flows
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.
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.
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.
On the solvability of initial boundary value problems for nonlinear ...
African Journals Online (AJOL)
In this paper, we study the initial boundary value problems for a non-linear time dependent Schrödinger equation with Dirichlet and Neumann boundary conditions, respectively. We prove the existence and uniqueness of solutions of the initial boundary value problems by using Galerkin's method. Keywords: Initial boundary ...
Wing aeroelasticity analysis based on an integral boundary-layer method coupled with Euler solver
Directory of Open Access Journals (Sweden)
Ma Yanfeng
2016-10-01
Full Text Available An interactive boundary-layer method, which solves the unsteady flow, is developed for aeroelastic computation in the time domain. The coupled method combines the Euler solver with the integral boundary-layer solver (Euler/BL in a “semi-inverse” manner to compute flows with the inviscid and viscous interaction. Unsteady boundary conditions on moving surfaces are taken into account by utilizing the approximate small-perturbation method without moving the computational grids. The steady and unsteady flow calculations for the LANN wing are presented. The wing tip displacement of high Reynolds number aero-structural dynamics (HIRENASD Project is simulated under different angles of attack. The flutter-boundary predictions for the AGARD 445.6 wing are provided. The results of the interactive boundary-layer method are compared with those of the Euler method and experimental data. The study shows that viscous effects are significant for these cases and the further data analysis confirms the validity and practicability of the coupled method.
Galerkin finite element methods for wave problems
Indian Academy of Sciences (India)
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 ...
On Formulations of Discontinuous Galerkin and Related Methods for Conservation Laws
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.
Solvability of second-order boundary-value problems at resonance involving integral conditions
Directory of Open Access Journals (Sweden)
Yujun Cui
2012-03-01
Full Text Available This article concerns the second-order differential equation with integral boundary conditions $$displaylines{ x''(t=f(t,x(t,x'(t,quad tin (0,1,cr x(0=int_0^1x(sdalpha(s,quad x(1=int_0^1x(sdeta(s. }$$ Under the resonance conditions, we construct a projector and then applying coincidence degree theory to establish the existence of solutions.
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Bashir Ahmad
2013-03-01
Full Text Available This paper investigates the existence of solutions for higher order fractional differential inclusions with fractional integral boundary conditions involving nonintersecting finite many strips of arbitrary length. Our study includes the cases when the right-hand side of the inclusion has convex as well non-convex values. Some standard fixed point theorems for multivalued maps are applied to establish the main results. An illustrative example is also presented.
Implicit Boundary Integral Methods for the Helmholtz Equation in Exterior Domains
2016-06-01
boundary-value problems for the wave equation and maxwell’s equations. Russian Math . Surv., 1965. [16] S. Reutskiy. The method of fundamental...for solving Helmholtz equations in the exterior domain. The algorithm not only combines the advantages of implicit surface representation and the...natural limit of the singular integrals via seamless extrapolation. We present numerical results for both two and three dimensional scattering problems
International Nuclear Information System (INIS)
Behbahani-Nejad, M.; Esfahanian, V.
2004-01-01
A general formulation is presented for evaluation of hypersingular integrals arising from computation of supersonic potential flows using boundary element method, where the element is partially inside the Mach forecone. The formulation is applied to higher order elements for any type of element intersection by the Mach forecone. General mappings are introduced to transform the inside-part of the elements partially inside the Mach forecone to another rectangular elements and analytical relations are derived for evaluation of the hypersingular integrals. Comparison between the results and exact solutions indicates that the method is not only general, but also is very accurate. (author)
Muskhelishvili, N I
2011-01-01
Singular integral equations play important roles in physics and theoretical mechanics, particularly in the areas of elasticity, aerodynamics, and unsteady aerofoil theory. They are highly effective in solving boundary problems occurring in the theory of functions of a complex variable, potential theory, the theory of elasticity, and the theory of fluid mechanics.This high-level treatment by a noted mathematician considers one-dimensional singular integral equations involving Cauchy principal values. Its coverage includes such topics as the Hölder condition, Hilbert and Riemann-Hilbert problem
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.
Singular Integral Operators Associated with Elliptic Boundary Value Problems in Non-smooth Domains
Awala, Hussein
Many boundary value problems of mathematical physics are modelled by elliptic differential operators L in a given domain O. An effective method for treating such problems is the method of layer potentials, whose essence resides in reducing matters to solving a boundary integral equation. This, in turn, requires inverting a singular integral operator, naturally associated with L and O, on appropriate function spaces on ∂O. When the operator L is of second order and the domain O is Lipschitz (i.e., O is locally the upper-graph of a Lipschitz function) the fundamental work of B. Dahlberg, C. Kenig, D. Jerison, E. Fabes, N. Riviere, G. Verchota, R. Brown, and many others, has opened the door for the development of a far-reaching theory in this setting, even though several very difficult questions still remain unanswered. In this dissertation, the goal is to solve a number of open questions regarding spectral properties of singular integral operators associated with second and higher-order elliptic boundary value problems in non-smooth domains. Among other spectral results, we establish symmetry properties of harmonic classical double layer potentials associated with the Laplacian in the class of Lipschitz domains in R2. An array of useful tools and techniques from Harmonic Analysis, Partial Differential Equations play a key role in our approach, and these are discussed as preliminary material in the thesis: • Mellin Transforms and Fourier Analysis; • Calderon-Zygmund Theory in Uniformly Rectifiable Domains; • Boundary Integral Methods. Chapter four deals with proving invertibility properties of singular integral operators naturally associated with the mixed (Zaremba) problem for the Laplacian and the Lame system in infinite sectors in two dimensions, when considering their action on the Lebesgue scale of p integrable functions, for $1 their action on the Lebesgue scale of p integrable functions, for 1 functions). Finally, chapter six, deals with spectral issues
Active flow control insight gained from a modified integral boundary layer equation
Seifert, Avraham
2016-11-01
Active Flow Control (AFC) can alter the development of boundary layers with applications (e.g., reducing drag by separation delay or separating the boundary layers and enhancing vortex shedding to increase drag). Historically, significant effects of steady AFC methods were observed. Unsteady actuation is significantly more efficient than steady. Full-scale AFC tests were conducted with varying levels of success. While clearly relevant to industry, AFC implementation relies on expert knowledge with proven intuition and or costly and lengthy computational efforts. This situation hinders the use of AFC while simple, quick and reliable design method is absent. An updated form of the unsteady integral boundary layer (UIBL) equations, that include AFC terms (unsteady wall transpiration and body forces) can be used to assist in AFC analysis and design. With these equations and given a family of suitable velocity profiles, the momentum thickness can be calculated and matched with an outer, potential flow solution in 2D and 3D manner to create an AFC design tool, parallel to proven tools for airfoil design. Limiting cases of the UIBL equation can be used to analyze candidate AFC concepts in terms of their capability to modify the boundary layers development and system performance.
A time-domain finite element boundary integration method for ultrasonic nondestructive evaluation.
Shi, Fan; Choi, Wonjae; Skelton, Elizabeth A; Lowe, Michael J S; Craster, Richard V
2014-12-01
A 2-D and 3-D numerical modeling approach for calculating the elastic wave scattering signals from complex stress-free defects is evaluated. In this method, efficient boundary integration across the complex boundary of the defect is coupled with a time-domain finite element (FE) solver. The model is designed to simulate time-domain ultrasonic nondestructive evaluation in bulk media. This approach makes use of the hybrid concept of linking a local numerical model to compute the near-field scattering behavior and theoretical mathematical formulas for postprocessing to calculate the received signals. It minimizes the number of monitoring signals from the FE calculation so that the computation effort in postprocessing decreases significantly. In addition, by neglecting the conventional regular monitoring box, the region for FE calculation can be made smaller. In this paper, the boundary integral method is implemented in a commercial FE code, and it is validated by comparing the scattering signals with results from corresponding full FE models. The coupled method is then implemented in real inspection scenarios in both 2-D and 3-D, and the accuracy and the efficiency are demonstrated. The limitations of the proposed model and future works are also discussed.
Integrity of the reactor coolant boundary of the European pressurized water reactor (EPR)
International Nuclear Information System (INIS)
Goetsch, D.; Bieniussa, K.; Schulz, H.; Jalouneix, J.
1997-01-01
This paper is an abstract of the work performed in the frame of the development of the IPSN/GRS approach in view of the EPR conceptual safety features. EPR is a pressurized water reactor which will be based on the experience gained by utilities and designers in France and in Germany. The reactor coolant boundary of a PWR includes the reactor pressure vessel (RPV), those parts of the steam generators (SGs) which contain primary coolant, the pressurizer (PSR), the reactor coolant pumps (RCPs), the main coolant lines (MCLs) with their branches as well as the other connecting pipes and all branching pipes including the second isolation valves. The present work covering the integrity of the reactor coolant boundary is mainly restricted to the integrity of the main coolant lines (MCLs) and reflects the design requirements for the main components of the reactor coolant boundary. In the following the conceptual aspects, i.e. design, manufacture, construction and operation, will be assessed. A main aspect is the definition of break postulates regarding overall safety implications
Integrity of the reactor coolant boundary of the European pressurized water reactor (EPR)
Energy Technology Data Exchange (ETDEWEB)
Goetsch, D.; Bieniussa, K.; Schulz, H.; Jalouneix, J.
1997-04-01
This paper is an abstract of the work performed in the frame of the development of the IPSN/GRS approach in view of the EPR conceptual safety features. EPR is a pressurized water reactor which will be based on the experience gained by utilities and designers in France and in Germany. The reactor coolant boundary of a PWR includes the reactor pressure vessel (RPV), those parts of the steam generators (SGs) which contain primary coolant, the pressurizer (PSR), the reactor coolant pumps (RCPs), the main coolant lines (MCLs) with their branches as well as the other connecting pipes and all branching pipes including the second isolation valves. The present work covering the integrity of the reactor coolant boundary is mainly restricted to the integrity of the main coolant lines (MCLs) and reflects the design requirements for the main components of the reactor coolant boundary. In the following the conceptual aspects, i.e. design, manufacture, construction and operation, will be assessed. A main aspect is the definition of break postulates regarding overall safety implications.
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.
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
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.
Boundary charges and integral identities for solitons in (d+1-dimensional field theories
Directory of Open Access Journals (Sweden)
Sven Bjarke Gudnason
2017-12-01
Full Text Available We establish a 3-parameter family of integral identities to be used on a class of theories possessing solitons with spherical symmetry in d spatial dimensions. The construction provides five boundary charges that are related to certain integrals of the profile functions of the solitons in question. The framework is quite generic and we give examples of both topological defects (like vortices and monopoles and topological textures (like Skyrmions in 2 and 3 dimensions. The class of theories considered here is based on a kinetic term and three functionals often encountered in reduced Lagrangians for solitons. One particularly interesting case provides a generalization of the well-known Pohozaev identity. Our construction, however, is fundamentally different from scaling arguments behind Derrick's theorem and virial relations. For BPS vortices, we find interestingly an infinity of integrals simply related to the topological winding number.
Boundary charges and integral identities for solitons in (d + 1)-dimensional field theories
Gudnason, Sven Bjarke; Gao, Zhifeng; Yang, Yisong
2017-12-01
We establish a 3-parameter family of integral identities to be used on a class of theories possessing solitons with spherical symmetry in d spatial dimensions. The construction provides five boundary charges that are related to certain integrals of the profile functions of the solitons in question. The framework is quite generic and we give examples of both topological defects (like vortices and monopoles) and topological textures (like Skyrmions) in 2 and 3 dimensions. The class of theories considered here is based on a kinetic term and three functionals often encountered in reduced Lagrangians for solitons. One particularly interesting case provides a generalization of the well-known Pohozaev identity. Our construction, however, is fundamentally different from scaling arguments behind Derrick's theorem and virial relations. For BPS vortices, we find interestingly an infinity of integrals simply related to the topological winding number.
Feng, Justin C.; Matzner, Richard A.
2017-11-01
We reexamine the relationship between the path integral and canonical formulation of quantum general relativity. In particular, we present a formal derivation of the Wheeler-DeWitt equation from the path integral for quantum general relativity by way of boundary variations. One feature of this approach is that it does not require an explicit 3 +1 splitting of spacetime in the bulk. For spacetimes with a spatial boundary, we show that the dependence of the transition amplitudes on spatial boundary conditions is determined by a Wheeler-DeWitt equation for the spatial boundary surface. We find that variations in the induced metric at the spatial boundary can be used to describe time evolution—time evolution in quantum general relativity is therefore governed by boundary conditions on the gravitational field at the spatial boundary. We then briefly describe a formalism for computing the dependence of transition amplitudes on spatial boundary conditions. Finally, we argue that for nonsmooth boundaries meaningful transition amplitudes must depend on boundary conditions at the joint surfaces.
Leise, Tanya L.
2009-08-19
We consider the problem of the dynamic, transient propagation of a semi-infinite, mode I crack in an infinite elastic body with a nonlinear, viscoelastic cohesize zone. Our problem formulation includes boundary conditions that preclude crack face interpenetration, in contrast to the usual mode I boundary conditions that assume all unloaded crack faces are stress-free. The nonlinear viscoelastic cohesive zone behavior is motivated by dynamic fracture in brittle polymers in which crack propagation is preceeded by significant crazing in a thin region surrounding the crack tip. We present a combined analytical/numerical solution method that involves reducing the problem to a Dirichlet-to-Neumann map along the crack face plane, resulting in a differo-integral equation relating the displacement and stress along the crack faces and within the cohesive zone. © 2009 Springer Science+Business Media B.V.
Numerical solution of fuzzy boundary value problems using Galerkin ...
Indian Academy of Sciences (India)
, 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, ...
Numerical solution of fuzzy boundary value problems using Galerkin ...
Indian Academy of Sciences (India)
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, ...
Accurate traveltime computation in complex anisotropic media with discontinuous Galerkin method
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
Hybridized Multiscale Discontinuous Galerkin Methods for Multiphysics
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.
Discontinuous Galerkin Method for Hyperbolic Conservation Laws
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.
Combining the boundary shift integral and tensor-based morphometry for brain atrophy estimation
Michalkiewicz, Mateusz; Pai, Akshay; Leung, Kelvin K.; Sommer, Stefan; Darkner, Sune; Sørensen, Lauge; Sporring, Jon; Nielsen, Mads
2016-03-01
Brain atrophy from structural magnetic resonance images (MRIs) is widely used as an imaging surrogate marker for Alzheimers disease. Their utility has been limited due to the large degree of variance and subsequently high sample size estimates. The only consistent and reasonably powerful atrophy estimation methods has been the boundary shift integral (BSI). In this paper, we first propose a tensor-based morphometry (TBM) method to measure voxel-wise atrophy that we combine with BSI. The combined model decreases the sample size estimates significantly when compared to BSI and TBM alone.
The boundary integral equations method for analysis of high-frequency vibrations of an elastic layer
Czech Academy of Sciences Publication Activity Database
Sorokin, S.; Kolman, Radek; Kopačka, Ján
2017-01-01
Roč. 87, č. 4 (2017), s. 737-750 ISSN 0939-1533 R&D Projects: GA ČR(CZ) GA16-03823S; GA MŠk(CZ) EF15_003/0000493 Institutional support: RVO:61388998 Keywords : an elastic layer * symmetric and skew-symmetric waves * the Green’s matrix * boundary integral equations * eigen frequencies Subject RIV: BI - Acoustics OBOR OECD: Acoustics Impact factor: 1.490, year: 2016 https://link.springer.com/article/10.1007/s00419-016-1220-y
Extending the diffusion approximation to the boundary using an integrated diffusion model
Energy Technology Data Exchange (ETDEWEB)
Chen, Chen; Du, Zhidong; Pan, Liang, E-mail: liangpan@purdue.edu [School of Mechanical Engineering, Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 (United States)
2015-06-15
The widely used diffusion approximation is inaccurate to describe the transport behaviors near surfaces and interfaces. To solve such stochastic processes, an integro-differential equation, such as the Boltzmann transport equation (BTE), is typically required. In this work, we show that it is possible to keep the simplicity of the diffusion approximation by introducing a nonlocal source term and a spatially varying diffusion coefficient. We apply the proposed integrated diffusion model (IDM) to a benchmark problem of heat conduction across a thin film to demonstrate its feasibility. We also validate the model when boundary reflections and uniform internal heat generation are present.
Extending the diffusion approximation to the boundary using an integrated diffusion model
Directory of Open Access Journals (Sweden)
Chen Chen
2015-06-01
Full Text Available The widely used diffusion approximation is inaccurate to describe the transport behaviors near surfaces and interfaces. To solve such stochastic processes, an integro-differential equation, such as the Boltzmann transport equation (BTE, is typically required. In this work, we show that it is possible to keep the simplicity of the diffusion approximation by introducing a nonlocal source term and a spatially varying diffusion coefficient. We apply the proposed integrated diffusion model (IDM to a benchmark problem of heat conduction across a thin film to demonstrate its feasibility. We also validate the model when boundary reflections and uniform internal heat generation are present.
Boundary integral equation methods and numerical solutions thin plates on an elastic foundation
Constanda, Christian; Hamill, William
2016-01-01
This book presents and explains a general, efficient, and elegant method for solving the Dirichlet, Neumann, and Robin boundary value problems for the extensional deformation of a thin plate on an elastic foundation. The solutions of these problems are obtained both analytically—by means of direct and indirect boundary integral equation methods (BIEMs)—and numerically, through the application of a boundary element technique. The text discusses the methodology for constructing a BIEM, deriving all the attending mathematical properties with full rigor. The model investigated in the book can serve as a template for the study of any linear elliptic two-dimensional problem with constant coefficients. The representation of the solution in terms of single-layer and double-layer potentials is pivotal in the development of a BIEM, which, in turn, forms the basis for the second part of the book, where approximate solutions are computed with a high degree of accuracy. The book is intended for graduate students and r...
Hu, Fang Q; Pizzo, Michelle E; Nark, Douglas M
2017-12-01
It has been well-known that under the assumption of a uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation. However, the constant mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the assumed uniform flow. A customary boundary condition for rigid surfaces is that the normal acoustic velocity be zero. In this paper, a careful study of the acoustic energy conservation equation is presented that shows such a boundary condition would in fact lead to source or sink points on solid surfaces. An alternative solid wall boundary condition, termed zero energy flux boundary condition, is proposed that conserves the acoustic energy and a time domain boundary integral equation is derived. Furthermore, stabilization of the integral equation by Burton-Miller type reformulation is presented. The stability is studied theoretically as well as numerically by an eigenvalue analysis. Numerical solutions are also presented that demonstrate the stability of the current formulation.
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Imen Boutana
2007-12-01
Full Text Available This paper provide some applications of Pettis integration to differential inclusions in Banach spaces with three point boundary conditions of the form $$ ddot{u}(t in F(t,u(t,dot u(t+H(t,u(t,dot u(t,quad hbox{a.e. } t in [0,1], $$ where $F$ is a convex valued multifunction upper semicontinuous on $Eimes E$ and $H$ is a lower semicontinuous multifunction. The existence of solutions is obtained under the non convexity condition for the multifunction $H$, and the assumption that $F(t,x,ysubset Gamma_{1}(t$, $H(t,x,ysubset Gamma_{2}(t$, where the multifunctions $Gamma_{1},Gamma_{2}:[0,1] ightrightarrows E$ are uniformly Pettis integrable.
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.
Discontinuous Galerkin finite element methods for hyperbolic differential equations
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
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.
Continuum damage growth analysis using element free Galerkin ...
Indian Academy of Sciences (India)
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 ...
Niu, Jun; Ren, Yi; Liu, Qing Huo
2017-10-02
In this work, we propose a numerical solver combining the spectral element - boundary integral (SEBI) method with the periodic layered medium dyadic Green's function. The periodic layered medium dyadic Green's function is formulated under matrix representation. The surface integral equations (SIEs) are then implemented as the radiation boundary condition to truncate the top and bottom computation domain. After describing the interior computation domain with the vector wave equations, and treating the lateral boundaries with Bloch periodic boundary conditions, the whole computation domains are discretized with mixed-order Gauss- Lobatto-Legendre basis functions in the SEBI method. This method avoids the discretization of the top and bottom layered media, so it can be much more efficient than conventional methods. Numerical results validate the proposed solver with fast convergence throughout the whole computation domain and good performance for typical multiscale nano-optical applications.
Uranus, H.P.; Hoekstra, Hugo; van Groesen, Embrecht W.C.
A simple high-order Galerkin finite element scheme is formulated to compute both the guided and leaky modes of anisotropic planar waveguides with a diagonal permitivity tensor. Transparent boundary conditions derived from the Sommerfeld radiation conditions are used to model the fields at the
Duemmler Kerstin
2015-01-01
Civic integration policies have become common in many European states and require that immigrants commit to integrating into the host society. This article draws on a study with young people in Swiss schools and investigates how these new political debates around civic integration find resonance in everyday narratives about immigration. The boundary approach is used as a framework to study the daily (re)production of the ‘Swiss–foreigner divide’. It reveals that assimilation into ‘Swiss cultu...
An Efficient Boundary Integral Formulation for Flow Through Fractured Porous Media
Lough, M. F.; Lee, S. H.; Kamath, J.
1998-07-01
In this paper we present a new model for flow in fractured porous media. We formulate our model in terms of a coupled system of boundary integral equations and present an efficient procedure for solving the equations using the boundary element method. In the new model, the flow in the matrix is governed by the usual Darcy law for porous media, with the fractures being treated as planar sources embedded in the matrix. The flow in an individual fracture is governed by a two-dimensional Darcy law (as in a Hele-Shaw cell), with an associated planar sink distribution. The essential feature of this approach is that the fractures are treated as special planes rather than narrow-gap voids. The error in the resulting system of equations is on the order of an intrinsic dimensionless parameter (the ratio of the fracture gap size to the scale of the volume under consideration). We also describe how we adapt the new model to compute effective grid block permeabilities. This was the principal motivation behind the development of the new model. Using effective grid block permeabilities to model flow in fractured oil and gas reservoirs is a much more efficient process than modeling the flow when every fracture is precisely represented. We present some numerical examples that illustrate the new flow model and how it is used to model flow in a reservoir.
Directory of Open Access Journals (Sweden)
Alsaedi Ahmed
2009-01-01
Full Text Available A generalized quasilinearization technique is developed to obtain a sequence of approximate solutions converging monotonically and quadratically to a unique solution of a boundary value problem involving Duffing type nonlinear integro-differential equation with integral boundary conditions. The convergence of order for the sequence of iterates is also established. It is found that the work presented in this paper not only produces new results but also yields several old results in certain limits.
Kramer, J.; Jecl, R.; Škerget, L.
2008-09-01
In the present work, a Boundary Domain Integral Method, which has been already established for the solution of viscous incompressible fluid flow through porous media, is extended to capture compressible fluid flow in porous media. The presented numerical scheme was used for solving the problem of double diffusive natural convection in a square porous cavity heated from a side, while the horizontal walls are maintained at different concentrations. The Brinkman extension of Darcy equation is used to model the flow through porous medium. The velocity-vorticity formulation is employed enabeling the computation scheme to be partitioned into kinematic and kinetic parts. The results of double diffusive natural convection in porous cavity are presented in terms of velocity, temperature and concentration redistributions.
An implicit boundary integral method for computing electric potential of macromolecules in solvent
Zhong, Yimin; Ren, Kui; Tsai, Richard
2018-04-01
A numerical method using implicit surface representations is proposed to solve the linearized Poisson-Boltzmann equation that arises in mathematical models for the electrostatics of molecules in solvent. The proposed method uses an implicit boundary integral formulation to derive a linear system defined on Cartesian nodes in a narrowband surrounding the closed surface that separates the molecule and the solvent. The needed implicit surface is constructed from the given atomic description of the molecules, by a sequence of standard level set algorithms. A fast multipole method is applied to accelerate the solution of the linear system. A few numerical studies involving some standard test cases are presented and compared to other existing results.
A Family of Well-Clear Boundary Models for the Integration of UAS in the NAS
Munoz, Cesar A.; Narkawicz, Anthony; Chamberlain, James; Consiglio, Maria; Upchurch, Jason
2014-01-01
The FAA-sponsored Sense and Avoid Workshop for Unmanned Aircraft Systems (UAS) defines the concept of sense and avoid for remote pilots as "the capability of a UAS to remain well clear from and avoid collisions with other airborne traffic." Hence, a rigorous definition of well clear is fundamental to any separation assurance concept for the integration of UAS into civil airspace. This paper presents a family of well-clear boundary models based on the TCAS II Resolution Advisory logic. For these models, algorithms that predict well-clear violations along aircraft current trajectories are provided. These algorithms are analogous to conflict detection algorithms but instead of predicting loss of separation, they predict whether well-clear violations will occur during a given lookahead time interval. Analytical techniques are used to study the properties and relationships satisfied by the models.
Furukawa, Hideaki; Miyazawa, Takaya; Wada, Naoya; Harai, Hiroaki
2014-01-13
Optical packet and circuit integrated (OPCI) networks provide both optical packet switching (OPS) and optical circuit switching (OCS) links on the same physical infrastructure using a wavelength multiplexing technique in order to deal with best-effort services and quality-guaranteed services. To immediately respond to changes in user demand for OPS and OCS links, OPCI networks should dynamically adjust the amount of wavelength resources for each link. We propose a resource-adjustable hybrid optical packet/circuit switch and transponder. We also verify that distributed control of resource adjustments can be applied to the OPCI ring network testbed we developed. In cooperation with the resource adjustment mechanism and the hybrid switch and transponder, we demonstrate that automatically allocating a shared resource and moving the wavelength resource boundary between OPS and OCS links can be successfully executed, depending on the number of optical paths in use.
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.
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.
The Galerkin finite element method for a multi-term time-fractional diffusion equation
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.
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 $f(u=u^{alpha}$, $0
Kimoto, K.; Hirose, S.
2002-05-01
This paper presents a boundary integral equation method for 3D ultrasonic scattering problems in a fluid-loaded elastic half space. Since full scale of numerical calculation using finite element or boundary element method is still very expensive, we formulate a boundary integral equation for the scattered field, which is amenable to numerical treatment. In order to solve the problem using the integral equation, however, the wave field without scattering objects, so-called free field need to be given in advance. We calculate the free field by the plane wave spectral method where the asymptotic approximation is introduced for computational efficiency. To show the efficiency of our method, scattering by a spherical cavity near fluid-solid interface is solved and the validity of the results is discussed.
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Xuemei Zhang
2014-01-01
Full Text Available This paper investigates the expression and properties of Green’s function for a second-order singular boundary value problem with integral boundary conditions and delayed argument -x′′t-atx′t+btxt=ωtft, xαt, t∈0, 1; x′0=0, x1-∫01htxtdt=0, where a∈0, 1, 0, +∞, b∈C0, 1, 0, +∞ and, ω may be singular at t=0 or/and at t=1. Furthermore, several new and more general results are obtained for the existence of positive solutions for the above problem by using Krasnosel’skii’s fixed point theorem. We discuss our problems with a delayed argument, which may concern optimization issues of some technical problems. Moreover, the approach to express the integral equation of the above problem is different from earlier approaches. Our results cover a second-order boundary value problem without deviating arguments and are compared with some recent results.
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.
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.
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Min Jia
2012-01-01
Full Text Available We study a model arising from porous media, electromagnetic, and signal processing of wireless communication system -tαx(t=f(t,x(t,x'(t,x”(t,…,x(n-2(t, 0
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 ℓ^{2}-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.
Gao, Y.; Balaram, P.; Islam, S.
2009-12-01
Water issues and problems have bewildered humankind for a long time yet a systematic approach for understanding such issues remain elusive. This is partly because many water-related problems are framed from a contested terrain in which many actors (individuals, communities, businesses, NGOs, states, and countries) compete to protect their own and often conflicting interests. We argue that origin of many water problems may be understood as a dynamic consequence of competition, interconnections, and feedback among variables in the Natural and Societal Systems (NSSs). Within the natural system, we recognize that triple constraints on water- water quantity (Q), water quality (P), and ecosystem (E)- and their interdependencies and feedback may lead to conflicts. Such inherent and multifaceted constraints of the natural water system are exacerbated often at the societal boundaries. Within the societal system, interdependencies and feedback among values and norms (V), economy (C), and governance (G) interact in various ways to create intractable contextual differences. The observation that natural and societal systems are linked is not novel. Our argument here, however, is that rigid disciplinary boundaries between these two domains will not produce solutions to the water problems we are facing today. The knowledge needed to address water problems need to go beyond scientific assessment in which societal variables (C, G, and V) are treated as exogenous or largely ignored, and policy research that does not consider the impact of natural variables (E, P, and Q) and that coupling among them. Consequently, traditional quantitative methods alone are not appropriate to address the dynamics of water conflicts, because we cannot quantify the societal variables and the exact mathematical relationships among the variables are not fully known. On the other hand, conventional qualitative study in societal domain has mainly been in the form of individual case studies and therefore
Finite element or Galerkin type semidiscrete schemes
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.
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.
On cell entropy inequality for discontinuous Galerkin methods
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.
Extreme Scale FMM-Accelerated Boundary Integral Equation Solver for Wave Scattering
AbdulJabbar, Mustafa Abdulmajeed
2018-03-27
Algorithmic and architecture-oriented optimizations are essential for achieving performance worthy of anticipated energy-austere exascale systems. In this paper, we present an extreme scale FMM-accelerated boundary integral equation solver for wave scattering, which uses FMM as a matrix-vector multiplication inside the GMRES iterative method. Our FMM Helmholtz kernels treat nontrivial singular and near-field integration points. We implement highly optimized kernels for both shared and distributed memory, targeting emerging Intel extreme performance HPC architectures. We extract the potential thread- and data-level parallelism of the key Helmholtz kernels of FMM. Our application code is well optimized to exploit the AVX-512 SIMD units of Intel Skylake and Knights Landing architectures. We provide different performance models for tuning the task-based tree traversal implementation of FMM, and develop optimal architecture-specific and algorithm aware partitioning, load balancing, and communication reducing mechanisms to scale up to 6,144 compute nodes of a Cray XC40 with 196,608 hardware cores. With shared memory optimizations, we achieve roughly 77% of peak single precision floating point performance of a 56-core Skylake processor, and on average 60% of peak single precision floating point performance of a 72-core KNL. These numbers represent nearly 5.4x and 10x speedup on Skylake and KNL, respectively, compared to the baseline scalar code. With distributed memory optimizations, on the other hand, we report near-optimal efficiency in the weak scalability study with respect to both the logarithmic communication complexity as well as the theoretical scaling complexity of FMM. In addition, we exhibit up to 85% efficiency in strong scaling. We compute in excess of 2 billion DoF on the full-scale of the Cray XC40 supercomputer.
The influence of a scaled boundary response on integral system transient behavior
International Nuclear Information System (INIS)
Dimenna, R.A.; Kullberg, C.M.
1989-01-01
Scaling relationships associated with the thermal-hydraulic response of a closed-loop system are applied to a calculational assessment of a feed-and-bleed recovery in a nuclear reactor integral effects test. The analysis demonstrates both the influence of scale on the system response and the ability of the thermal-hydraulics code to represent those effects. The qualitative response of the fluid is shown to be coupled to the behavior of the bounding walls through the energy equation. The results of the analysis described in this paper influence the determination of computer code applicability. The sensitivity of the code response to scaling variations introduced in the analysis is found to be appropriate with respect to scaling criteria determined from the scaling literature. Differences in the system response associated with different scaling criteria are found to be plausible and easily explained using well-known principles of heat transfer. Therefore, it is concluded that RELAP5/MOD2 can adequately represent the scaled effects of heat transfer boundary conditions of the thermal-hydraulic calculations through the mechanism of communicating walls. The results of the analysis also serve to clarify certain aspects of experiment and facility design
International Nuclear Information System (INIS)
Esmaeilzadeh, Hamid; Arzi, Ezatollah; Légaré, François; Hassani, Alireza
2013-01-01
In this paper, using the boundary integral method (BIM), we simulate the effect of temperature fluctuation on the sensitivity of microstructured optical fibre (MOF) surface plasmon resonance (SPR) sensors. The final results indicate that, as the temperature increases, the refractometry sensitivity of our sensor decreases from 1300 nm/RIU at 0 °C to 1200 nm/RIU at 50 °C, leading to ∼7.7% sensitivity reduction and the sensitivity temperature error of 0.15% °C −1 for this case. These results can be used for biosensing temperature-error adjustment in MOF SPR sensors, since biomaterials detection usually happens in this temperature range. Moreover, the signal-to-noise ratio (SNR) of our sensor decreases from 0.265 at 0 °C to 0.154 at 100 °C with the average reduction rate of ∼0.42% °C −1 . The results suggest that at lower temperatures the sensor has a higher SNR. (paper)
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)
Galerkin FEM for Fractional Order Parabolic Equations with Initial Data in H − s , 0 ≤ s ≤ 1
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.
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.
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.
Moore, Benjamin L; Aitken, Stuart; Semple, Colin A
2015-05-27
Interphase chromosomes adopt a hierarchical structure, and recent data have characterized their chromatin organization at very different scales, from sub-genic regions associated with DNA-binding proteins at the order of tens or hundreds of bases, through larger regions with active or repressed chromatin states, up to multi-megabase-scale domains associated with nuclear positioning, replication timing and other qualities. However, we have lacked detailed, quantitative models to understand the interactions between these different strata. Here we collate large collections of matched locus-level chromatin features and Hi-C interaction data, representing higher-order organization, across three human cell types. We use quantitative modeling approaches to assess whether locus-level features are sufficient to explain higher-order structure, and identify the most influential underlying features. We identify structurally variable domains between cell types and examine the underlying features to discover a general association with cell-type-specific enhancer activity. We also identify the most prominent features marking the boundaries of two types of higher-order domains at different scales: topologically associating domains and nuclear compartments. We find parallel enrichments of particular chromatin features for both types, including features associated with active promoters and the architectural proteins CTCF and YY1. We show that integrative modeling of large chromatin dataset collections using random forests can generate useful insights into chromosome structure. The models produced recapitulate known biological features of the cell types involved, allow exploration of the antecedents of higher-order structures and generate testable hypotheses for further experimental studies.
A Galerkin formulation of the MIB method for three dimensional elliptic interface problems.
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
Becker, A.; Hansen, V.
2003-05-01
In this paper a hybrid method combining the FDTD/FIT with a Time Domain Boundary-Integral Marching-on-in-Time Algorithm (TD-BIM) is presented. Inhomogeneous regions are modelled with the FIT-method, an alternative formulation of the FDTD. Homogeneous regions (which is in the presented numerical example the open space) are modelled using a TD-BIM with equivalent electric and magnetic currents flowing on the boundary between the inhomogeneous and the homogeneous regions. The regions are coupled by the tangential magnetic fields just outside the inhomogeneous regions. These fields are calculated by making use of a Mixed Potential Integral Formulation for the magnetic field. The latter consists of equivalent electric and magnetic currents on the boundary plane between the homogeneous and the inhomogeneous region. The magnetic currents result directly from the electric fields of the Yee lattice. Electric currents in the same plane are calculated by making use of the TD-BIM and using the electric field of the Yee lattice as boundary condition. The presented hybrid method only needs the interpolations inherent in FIT and no additional interpolation. A numerical result is compared to a calculation that models both regions with FDTD.
Directory of Open Access Journals (Sweden)
A. Becker
2003-01-01
Full Text Available In this paper a hybrid method combining the FDTD/FIT with a Time Domain Boundary-Integral Marching-on-in-Time Algorithm (TD-BIM is presented. Inhomogeneous regions are modelled with the FIT-method, an alternative formulation of the FDTD. Homogeneous regions (which is in the presented numerical example the open space are modelled using a TD-BIM with equivalent electric and magnetic currents flowing on the boundary between the inhomogeneous and the homogeneous regions. The regions are coupled by the tangential magnetic fields just outside the inhomogeneous regions. These fields are calculated by making use of a Mixed Potential Integral Formulation for the magnetic field. The latter consists of equivalent electric and magnetic currents on the boundary plane between the homogeneous and the inhomogeneous region. The magnetic currents result directly from the electric fields of the Yee lattice. Electric currents in the same plane are calculated by making use of the TD-BIM and using the electric field of the Yee lattice as boundary condition. The presented hybrid method only needs the interpolations inherent in FIT and no additional interpolation. A numerical result is compared to a calculation that models both regions with FDTD.
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
The dimension split element-free Galerkin method for three-dimensional potential problems
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.
Comparison of the constant and linear boundary element method for EEG and MEG forward modeling
Energy Technology Data Exchange (ETDEWEB)
Mosher, J.C. [Los Alamos National Lab., NM (United States); Chang, C.H.; Leahy, R.M. [University of Southern California, Los Angeles, CA (United States)
1996-07-01
We present a comparison of boundary element methods for solving the forward problem in EEG and MEG. We use the method of weighted residuals and focus on the collocation and Galerkin forms for constant and linear basis functions. We also examine the effect of the isolated skull approach for reducing numerical errors due to the low conductivity of the skull. We demonstrate the improvement that a linear Galerkin approach may yield in solving the forward problem.
In Vivo Evidence of Reduced Integrity of the Gray-White Matter Boundary in Autism Spectrum Disorder.
Andrews, Derek Sayre; Avino, Thomas A; Gudbrandsen, Maria; Daly, Eileen; Marquand, Andre; Murphy, Clodagh M; Lai, Meng-Chuan; Lombardo, Michael V; Ruigrok, Amber N V; Williams, Steven C; Bullmore, Edward T; The Mrc Aims Consortium; Suckling, John; Baron-Cohen, Simon; Craig, Michael C; Murphy, Declan G M; Ecker, Christine
2017-02-01
Atypical cortical organization and reduced integrity of the gray-white matter boundary have been reported by postmortem studies in individuals with autism spectrum disorder (ASD). However, there are no in vivo studies that examine these particular features of cortical organization in ASD. Hence, we used structural magnetic resonance imaging to examine differences in tissue contrast between gray and white matter in 98 adults with ASD and 98 typically developing controls, to test the hypothesis that individuals with ASD have significantly reduced tissue contrast. More specifically, we examined contrast as a percentage between gray and white matter tissue signal intensities (GWPC) sampled at the gray-white matter boundary, and across different cortical layers. We found that individuals with ASD had significantly reduced GWPC in several clusters throughout the cortex (cluster, P < 0.05). As expected, these reductions were greatest when tissue intensities were sampled close to gray-white matter interface, which indicates a less distinct gray-white matter boundary in ASD. Our in vivo findings of reduced GWPC in ASD are therefore consistent with prior postmortem findings of a less well-defined gray-white matter boundary in ASD. Taken together, these results indicate that GWPC might be utilized as an in vivo proxy measure of atypical cortical microstructural organization in future studies. © The Author 2017. Published by Oxford University Press.
Directory of Open Access Journals (Sweden)
Hristov Jordan
2016-01-01
Full Text Available A new approach to integral-balance solutions of the diffusion equation of heat (mass with constant transport properties by applying time-fractional semi-derivatives and semi-integrals of Riemann-Liouville sense has been developed. The time-fractional semiderivatives and semiintegrals replace the surface gradient (temperature which in the classical Heat-balance integral method (HBIM of Goodman and the Double-integration method (DIM should be expressed through the assumed profile. The application of semiderivatives and semiintegrals reduces the approximation errors to levels less than the ones exhibited by the classical HBIM and DIM. The method is exemplified by solutions of Dirichlet and Neumann boundary condition problems.
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...
Thomas B. Lynch; Jeffrey H. Gove
2014-01-01
The typical "double counting" application of the mirage method of boundary correction cannot be applied to sampling systems such as critical height sampling (CHS) that are based on a Monte Carlo sample of a tree (or debris) attribute because the critical height (or other random attribute) sampled from a mirage point is generally not equal to the critical...
Integrable boundary conditions for a non-Abelian anyon chain with D(D{sub 3}) symmetry
Energy Technology Data Exchange (ETDEWEB)
Dancer, K.A.; Finch, P.E.; Isaac, P.S. [The University of Queensland, Centre for Mathematical Physics, School of Physical Sciences, 4072 (Australia); Links, J. [The University of Queensland, Centre for Mathematical Physics, School of Physical Sciences, 4072 (Australia)], E-mail: jrl@maths.uq.edu.au
2009-05-11
A general formulation of the Boundary Quantum Inverse Scattering Method is given which is applicable in cases where R-matrix solutions of the Yang-Baxter equation do not have the property of crossing unitarity. Suitably modified forms of the reflection equations are presented which permit the construction of a family of commuting transfer matrices. As an example, we apply the formalism to determine the most general solutions of the reflection equations for a solution of the Yang-Baxter equation with underlying symmetry given by the Drinfeld double D(D{sub 3}) of the dihedral group D{sub 3}. This R-matrix does not have the crossing unitarity property. In this manner we derive integrable boundary conditions for an open chain model of interacting non-Abelian anyons.
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)
Divergence-Conforming Discontinuous Galerkin Methods and $C^0$ Interior Penalty Methods
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.
POD-Galerkin Model for Incompressible Single-Phase Flow in Porous Media
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.
Discontinuous Galerkin Subgrid Finite Element Method for Heterogeneous Brinkman’s Equations
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.
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.
DEFF Research Database (Denmark)
Aarhus, Rikke; Ballegaard, Stinne Aaløkke
2010-01-01
to maintain the order of the home when managing disease and adopting new healthcare technology. In our analysis we relate this boundary work to two continuums of visibility-invisibility and integration-segmentation in disease management. We explore five factors that affect the boundary work: objects......To move treatment successfully from the hospital to that of technology assisted self-care at home, it is vital in the design of such technologies to understand the setting in which the health IT should be used. Based on qualitative studies we find that people engage in elaborate boundary work......, activities, places, character of disease, and collaboration. Furthermore, the processes are explored of how boundary objects move between social worlds pushing and shaping boundaries. From this we discuss design implications for future healthcare technologies for the home....
DEFF Research Database (Denmark)
Zølner, Mette
The paper explores how locals span boundaries between corporate and local levels. The aim is to better comprehend potentialities and challenges when MNCs draws on locals’ culture specific knowledge. The study is based on an in-depth, interpretive case study of boundary spanning by local actors...... in the period of post-acquisition when their organization is being integrated into the acquiring MNC. The paper contributes to the literature on boundary spanning in three ways: First, by illustrating that boundary spanning is performed by numerous organizational actors in a variety of positions in MNCs......, inclusively by locals in subsidiaries. Second, by showing that boundary spanning is ‘situated’ in the sense that its result depends on the kind of knowledge to be transmitted and the attitude of the receivers. A third contribution is methodological. The study illustrates that combining bottom-up grounded...
A penalty-based nodal discontinuous Galerkin method for spontaneous rupture dynamics
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.
Czech Academy of Sciences Publication Activity Database
Mácha, Václav; Tichý, J.
2014-01-01
Roč. 16, č. 4 (2014), s. 823-845 ISSN 1422-6928 R&D Projects: GA ČR GA201/09/0917 Institutional support: RVO:67985840 Keywords : generalized Stokes system * perfect slip boundary conditions * Lq theory Subject RIV: BA - General Math ematics Impact factor: 1.186, year: 2014 http://link.springer.com/article/10.1007%2Fs00021-014-0190-5
International Nuclear Information System (INIS)
Orlowska, S; Beroual, A; Fleszynski, J
2004-01-01
This paper deals with the analysis of the influence of moisture on the dielectric properties of a composite insulator core made of epoxy resin and fibre glass, through measurements of the effective permittivity. The experiments are carried out on different core samples-dry and boiled in distilled water over different time intervals. The measured values of the complex permittivity of the core samples are discussed in the light of the results obtained by a numerical approach based on the boundary integral equation method and the PHI3D package. The comparison of the experimental and simulated results aims at finding the water content in the fibre glass
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 ...
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
Local discontinuous Galerkin methods for phase transition problems
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
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.
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.
An implicit discontinuous Galerkin finite element model for water waves
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
Space-time discontinuous Galerkin finite element methods
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
A Multi-wavelet type limiter for discontinuous Galerkin approximations
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).
Space-time discontinuous Galerkin method for compressible flow
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
Continuum damage growth analysis using element free Galerkin ...
Indian Academy of Sciences (India)
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 ...
Wong, Rene; Breiner, Petra; Mylopoulos, Maria
2014-09-01
This article reports on research into the relationships that emerged between hospital-based and community-based interprofessional diabetes programs involved in inter-agency care. Using constructivist grounded theory methodology we interviewed a purposive theoretical sample of 21 clinicians and administrators from both types of programs. Emergent themes were identified through a process of constant comparative analysis. Initial boundaries were constructed based on contrasts in beliefs, practices and expertise. In response to bureaucratic and social pressures, boundaries were redefined in a way that created role uncertainty and disempowered community programs, ultimately preventing collaboration. We illustrate the dynamic and multi-dimensional nature of social and symbolic boundaries in inter-agency diabetes care and the tacit ways in which hospitals can maintain a power position at the expense of other actors in the field. As efforts continue in Canada and elsewhere to move knowledge and resources into community sectors, we highlight the importance of hospitals seeing beyond their own interests and adopting more altruistic models of inter-agency integration.
International Nuclear Information System (INIS)
Pereira, Luis Carlos Martins
1998-06-01
New Petrov-Galerkin formulations on the finite element methods for convection-diffusion problems with boundary layers are presented. Such formulations are based on a consistent new theory on discontinuous finite element methods. Existence and uniqueness of solutions for these problems in the new finite element spaces are demonstrated. Some numerical experiments shows how the new formulation operate and also their efficacy. (author)
Error Analysis for Discontinuous Galerkin Method for Parabolic Problems
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.
Directory of Open Access Journals (Sweden)
A.S. Gjam
2013-10-01
The obtained results are discussed and boundary curves for unknown functions are provided, as well as three-dimensional plots for quantities of practical interest. The efficiency of the used numerical schemes is discussed, in what concerns the number of boundary nodes needed to calculate the approximate solution.
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
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.
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.
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.
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.
Galenko, Peter K; Alexandrov, Dmitri V; Titova, Ekaterina A
2018-02-28
The boundary integral method for propagating solid/liquid interfaces is detailed with allowance for the thermo-solutal Stefan-type models. Two types of mass transfer mechanisms corresponding to the local equilibrium (parabolic-type equation) and local non-equilibrium (hyperbolic-type equation) solidification conditions are considered. A unified integro-differential equation for the curved interface is derived. This equation contains the steady-state conditions of solidification as a special case. The boundary integral analysis demonstrates how to derive the quasi-stationary Ivantsov and Horvay-Cahn solutions that, respectively, define the paraboloidal and elliptical crystal shapes. In the limit of highest Péclet numbers, these quasi-stationary solutions describe the shape of the area around the dendritic tip in the form of a smooth sphere in the isotropic case and a deformed sphere along the directions of anisotropy strength in the anisotropic case. A thermo-solutal selection criterion of the quasi-stationary growth mode of dendrites which includes arbitrary Péclet numbers is obtained. To demonstrate the selection of patterns, computational modelling of the quasi-stationary growth of crystals in a binary mixture is carried out. The modelling makes it possible to obtain selected structures in the form of dendritic, fractal or planar crystals.This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'. © 2018 The Author(s).
Galenko, Peter K.; Alexandrov, Dmitri V.; Titova, Ekaterina A.
2018-01-01
The boundary integral method for propagating solid/liquid interfaces is detailed with allowance for the thermo-solutal Stefan-type models. Two types of mass transfer mechanisms corresponding to the local equilibrium (parabolic-type equation) and local non-equilibrium (hyperbolic-type equation) solidification conditions are considered. A unified integro-differential equation for the curved interface is derived. This equation contains the steady-state conditions of solidification as a special case. The boundary integral analysis demonstrates how to derive the quasi-stationary Ivantsov and Horvay-Cahn solutions that, respectively, define the paraboloidal and elliptical crystal shapes. In the limit of highest Péclet numbers, these quasi-stationary solutions describe the shape of the area around the dendritic tip in the form of a smooth sphere in the isotropic case and a deformed sphere along the directions of anisotropy strength in the anisotropic case. A thermo-solutal selection criterion of the quasi-stationary growth mode of dendrites which includes arbitrary Péclet numbers is obtained. To demonstrate the selection of patterns, computational modelling of the quasi-stationary growth of crystals in a binary mixture is carried out. The modelling makes it possible to obtain selected structures in the form of dendritic, fractal or planar crystals. This article is part of the theme issue `From atomistic interfaces to dendritic patterns'.
Lagrange–Galerkin methods for the incompressible Navier-Stokes equations: a review
Directory of Open Access Journals (Sweden)
Bermejo Rodolfo
2016-09-01
Full Text Available We review in this paper the development of Lagrange-Galerkin (LG methods to integrate the incompressible Navier-Stokes equations (NSEs for engineering applications. These methods were introduced in the computational fluid dynamics community in the early eighties of the past century, and at that time they were considered good methods for both their theoretical stability properties and the way of dealing with the nonlinear terms of the equations; however, the numerical experience gained with the application of LG methods to different problems has identified drawbacks of them, such as the calculation of specific integrals that arise in their formulation and the calculation of the ow trajectories, which somehow have hampered the applicability of LG methods. In this paper, we focus on these issues and summarize the convergence results of LG methods; furthermore, we shall briefly introduce a new stabilized LG method suitable for high Reynolds numbers.
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
The Blurred Boundaries and Multiple Effects of European Integration and Globalisation
DEFF Research Database (Denmark)
Lynggaard, Kennet
2015-01-01
This chapter presents analytical strategies for the study of European integration and Globalisation in concert. This is an increasingly important as well as a highly diverse field of inquiry. The chapter presents a series of research clusters in various ways concerned with the fundamental questions...... of how European integration contribute to, and are effected by, globalisation. By means of concrete research examples the chapter discusses the advantages of the research strategies and tools typically applied on the area and the challenges we face in this regard. This includes discussions of top...
Galerkin CFD solvers for use in a multi-disciplinary suite for modeling advanced flight vehicles
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
Tello-Leal, Edgar; Chiotti, Omar; Villarreal, Pablo David
2012-12-01
The paper presents a methodology that follows a top-down approach based on a Model-Driven Architecture for integrating and coordinating healthcare services through cross-organizational processes to enable organizations providing high quality healthcare services and continuous process improvements. The methodology provides a modeling language that enables organizations conceptualizing an integration agreement, and identifying and designing cross-organizational process models. These models are used for the automatic generation of: the private view of processes each organization should perform to fulfill its role in cross-organizational processes, and Colored Petri Net specifications to implement these processes. A multi-agent system platform provides agents able to interpret Colored Petri-Nets to enable the communication between the Healthcare Information Systems for executing the cross-organizational processes. Clinical documents are defined using the HL7 Clinical Document Architecture. This methodology guarantees that important requirements for healthcare services integration and coordination are fulfilled: interoperability between heterogeneous Healthcare Information Systems; ability to cope with changes in cross-organizational processes; guarantee of alignment between the integrated healthcare service solution defined at the organizational level and the solution defined at technological level; and the distributed execution of cross-organizational processes keeping the organizations autonomy.
A Streaming Language Implementation of the Discontinuous Galerkin Method
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.
Modeling shallow water flows using the discontinuous Galerkin method
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...
Modeling shallow water flows using the discontinuous galerkin method
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...
Directory of Open Access Journals (Sweden)
Mohamed Jleli
2017-03-01
where $n\\in \\mathbb N$, $n\\geq 2$, $n-1<\\alpha
Stability Analysis of Discontinuous Galerkin Approximations to the Elastodynamics Problem
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.
The discrete maximum principle for Galerkin solutions of elliptic problems
Czech Academy of Sciences Publication Activity Database
Vejchodský, Tomáš
2012-01-01
Roč. 10, č. 1 (2012), s. 25-43 ISSN 1895-1074 R&D Projects: GA AV ČR IAA100760702 Institutional research plan: CEZ:AV0Z10190503 Keywords : discrete maximum principle * monotone methods * Galerkin solution Subject RIV: BA - General Mathematics Impact factor: 0.405, year: 2012 http://www.springerlink.com/content/x73624wm23x4wj26
A discontinuous Galerkin method on kinetic flocking models
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.
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
Dual-scale Galerkin methods for Darcy flow
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.
A nearest-neighbour discretisation of the regularized stokeslet boundary integral equation
Smith, David J.
2018-04-01
The method of regularized stokeslets is extensively used in biological fluid dynamics due to its conceptual simplicity and meshlessness. This simplicity carries a degree of cost in computational expense and accuracy because the number of degrees of freedom used to discretise the unknown surface traction is generally significantly higher than that required by boundary element methods. We describe a meshless method based on nearest-neighbour interpolation that significantly reduces the number of degrees of freedom required to discretise the unknown traction, increasing the range of problems that can be practically solved, without excessively complicating the task of the modeller. The nearest-neighbour technique is tested against the classical problem of rigid body motion of a sphere immersed in very viscous fluid, then applied to the more complex biophysical problem of calculating the rotational diffusion timescales of a macromolecular structure modelled by three closely-spaced non-slender rods. A heuristic for finding the required density of force and quadrature points by numerical refinement is suggested. Matlab/GNU Octave code for the key steps of the algorithm is provided, which predominantly use basic linear algebra operations, with a full implementation being provided on github. Compared with the standard Nyström discretisation, more accurate and substantially more efficient results can be obtained by de-refining the force discretisation relative to the quadrature discretisation: a cost reduction of over 10 times with improved accuracy is observed. This improvement comes at minimal additional technical complexity. Future avenues to develop the algorithm are then discussed.
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.
Sezen-Barrie, Asli; Moore, Joel; Roig, Cara E.
2015-08-01
Drawn from the norms and rules of their fields, scientists use variety of practices, such as asking questions and arguing based on evidence, to engage in research that will contribute to our understanding of Earth and beyond. In this study, we explore how preservice teachers' learn to teach scientific practices while teaching plate tectonic theory. In particular, our aim is to observe which scientific practices preservice teachers use while teaching an earth science unit, how do they integrate these practices into their lessons, and what challenges do they face during their first time teaching of an earth science content area integrated with scientific practices. The study is designed as a qualitative, exploratory case study of seven preservice teachers while they were learning to teach plate tectonic theory to a group of middle school students. The data were driven from the video records and artifacts of the preservice teachers' learning and teaching processes as well as written reflections on the teaching. Intertextual discourse analysis was used to understand what scientific practices preservice teachers choose to integrate into their teaching experience. Our results showed that preservice teachers chose to focus on four aspects of scientific practices: (1) employing historical understanding of how the theory emerged, (2) encouraging the use of evidence to build up a theory, (3) observation and interpretation of data maps, and (4) collaborative practices in making up the theory. For each of these practices, we also looked at the common challenges faced by preservice teachers by using constant comparative analysis. We observed the practices that preservice teachers decided to use and the challenges they faced, which were determined by what might have come as in their personal history as learners. Therefore, in order to strengthen preservice teachers' background, college courses should be arranged to teach important scientific ideas through scientific practices
International Nuclear Information System (INIS)
Fleming, K. N.; Gamble, R.; Gosselin, S.; Fletcher, J.; Broom, N.
2008-01-01
The purpose of this paper is to present the results of a study to establish strategies for the reliability and integrity management (RIM) of passive metallic components for the PBMR. The RIM strategies investigated include design elements, leak detection and testing approaches, and non-destructive examinations. Specific combinations of strategies are determined to be necessary and sufficient to achieve target reliability goals for passive components. This study recommends a basis for the RIM program for the PBMR Demonstration Power Plant (DPP) and provides guidance for the development by the American Society of Mechanical Engineers (ASME) of RIM requirements for Modular High Temperature Gas-Cooled Reactors (MHRs). (authors)
A Galleria Boundary Element Method for two-dimensional nonlinear magnetostatics
Brovont, Aaron D.
The Boundary Element Method (BEM) is a numerical technique for solving partial differential equations that is used broadly among the engineering disciplines. The main advantage of this method is that one needs only to mesh the boundary of a solution domain. A key drawback is the myriad of integrals that must be evaluated to populate the full system matrix. To this day these integrals have been evaluated using numerical quadrature. In this research, a Galerkin formulation of the BEM is derived and implemented to solve two-dimensional magnetostatic problems with a focus on accurate, rapid computation. To this end, exact, closed-form solutions have been derived for all the integrals comprising the system matrix as well as those required to compute fields in post-processing; the need for numerical integration has been eliminated. It is shown that calculation of the system matrix elements using analytical solutions is 15-20 times faster than with numerical integration of similar accuracy. Furthermore, through the example analysis of a c-core inductor, it is demonstrated that the present BEM formulation is a competitive alternative to the Finite Element Method (FEM) for linear magnetostatic analysis. Finally, the BEM formulation is extended to analyze nonlinear magnetostatic problems via the Dual Reciprocity Method (DRBEM). It is shown that a coarse, meshless analysis using the DRBEM is able to achieve RMS error of 3-6% compared to a commercial FEM package in lightly saturated conditions.
The influence of a scaled boundary response on integral system transient behavior
International Nuclear Information System (INIS)
Dimenna, R.A.; Kullberg, C.M.
1989-01-01
In this paper, scaling relationships associated with the thermal-hydraulic response of a closed loop system are applied to a calculational assessment of a feed-and-bleed recovery in a nuclear reactor integral effects test. The analysis demonstrates both the influence of scale on the system response and the ability of the thermal-hydraulics code to represent those effects. The qualitative response of the fluid is shown to be coupled to the behavior of the bounding walls through the energy equation. A variety of scaling relationships associated with an integral system test facility are applied to computer models representing a feed and bleed transient in a nuclear reactor. the difference in scaled behavior between the solid walls and the two-phase fluid is shown to have a significant impact on the qualitative nature of the results, both in the calculations and in the experiment. The principal effect for the transient addressed is shown to be the behavior of the pressurizer walls. The energy transfer rate from the walls to the fluid has a direct influence on the mass discharge rate from the primary system
Shock capturing in discontinuous Galerkin spectral elements via the entropy viscosity method
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.
Modeling the mechanics of HMX detonation using a Taylor–Galerkin scheme
Directory of Open Access Journals (Sweden)
Adam V. Duran
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.
An hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations
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.
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.
Self-Trail, J. M.; Robinson, M. M.; Edwards, L. E.; Powars, D. S.; Wandless, G. A.; Willard, D. A.
2013-12-01
An exceptional Paleocene-Eocene boundary section occurs in a cluster of six short (Paleocene Aquia Formation and silty clay of the lower Eocene Marlboro Clay. Sediment samples were analyzed for carbon and oxygen isotopes, percent calcium carbonate, calcareous nannofossils, planktic and benthic foraminifera, dinoflagellates, pollen, and lithology. A well-defined carbon isotope excursion (CIE) documents a gradual negative shift in δ13C values that starts below the lithologic break between the Aquia Formation and the Marlboro Clay. A benthic foraminifer extinction event, reduction of calcareous nannofossil assemblages, and change in core color from gray to alternating gray and pink also occurs within the CIE transition. These alternating changes in color coincide with cyclic peaks in the carbon isotope and percent calcium carbonate curves, where gray color corresponds to a positive shift in carbon isotope values and to a corresponding increase in percent benthic and planktic foraminifera. The upper third of the Marlboro Clay is barren of all calcareous microfossil material, although the presence of foraminiferal molds and linings proves that deposition occurred in a marine environment. Co-occurrence of the dinoflagellates Apectodinium augustum and Phthanoperidinium crenulatum at the top of the Marlboro Clay suggests that the Marlboro Clay at Mattawoman Creek is truncated. This is corroborated by the absence in the Marlboro of specimens of the calcareous nannofossil Rhomboaster-Discoaster assemblage, which is restricted to early Eocene Zone NP9b. Based on planktic/benthic foraminifera ratios, deposition of sediments at Mattawoman Creek occurred predominantly in an inner neritic environment, at water depths between 25-50 m. Occasional deepening to approximately 75m (middle neritic environment) occurred in the early Eocene, as represented by the basal Marlboro Clay. The planktic/benthic ratio, however, could also be affected by surface productivity and/or river runoff
Study of pollutant transport in surface boundary layer by generalized integral transform technique
Energy Technology Data Exchange (ETDEWEB)
Guerrero, Jesus S.P.; Heilbron Filho, Paulo F.L. [Comissao Nacional de Energia Nuclear (CNEN), Rio de Janeiro, RJ (Brazil); Pimentel, Luiz C.G. [Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, RJ (Brazil). Dept. de Meteorologia. Lab. de Modelagem de Processos Marinhos e Atmosfericos (LAMMA); Cataldi, Marcio [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil). Coordenacao dos Programas de Pos-Graduacao de Engenharia (COPPE)
2001-07-01
A theoretical study was developed to obtain solutions of the atmospheric diffusion equation for various point source, considering radioactive decay and axial diffusion, under neutral atmospheric conditions. It was used an algebraic turbulence model available in the literature, based on Monin-Obukhov similarity theory, for the representation of the turbulent transport in the vertical direction, in the longitudinal directions was considered a constant mass eddy diffusivity . The bi-dimensional transient partial differential equation, representative of the physical phenomena, was transformed into a coupled one-dimensional transient equation system by applying the Generalized Integral Transform Technique. The coupled system was solved numerically using a subroutine based in the lines method. In order to evaluate the computational algorithm were analyzed some representative physical situations. (author)
Study of pollutant transport in surface boundary layer by generalized integral transform technique
International Nuclear Information System (INIS)
Guerrero, Jesus S.P.; Heilbron Filho, Paulo F.L.; Pimentel, Luiz C.G.; Cataldi, Marcio
2001-01-01
A theoretical study was developed to obtain solutions of the atmospheric diffusion equation for various point source, considering radioactive decay and axial diffusion, under neutral atmospheric conditions. It was used an algebraic turbulence model available in the literature, based on Monin-Obukhov similarity theory, for the representation of the turbulent transport in the vertical direction, in the longitudinal directions was considered a constant mass eddy diffusivity . The bi-dimensional transient partial differential equation, representative of the physical phenomena, was transformed into a coupled one-dimensional transient equation system by applying the Generalized Integral Transform Technique. The coupled system was solved numerically using a subroutine based in the lines method. In order to evaluate the computational algorithm were analyzed some representative physical situations. (author)
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.
Energy Technology Data Exchange (ETDEWEB)
Guirao, Julio, E-mail: julio@natec-ingenieros.com [Numerical Analysis Technologies S.L. (NATEC), Gijon (Spain); Iglesias, Silvia; Vacas, Christian; Udintsev, Victor [CHD, Diagnostic Division, ITER Organization, Route de Vinon-sur-Verdon, CS 90 046, 13067 St. Paul Lez Durance Cedex (France); Pak, Sunil [Diagnostic and Control Team, National Fusion Research Institute, Daejeon (Korea, Republic of); Maquet, Philippe [CHD, Diagnostic Division, ITER Organization, Route de Vinon-sur-Verdon, CS 90 046, 13067 St. Paul Lez Durance Cedex (France); Rodriguez, Eduardo; Roces, Jorge [Department of Construction and Manufacturing Engineering, University of Oviedo, Gijon (Spain)
2015-10-15
Highlights: • A parametric submodel of the spot under study is developed. • The associated macro has the capability to successively re-build the submodel implementing the crack with the geometry of the updated crack front as a function of the predicted increments of length in the apexes of the crack from the calculated stress intensity factor at the crack front. • The analysis incorporates the crack behavior model to predict the evolution of the postulated defect under the application of the different transients. • The analysis is based on the Elasto-Plastic Fracture Mechanics (EPFM) theory to account for the ductility of the materials (316LN type stainless steel). - Abstract: This paper demonstrates structural integrity of the first confinement boundary in Generic Upper Port Plug structures against cracking during service. This constitutes part of the justification to demonstrate that the non-aggression to the confinement barrier requirement may be compatible with the absent of a specific in-service inspections (ISI) program in the trapezoidal section. Since the component will be subjected to 100% volumetric inspections it can be assumed that no defects below the threshold of applied Nondestructive Evaluation techniques will be present before its commissioning. Cracks during service would be associated to defects under Code acceptance limit. This limit can be reasonably taken as 2 mm. Using elastic–plastic fracture mechanics an initial defect is postulated at the worst location in terms of probability and impact on the confinement boundary. Its evolution is simulated through finite element analysis and final dimension at the end of service is estimated. Applying the procedures in RCC-MR 2007 (App-16) the stability of the crack is assessed. As relative high safety margin was achieved, a complementary assessment postulating an initial defect of 6 mm was also conducted. New margin calculated provides a more robust design.
Yan, Zhenya
2017-05-01
We extend the idea of the Fokas unified transform to investigate the initial-boundary value problem for the integrable spin-1 Gross-Pitaevskii equations with a 4 × 4 Lax pair on the half-line. The solution of this system can be expressed in terms of the solution of a 4 × 4 matrix Riemann-Hilbert (RH) problem formulated in the complex k-plane. The relevant jump matrices of the RH problem can be explicitly found using the two spectral functions s(k) and S(k), which can be defined by the initial data, the Dirichlet-Neumann boundary data at x = 0. The global relation is established between the two dependent spectral functions. The general mappings between Dirichlet and Neumann boundary values are analyzed in terms of the global relation. These results may be of the potential significance in both spinor Bose-Einstein condensates and the theory of multi-component integrable systems.
One-dimensional Galerkin methods and superconvergence at interior nodal points
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
Discontinuous Galerkin finite element method for shallow two-phase flows
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
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
Simplified Discontinuous Galerkin Methods for Systems of Conservation Laws with Convex Extension
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.
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
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
A coupled electro-thermal Discontinuous Galerkin method
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.
Discontinuous Galerkin flood model formulation: Luxury or necessity?
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.
Shobeiri, Vahid
2016-03-01
In this article, the bi-directional evolutionary structural optimization (BESO) method based on the element-free Galerkin (EFG) method is presented for topology optimization of continuum structures. The mathematical formulation of the topology optimization is developed considering the nodal strain energy as the design variable and the minimization of compliance as the objective function. The EFG method is used to derive the shape functions using the moving least squares approximation. The essential boundary conditions are enforced by the method of Lagrange multipliers. Several topology optimization problems are presented to show the effectiveness of the proposed method. Many issues related to topology optimization of continuum structures, such as chequerboard patterns and mesh dependency, are studied in the examples.
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.
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.
Li, Ping
2018-04-13
It is well known that graphene demonstrates spatial dispersion properties, i.e., its conductivity is nonlocal and a function of spectral wave number (momentum operator) q. In this paper, to account for effects of spatial dispersion on transmission of high speed signals along graphene nano-ribbon (GNR) interconnects, a discontinuous Galerkin time-domain (DGTD) algorithm is proposed. The atomically-thick GNR is modeled using a nonlocal transparent surface impedance boundary condition (SIBC) incorporated into the DGTD scheme. Since the conductivity is a complicated function of q (and one cannot find an analytical Fourier transform pair between q and spatial differential operators), an exact time domain SIBC model cannot be derived. To overcome this problem, the conductivity is approximated by its Taylor series in spectral domain under low-q assumption. This approach permits expressing the time domain SIBC in the form of a second-order partial differential equation (PDE) in current density and electric field intensity. To permit easy incorporation of this PDE with the DGTD algorithm, three auxiliary variables, which degenerate the second-order (temporal and spatial) differential operators to first-order ones, are introduced. Regarding to the temporal dispersion effects, the auxiliary differential equation (ADE) method is utilized to eliminates the expensive temporal convolutions. To demonstrate the applicability of the proposed scheme, numerical results, which involve characterization of spatial dispersion effects on the transfer impedance matrix of GNR interconnects, are presented.
A stochastic Galerkin method for the Euler equations with Roe variable transformation
Pettersson, Per
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.
Robust and Accurate Shock Capturing Method for High-Order Discontinuous Galerkin Methods
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.
Terraneo, Tullia Isotta
2015-12-01
In the present study the species boundaries of the scleractinian coral genus Goniopora from the Saudi Arabian Red Sea were investigated. An integrated morpho-molecular approach was used to better clarify the complex scenario derived from traditional classification efforts based on skeletal morphology. Traditional taxonomy of this genus considers skeletal morphology first and polyp morphology as a secondary discriminating character. This leads to potential complication due to plasticity in skeletal features within a species. To address this issue, molecular analyses of evolutionary relationships between nine traditional morphospecies of Goniopora from the Red Sea were performed and were used to re-evaluate the informativeness of macromorphological and micromorphological features. Between four and six putative molecular lineages were identified within Goniopora samples from the Saudi Arabian Red Sea on the basis of four molecular markers: the mitochondrial intergenic spacer between Cytochrome b and the NADH dehydrogenase subunit 2, the entire nuclear ribosomal internal transcribed spacer region, the ATP synthase subunit β gene, and a portion of the Calmodulin gene. The results were strongly corroborated by three distinct analyses of species delimitation. Subsequent analyses of micromorphological and microstructural skeletal features identified the presence of distinctive characters in each of the molecular clades. Unique in vivo morphologies were associated with the genetic-delimited lineages, further supporting the molecular findings. The proposed re-organization of Goniopora will resolve several taxonomic problems in this genus while reconciling molecular and morphological evidence. Reliable species-level identification of Goniopora spp. can be achieved with polyp morphology under the proposed revision.
LATORTUE, Xavier; MINEL, Stephanie; POMPIDOU, Stéphane; PERRY, Nicolas
2015-01-01
Participatory design is perceived as a way of improvement in both manufactured and building design. Nonetheless high level of user involvement has its limits. Part of the difficulties of the participatory design is due to the tacit nature of conventions that are shared between professionals. Boundary objects are described as an interesting tool to bridge those boundaries and should be investigated in the context of participatory design in building projects.
Multimode Analysis of the Dynamics and Integrity of Electrically Actuated MEMS Resonators
Directory of Open Access Journals (Sweden)
Serge Bruno Yamgoué
2014-01-01
technique to reduce the partial integro-differential equation governing the dynamics of the microbeam to a system of coupled ordinary differential equations which describe the interactions of the linear mode shapes of the microbeam. Analytical solutions are derived and their stability is studied for the simplest reduced-order model which takes into account only the first linear mode in the Galerkin procedure. We further investigate the influence of the first few higher modes on the Galerkin procedure, and hence its convergence, by analysing the boundaries between pull-in and pull-in-free vibrations domains in the space of actuation parameters. These are determined for the various multimode combinations using direct numerical time integration. Our results show that unsafe domains form V-like shapes for actuation frequencies close to the superharmonic, fundamental, and subharmonic resonances. They also reveal that the single first-mode reduced model usually considered underestimates the left branches and overestimates the right branches of these boundaries.
Discontinuous Galerkin Methods for NonLinear Differential Systems
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.
A zonal Galerkin-free POD model for incompressible flows
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.
Finite element and discontinuous Galerkin methods for transient wave equations
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 ...
A Resistive Boundary Condition Enhanced DGTD Scheme for the Transient Analysis of Graphene
Li, Ping
2015-04-24
In this paper, the electromagnetic (EM) features of graphene are characterized by a discontinuous Galerkin timedomain (DGTD) algorithm with a resistive boundary condition (RBC). The atomically thick graphene is equivalently modeled using a RBC by regarding the graphene as an infinitesimally thin conductive sheet. To incorporate RBC into the DGTD analysis, the surface conductivity of the graphene composed of contributions from both intraband and interband terms is firstly approximated by rational basis functions using the fastrelaxation vector-fitting (FRVF) method in the Laplace-domain. Next, through the inverse Laplace transform, the corresponding time-domain matrix equations in integral can be obtained. Finally, these matrix equations are solved by time-domain finite integral technique (FIT). For elements not touching the graphene sheet, however, the well-known Runge-Kutta (RK) method is employed to solve the two first-order time-derivative Maxwell’s equations. The application of the surface boundary condition significantly alleviates the memory consuming and the limitation of time step size required by Courant-Friedrichs-Lewy (CFL) condition. To validate the proposed algorithm, various numerical examples are presented and compared with available references.
Implementation of the entropy viscosity method with the discontinuous Galerkin method
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.
Directory of Open Access Journals (Sweden)
GIULIO PAVIA
2004-03-01
Full Text Available This paper deals with a definition of the lower boundary stratotype of the Tithonian Stage in the Upper Jurassic succession of Monte Inici, Western Sicily. The upper member of the Rosso Ammonitico Fm. is 27 m thick and shows a typical nodular-calcareous lithofacies; its lower beds have been sampled for biostratigraphic and paleomagnetic purposes. Though the succession is affected by high stratigraphic condensation, the resulting hiatuses have been shown to be below biochronological resolution and thus do not hinder any biostratigraphic definition. The biostratigraphic analysis has been based on the rich ammonite assemblages in which the common genus Hybonoticeras is the index-key for characterizing the Kimmeridgian-Tithonian boundary. Four ammonite biozones have been identified; the basal Tithonian one is defined by the assemblage of Hybonoticeras gr. hybonotum and Haploceras staszycii. The recorded calcareous nannofossil bioevents allow recognition of the V. stradneri and C. mexicana Zones, whose boundary is located a little below the identified Tithonian lower boundary. The paleomagnetic record shows normal polarity in the S. darwini/V. albertinum Zone and mainly reverse polarity in the H. beckeri and H. hybonotum Zones, with three minor normal polarity intervals; the lower boundary of the Tithonian falls in the oldest of these intervals. The integrated multidisciplinary stratigraphic information gathered from the Contrada Fornazzo section defines the lower boundary of the H. hybonotum Zone at the base of Bed 110, and supplies elements of chrono-correlation sufficient to regard this section as a possible G.S.S.P. of the Tithonian Stage.
Adaptive Wavelet Galerkin Methods on Distorted Domains: Setup of the Algebraic System
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
Yang, Tung-Mou
2011-01-01
Information sharing and integration has long been considered an important approach for increasing organizational efficiency and performance. With advancements in information and communication technologies, sharing and integrating information across organizations becomes more attractive and practical to organizations. However, achieving…
Mark D. Nelson; W. Keith Moser
2007-01-01
The USDA Forest Service's Forest Inventory and Analysis (FIA) program conducts strategic inventories of our Nation's forest resources. There is increasing need to assess effects of forest disturbance from catastrophic events, often within geographic extents not typically addressed by strategic forest inventories. One such event occurred within the Boundary...
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...
International Nuclear Information System (INIS)
Mello, Kelen Berra de
2005-02-01
In this work is shown the solution of the advection-diffusion equation to simulate a pollutant dispersion in the Planetary Boundary Layer. The solution is obtained through of the GILTT (Generalized Integral Laplace Transform Technique) analytic method and of the numerical inversion Gauss Quadrature. The validity of the solution is proved using concentration obtained from the model with concentration obtained for Copenhagen experiment. In this comparison was utilized potential and logarithmic wind profile and eddy diffusivity derived by Degrazia et al (1997) [17] and (2002) [19]. The best results was using the potential wind profile and the eddy diffusivity derived by Degrazia et al (1997). The vertical velocity influence is shown in the plume behavior of the pollutant concentration. Moreover, the vertical and longitudinal velocity provided by Large Eddy Simulation (LES) was stood in the model to simulate the turbulent boundary layer more realistic, the result was satisfactory when compared with contained in the literature. (author)
Wavelet-based regularization of the Galerkin truncated three-dimensional incompressible Euler flows.
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.
Local bounds preserving stabilization for continuous Galerkin discretization of hyperbolic systems
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.
CosmosDG: An hp -adaptive Discontinuous Galerkin Code for Hyper-resolved Relativistic MHD
Energy Technology Data Exchange (ETDEWEB)
Anninos, Peter; Lau, Cheuk [Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, CA 94550 (United States); Bryant, Colton [Department of Engineering Sciences and Applied Mathematics, Northwestern University, 2145 Sheridan Road, Evanston, Illinois, 60208 (United States); Fragile, P. Chris [Department of Physics and Astronomy, College of Charleston, 66 George Street, Charleston, SC 29424 (United States); Holgado, A. Miguel [Department of Astronomy and National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign, Urbana, Illinois, 61801 (United States); Nemergut, Daniel [Operations and Engineering Division, Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218 (United States)
2017-08-01
We have extended Cosmos++, a multidimensional unstructured adaptive mesh code for solving the covariant Newtonian and general relativistic radiation magnetohydrodynamic (MHD) equations, to accommodate both discrete finite volume and arbitrarily high-order finite element structures. The new finite element implementation, called CosmosDG, is based on a discontinuous Galerkin (DG) formulation, using both entropy-based artificial viscosity and slope limiting procedures for the regularization of shocks. High-order multistage forward Euler and strong-stability preserving Runge–Kutta time integration options complement high-order spatial discretization. We have also added flexibility in the code infrastructure allowing for both adaptive mesh and adaptive basis order refinement to be performed separately or simultaneously in a local (cell-by-cell) manner. We discuss in this report the DG formulation and present tests demonstrating the robustness, accuracy, and convergence of our numerical methods applied to special and general relativistic MHD, although we note that an equivalent capability currently also exists in CosmosDG for Newtonian systems.
CosmosDG: An hp-adaptive Discontinuous Galerkin Code for Hyper-resolved Relativistic MHD
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Pereira, Luis Carlos Martins
1998-06-15
New Petrov-Galerkin formulations on the finite element methods for convection-diffusion problems with boundary layers are presented. Such formulations are based on a consistent new theory on discontinuous finite element methods. Existence and uniqueness of solutions for these problems in the new finite element spaces are demonstrated. Some numerical experiments shows how the new formulation operate and also their efficacy. (author)
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.
A Meshless Local Petrov-Galerkin Shepard and Least-Squares Method Based on Duo Nodal Supports
Directory of Open Access Journals (Sweden)
Xiaoying Zhuang
2014-01-01
Full Text Available The meshless Shepard and least-squares (MSLS interpolation is a newly developed partition of unity- (PU- based method which removes the difficulties with many other meshless methods such as the lack of the Kronecker delta property. The MSLS interpolation is efficient to compute and retain compatibility for any basis function used. In this paper, we extend the MSLS interpolation to the local Petrov-Galerkin weak form and adopt the duo nodal support domain. In the new formulation, there is no need for employing singular weight functions as is required in the original MSLS and also no need for background mesh for integration. Numerical examples demonstrate the effectiveness and robustness of the present method.
Directory of Open Access Journals (Sweden)
Xinming Zhang
2009-01-01
Full Text Available A wavelet Galerkin finite-element method is proposed by combining the wavelet analysis with traditional finite-element method to analyze wave propagation phenomena in fluid-saturated porous medium. The scaling functions of Daubechies wavelets are considered as the interpolation basis functions to replace the polynomial functions, and then the wavelet element is constructed. In order to overcome the integral difficulty for lacking of the explicit expression for the Daubechies wavelets, a kind of characteristic function is introduced. The recursive expression of calculating the function values of Daubechies wavelets on the fraction nodes is deduced, and the rapid wavelet transform between the wavelet coefficient space and the wave field displacement space is constructed. The results of numerical simulation demonstrate that the method is effective.
Tuma, Julio R
2011-12-01
The intersection of ELSI and science forms a complicated nexus yet their integration is an important goal both for society and for the successful advancement of science. In what follows, I present a heuristic that makes boundary identification and crossing an important tool in the discovery of potential areas of ethical, legal, and social concern in science. A dynamic and iterative application of the heuristic can lead towards a fuller integration and appreciation of the concerns of ELSI and of science from both sides of the divide.
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.
Adaptive stochastic Galerkin FEM with hierarchical tensor representations
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.
ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics
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.
Very high order discontinuous Galerkin method in elliptic problems
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.
Suryantini; Rachmawati, C.; Abdurrahman, M.
2017-12-01
Patuha Geothermal System is a volcanic hydrothermal system. In this type of system, the boundary of the system is often determined by low resistivity (10 ohm.m) anomaly from Magnetotelluric (MT) or DC-Resistivity survey. On the contrary, during geothermal exploration, the system boundary often need to be determined as early as possible even prior of resistivity data available. Thus, a method that use early stage survey data must be developed properly to reduce the uncertainty of the geothermal area extent delineation at the time the geophysical data unavailable. Geological field mapping, volcanostratigraphy analysis and fluid chemistry of thermal water and cold water are the data available at the early stage of exploration. This study integrates this data to delineate the geothermal system boundary. The geological mapping and volcanostratigraphy are constructed to limit the extent of thermal and cold springs. It results that springs in the study area are controlled hydrologically by topography of Patuha Volcanic Crown (complex) or so called PVC, the current geothermal field and Masigit Volcanic Crown (complex) or so called MVC, the dormant volcano not associated with active geothermal system. Some of the cold springs at PVC are contaminated by subsurface steam heated outflow while others are not contaminated. The contaminated cold springs have several characteristics such as higher water temperature than ambient temperature at the time it was measured, higher total disolved solid (TDS), and lower pH. The soluble elements analysis support the early contamination indication by showing higher cation and anion, and positive oxygen shifting of stable isotope of these cool springs. Where as the uncontaminated spring shows similar characteristic with cool springs occur at MVC. The boundary of the system is delineated by an arbitrary line drawn between distal thermal springs from the upflow or contaminated cool springs with the cool uncontaminated springs. This boundary is
Tinto, K. J.; Siddoway, C. S.; Bell, R. E.; Lockett, A.; Wilner, J.
2017-12-01
Now submerged within marine plateaus and rises bordering Antarctica, Australia and Zealandia, the East Gondwana accretionary margin was a belt of terranes and stitched by magmatic arcs, later stretched into continental ribbons separated by narrow elongate rifts. This crustal architecture is known from marine geophysical exploration and ocean drilling of the mid-latitude coastal plateaus and rises. A concealed sector of the former East Gondwana margin that underlies the Ross Ice Shelf (RIS), Antarctica, is the focus of ROSETTA-ICE, a new airborne data acquisition campaign that explores the crustal makeup, tectonic boundaries and seafloor bathymetry beneath RIS. Gravimeters and a magnetometer are deployed by LC130 aircraft surveying along E-W lines spaced at 10 km, and N-S tie lines at 55 km, connect 1970s points (RIGGS) for controls on ocean depth and gravity. The ROSETTA-ICE survey, 2/3 completed thus far, provides magnetic anomalies, Werner depth-to-basement solutions, a new gravity-based bathymetric model at 20-km resolution, and a new crustal density map tied to the 1970s data. Surprisingly, the data reveal that the major lithospheric boundary separating East and West Antarctica lies 300 km east of the Transantarctic Mountains, beneath the floating RIS. The East and West regions have contrasting geophysical characteristics and bathymetry, with relatively dense lithosphere, low amplitude magnetic anomalies, and deep bathymetry on the East Antarctica side, and high amplitude magnetic anomalies, lower overall density and shallower water depths on the West Antarctic side. The Central High, a basement structure cored at DSDP Site 270 and seismically imaged in the Ross Sea, continues beneath RIS as a faulted but coherent crustal ribbon coincident with the tectonic boundary. The continuity of Gondwana margin crustal architecture discovered beneath the West Antarctic Ice Sheet requires a revision of the existing tectonic framework. The sub-RIS narrow rift basins and
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
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.
Shapkalijevski, Metodija M.; Ouwersloot, Huug G.; Moene, Arnold F.; Vilà-Guerau de Arrellano, Jordi
2017-02-01
By characterizing the dynamics of a convective boundary layer above a relatively sparse and uniform orchard canopy, we investigated the impact of the roughness-sublayer (RSL) representation on the predicted diurnal variability of surface fluxes and state variables. Our approach combined numerical experiments, using an atmospheric mixed-layer model including a land-surface-vegetation representation, and measurements from the Canopy Horizontal Array Turbulence Study (CHATS) field experiment near Dixon, California. The RSL is parameterized using an additional factor in the standard Monin-Obukhov similarity theory flux-profile relationships that takes into account the canopy influence on the atmospheric flow. We selected a representative case characterized by southerly wind conditions to ensure well-developed RSL over the orchard canopy. We then investigated the sensitivity of the diurnal variability of the boundary-layer dynamics to the changes in the RSL key scales, the canopy adjustment length scale, Lc, and the β = u*/|U| ratio at the top of the canopy due to their stability and dependence on canopy structure. We found that the inclusion of the RSL parameterization resulted in improved prediction of the diurnal evolution of the near-surface mean quantities (e.g. up to 50 % for the wind velocity) and transfer (drag) coefficients. We found relatively insignificant effects on the modelled surface fluxes (e.g. up to 5 % for the friction velocity, while 3 % for the sensible and latent heat), which is due to the compensating effect between the mean gradients and the drag coefficients, both of which are largely affected by the RSL parameterization. When varying Lc (from 10 to 20 m) and β (from 0.25 to 0.4 m), based on observational evidence, the predicted friction velocity is found to vary by up to 25 % and the modelled surface-energy fluxes (sensible heat, SH, and latent heat of evaporation, LE) vary up to 2 and 9 %. Consequently, the boundary-layer height varies up to
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...
Super-convergence of Discontinuous Galerkin Method Applied to the Navier-Stokes Equations
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.
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.
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.
Analysis of circular fibers with an arbitrary index profile by the Galerkin method.
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.
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
International Nuclear Information System (INIS)
Obradovic, D.
1970-04-01
In the study of the nuclear reactors space-time behaviour the modal analysis is very often used though some basic mathematical problems connected with application of this methods are still unsolved. In this paper the modal analysis is identified as a set of the methods in the mathematical literature known as the Galerkin methods (or projection methods, or sometimes direct methods). Using the results of the mathematical investigations of these methods the applicability of the Galerkin type methods to the calculations of the eigenvalue and eigenvectors of the stationary and non-stationary diffusion operator, as well as for the solutions of the corresponding functional equations, is established (author)
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.
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.
Directory of Open Access Journals (Sweden)
Jelena Ačanski
2016-10-01
Full Text Available Several recent studies have detected and described complexes of cryptic and sibling species in the genus Merodon (Diptera, Syrphidae. One representative of these complexes is the Merodon avidus complex that contains four sibling species, which have proven difficult to distinguish using traditional morphological characters. In the present study, we use two geometric morphometric approaches, as well as molecular characters of the 5’-end of the mtDNA COI gene, to delimit sibling taxa. Analyses based on these data were used to strengthen species boundaries within the complex, and to validate the status of a previously-recognized cryptic taxon from Lesvos Island (Greece, here described as Merodon megavidus Vujić & Radenković sp. nov. Geometric morphometric results of both wing and surstylus shape confirm the present classification for three sibling species－M. avidus (Rossi, 1790, M. moenium Wiedemann in Meigen, 1822 and M. ibericus Vujić, 2015－and, importantly, clearly discriminate the newly-described taxon Merodon megavidus sp. nov. In addition to our geometric morphometric results, supporting characters were obtained from molecular analyses of mtDNA COI sequences, which clearly differentiated M. megavidus sp. nov. from the other members of the M. avidus complex. Molecular analyses revealed that the earliest divergence of M. ibericus occurred around 800 ky BP, while the most recent separation happened between M. avidus and M. moenium around 87 ky BP.
International Nuclear Information System (INIS)
Wang, J; Song, J; Gao, M; Zhu, L
2014-01-01
The trans-boundary area between Northern China, Mongolia and eastern Siberia of Russia is a continuous geographical area located in north eastern Asia. Many common issues in this region need to be addressed based on a uniform resources and environmental data warehouse. Based on the practice of joint scientific expedition, the paper presented a data integration solution including 3 steps, i.e., data collection standards and specifications making, data reorganization and process, data warehouse design and development. A series of data collection standards and specifications were drawn up firstly covering more than 10 domains. According to the uniform standard, 20 resources and environmental survey databases in regional scale, and 11 in-situ observation databases were reorganized and integrated. North East Asia Resources and Environmental Data Warehouse was designed, which included 4 layers, i.e., resources layer, core business logic layer, internet interoperation layer, and web portal layer. The data warehouse prototype was developed and deployed initially. All the integrated data in this area can be accessed online
Wang, J.; Song, J.; Gao, M.; Zhu, L.
2014-02-01
The trans-boundary area between Northern China, Mongolia and eastern Siberia of Russia is a continuous geographical area located in north eastern Asia. Many common issues in this region need to be addressed based on a uniform resources and environmental data warehouse. Based on the practice of joint scientific expedition, the paper presented a data integration solution including 3 steps, i.e., data collection standards and specifications making, data reorganization and process, data warehouse design and development. A series of data collection standards and specifications were drawn up firstly covering more than 10 domains. According to the uniform standard, 20 resources and environmental survey databases in regional scale, and 11 in-situ observation databases were reorganized and integrated. North East Asia Resources and Environmental Data Warehouse was designed, which included 4 layers, i.e., resources layer, core business logic layer, internet interoperation layer, and web portal layer. The data warehouse prototype was developed and deployed initially. All the integrated data in this area can be accessed online.
Directory of Open Access Journals (Sweden)
Aimé Lachal
2011-01-01
Full Text Available Let ((∈[0,1] be the linear Brownian motion and ((∈[0,1] the (−1-fold integral of Brownian motion, with being a positive integer: ∫(=0((−−1/(−1!d( for any ∈[0,1]. In this paper we construct several bridges between times 0 and 1 of the process ((∈[0,1] involving conditions on the successive derivatives of at times 0 and 1. For this family of bridges, we make a correspondence with certain boundary value problems related to the one-dimensional polyharmonic operator. We also study the classical problem of prediction. Our results involve various Hermite interpolation polynomials.
Vragov’s boundary value problem for an implicit equation of mixed type
Egorov, I. E.
2017-10-01
We study a Vragov boundary value problem for a third-order implicit equation of mixed type with an arbitrary manifold of type switch. These Sobolev-type equations arise in many important applied problems. Given certain constraints on the coefficients and the right-hand side of the equation, we demonstrate, using nonstationary Galerkin method and regularization method, the unique regular solvability of the boundary value problem. We also obtain an error estimate for approximate solutions of the boundary value problem in terms of the regularization parameter and the eigenvalues of the Dirichlet spectral problem for the Laplace operator.
Goswami, Deepjyoti
2011-09-01
In this article, we propose and analyze an alternate proof of a priori error estimates for semidiscrete Galerkin approximations to a general second order linear parabolic initial and boundary value problem with rough initial data. Our analysis is based on energy arguments without using parabolic duality. Further, it follows the spirit of the proof technique used for deriving optimal error estimates for finite element approximations to parabolic problems with smooth initial data and hence, it unifies both theories, that is, one for smooth initial data and other for nonsmooth data. Moreover, the proposed technique is also extended to a semidiscrete mixed method for linear parabolic problems. In both cases, optimal L2-error estimates are derived, when the initial data is in L2. A superconvergence phenomenon is also observed, which is then used to prove L∞-estimates for linear parabolic problems defined on two-dimensional spatial domain again with rough initial data. Copyright © Taylor & Francis Group, LLC.
Tsalamengas, John L.
2016-11-01
We present Gauss-Jacobi quadrature rules in terms of hypergeometric functions for the discretization of weakly singular, strongly singular, hypersingular, and nearly singular integrals that arise in integral equation formulations of potential problems for domains with sharp edges and corners. The rules are tailored to weight functions with algebraic endpoint singularities of a fairly general form, thus allowing one to easily incorporate a wide class of domains into the analysis. Numerical examples illustrate the accuracy and stability of the proposed algorithms; it is shown that the same level of high accuracy can be achieved for any choice of the external variable. The usefulness of the method is exemplified by application to the solution of a singular integral equation that arises in time-harmonic electromagnetic scattering by either closed or open perfectly conducting cylindrical objects with edges and corners, such as polygon cylinders and bent strips. Some practical aspects concerning the role of nearby singularities in achieving a highly accurate solution of singular integral equations are, also, discussed.
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
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.
Discontinuous Galerkin finite element methods for (non)conservative partial differential equations
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
Space-time discontinuous Galerkin method for parabolic problems in time-dependent domains
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
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.
Two fluid space-time discontinuous Galerkin finite element method. Part II: Applications
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 -
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
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
Discontinuous Galerkin Approximations for Computing Electromagnetic Bloch Modes in Photonic Crystals
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
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.
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
MHD boundary layer flow and heat transfer in an inclined porous square cavity filled with nanofluids
Chandra Shekar Balla; Naikoti Kishan; Rama S.R. Gorla; B.J. Gireesha
2017-01-01
The present paper deals with the magnetohydrodynamic boundary layer flow of a free convection heat transfer in an inclined square cavity filled with nanofluid-saturated porous medium. The effects of different nanoparticles Cu, Al2O3, TiO2 and SiO2 are considered. The top and bottom horizontal walls of cavity are considered adiabatic, while the vertical walls are kept at constant temperatures. The governing partial differential equations are solved by finite element method of Galerkin weighted...
Sava, E.; Cervone, G.; Kalyanapu, A. J.; Sampson, K. M.
2017-12-01
The increasing trend in flooding events, paired with rapid urbanization and an aging infrastructure is projected to enhance the risk of catastrophic losses and increase the frequency of both flash and large area floods. During such events, it is critical for decision makers and emergency responders to have access to timely actionable knowledge regarding preparedness, emergency response, and recovery before, during and after a disaster. Large volumes of data sets derived from sophisticated sensors, mobile phones, and social media feeds are increasingly being used to improve citizen services and provide clues to the best way to respond to emergencies through the use of visualization and GIS mapping. Such data, coupled with recent advancements in data fusion techniques of remote sensing with near real time heterogeneous datasets have allowed decision makers to more efficiently extract precise and relevant knowledge and better understand how damage caused by disasters have real time effects on urban population. This research assesses the feasibility of integrating multiple sources of contributed data into hydrodynamic models for flood inundation simulation and estimating damage assessment. It integrates multiple sources of high-resolution physiographic data such as satellite remote sensing imagery coupled with non-authoritative data such as Civil Air Patrol (CAP) and `during-event' social media observations of flood inundation in order to improve the identification of flood mapping. The goal is to augment remote sensing imagery with new open-source datasets to generate flood extend maps at higher temporal and spatial resolution. The proposed methodology is applied on two test cases, relative to the 2013 Boulder Colorado flood and the 2015 floods in Texas.
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.
Boyce, E. S.; Bierma, R. M.; Willoughby, H.; Feaux, K.; Mattioli, G. S.; Enders, M.; Busby, R. W.
2014-12-01
EarthScope's geodetic component in Alaska, the UNAVCO-operated Plate Boundary Observatory (PBO) network, includes 139 continuous GPS sites and 41 supporting telemetry relays. These are spread across a vast area, from northern AK to the Aleutians. Forty-five of these stations were installed or have been upgraded in cooperation with various partner agencies and currently provide data collection and transmission for more than one group. Leveraging existing infrastructure normally has multiple benefits, such as easier permitting requirements and costs savings through reduced overall construction and maintenance expenses. At some sites, PBO-AK power and communications systems have additional capacity beyond that which is needed for reliable acquisition of GPS data. Where permits allow, such stations could serve as platforms for additional instrumentation or real-time observing needs. With the expansion of the Transportable Array (TA) into Alaska, there is increased interest to leverage existing EarthScope resources for station co-location and telemetry integration. Because of the complexity and difficulty of long-term O&M at PBO sites, however, actual integration of GPS and seismic equipment must be considered on a case-by-case basis. UNAVCO currently operates two integrated GPS/seismic stations in collaboration with the Alaska Earthquake Center, and three with the Alaska Volcano Observatory. By the end of 2014, PBO and TA plan to install another four integrated and/or co-located geodetic and seismic systems. While three of these are designed around existing PBO stations, one will be a completely new TA installation, providing PBO with an opportunity to expand geodetic data collection in Alaska within the limited operations and maintenance phase of the project. We will present some of the design considerations, outcomes, and lessons learned from past and ongoing projects to integrate seismometers and other instrumentation at PBO-Alaska stations. Developing the PBO
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.
Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.
2015-01-01
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.
Entropy Stable Wall Boundary Conditions for the Compressible Navier-Stokes Equations
Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.
2014-01-01
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite volume, finite difference, discontinuous Galerkin, and flux reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.
DEFF Research Database (Denmark)
Zølner, Mette
The paper explores how locals span boundaries between corporate and local levels. The aim is to better comprehend potentialities and challenges when MNCs draws on locals’ culture specific knowledge. The study is based on an in-depth, interpretive case study of boundary spanning by local actors in...... approach with pattern matching is a way to shed light on the tacit local knowledge that organizational actors cannot articulate and that an exclusively inductive research is not likely to unveil....
Davarzani, Hossein; Smits, Kathleen; Tolene, Ryan M; Illangasekare, Tissa
2014-01-01
In an effort to develop methods based on integrating the subsurface to the atmospheric boundary layer to estimate evaporation, we developed a model based on the coupling of Navier-Stokes free flow and Darcy flow in porous medium. The model was tested using experimental data to study the effect of wind speed on evaporation. The model consists of the coupled equations of mass conservation for two-phase flow in porous medium with single-phase flow in the free-flow domain under nonisothermal, nonequilibrium phase change conditions. In this model, the evaporation rate and soil surface temperature and relative humidity at the interface come directly from the integrated model output. To experimentally validate numerical results, we developed a unique test system consisting of a wind tunnel interfaced with a soil tank instrumented with a network of sensors to measure soil-water variables. Results demonstrated that, by using this coupling approach, it is possible to predict the different stages of the drying process with good accuracy. Increasing the wind speed increases the first stage evaporation rate and decreases the transition time between two evaporative stages (soil water flow to vapor diffusion controlled) at low velocity values; then, at high wind speeds the evaporation rate becomes less dependent on the wind speed. On the contrary, the impact of wind speed on second stage evaporation (diffusion-dominant stage) is not significant. We found that the thermal and solute dispersion in free-flow systems has a significant influence on drying processes from porous media and should be taken into account. PMID:25309005
Davarzani, Hossein; Smits, Kathleen; Tolene, Ryan M; Illangasekare, Tissa
2014-01-01
In an effort to develop methods based on integrating the subsurface to the atmospheric boundary layer to estimate evaporation, we developed a model based on the coupling of Navier-Stokes free flow and Darcy flow in porous medium. The model was tested using experimental data to study the effect of wind speed on evaporation. The model consists of the coupled equations of mass conservation for two-phase flow in porous medium with single-phase flow in the free-flow domain under nonisothermal, nonequilibrium phase change conditions. In this model, the evaporation rate and soil surface temperature and relative humidity at the interface come directly from the integrated model output. To experimentally validate numerical results, we developed a unique test system consisting of a wind tunnel interfaced with a soil tank instrumented with a network of sensors to measure soil-water variables. Results demonstrated that, by using this coupling approach, it is possible to predict the different stages of the drying process with good accuracy. Increasing the wind speed increases the first stage evaporation rate and decreases the transition time between two evaporative stages (soil water flow to vapor diffusion controlled) at low velocity values; then, at high wind speeds the evaporation rate becomes less dependent on the wind speed. On the contrary, the impact of wind speed on second stage evaporation (diffusion-dominant stage) is not significant. We found that the thermal and solute dispersion in free-flow systems has a significant influence on drying processes from porous media and should be taken into account.
A new operational matrix of fractional order integration for the ...
Indian Academy of Sciences (India)
M H HEYDARI
2018-04-24
Apr 24, 2018 ... By using the CWs and their operational matrix of fractional order integration and Galerkin method, the ... tional order integration for the Haar wavelets [36], Legendre wavelets [23–25,29,30,47] and the ... the resulting approximation is continuous and can not properly model the discontinuities. In remote ...
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
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.
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.
A subgrid viscosity Lagrance-Galerkin method for convection-diffusion problems
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...
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.
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
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.
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.
Development of Galerkin Method for Solving the Generalized Burger's-Huxley Equation
Directory of Open Access Journals (Sweden)
M. El-Kady
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.
Gerbi, Stéphane
2013-01-15
The goal of this work is to study a model of the wave equation with dynamic boundary conditions and a viscoelastic term. First, applying the Faedo-Galerkin method combined with the fixed point theorem, we show the existence and uniqueness of a local in time solution. Second, we show that under some restrictions on the initial data, the solution continues to exist globally in time. On the other hand, if the interior source dominates the boundary damping, then the solution is unbounded and grows as an exponential function. In addition, in the absence of the strong damping, then the solution ceases to exist and blows up in finite time.
Directory of Open Access Journals (Sweden)
Ilaria Iaconeta
2017-09-01
Full Text Available The simulation of large deformation problems, involving complex history-dependent constitutive laws, is of paramount importance in several engineering fields. Particular attention has to be paid to the choice of a suitable numerical technique such that reliable results can be obtained. In this paper, a Material Point Method (MPM and a Galerkin Meshfree Method (GMM are presented and verified against classical benchmarks in solid mechanics. The aim is to demonstrate the good behavior of the methods in the simulation of cohesive-frictional materials, both in static and dynamic regimes and in problems dealing with large deformations. The vast majority of MPM techniques in the literatrue are based on some sort of explicit time integration. The techniques proposed in the current work, on the contrary, are based on implicit approaches, which can also be easily adapted to the simulation of static cases. The two methods are presented so as to highlight the similarities to rather than the differences from “standard” Updated Lagrangian (UL approaches commonly employed by the Finite Elements (FE community. Although both methods are able to give a good prediction, it is observed that, under very large deformation of the medium, GMM lacks robustness due to its meshfree natrue, which makes the definition of the meshless shape functions more difficult and expensive than in MPM. On the other hand, the mesh-based MPM is demonstrated to be more robust and reliable for extremely large deformation cases.
SpECTRE: A task-based discontinuous Galerkin code for relativistic astrophysics
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.
DEFF Research Database (Denmark)
Neergaard, Ulla; Nielsen, Ruth
2010-01-01
of welfare functions into EU law both from an internal market law and a constitutional law perspective. The main problem areas covered by the Blurring Boundaries project were studied in sub-projects on: 1) Internal market law and welfare services; 2) Fundamental rights and non-discrimination law aspects......; and 3) Services of general interest. In the Blurring Boundaries project, three aspects of the European Social Model have been particularly highlighted: the constitutionalisation of the European Social Model, its multi-level legal character, and the clash between market access justice at EU level...... and distributive justice at national level....
International Nuclear Information System (INIS)
Rosato, Antonio; Sibilio, Sergio; Scorpio, Michelangelo
2014-01-01
Highlights: • A building-integrated micro-cogeneration system was dynamically simulated. • Simulation data were analyzed from both environmental and economic point of views. • The proposed system was compared with a conventional supply system. • The proposed system reduces the environmental impact under heat-led operation. • The proposed system reduces the operating costs whatever the control logic is. - Abstract: This work examines the performance of a residential building-integrated micro-cogeneration system during the winter by means of a whole building simulation software. The cogeneration unit was coupled with a multi-family house composed of three floors, compliant with the transmittance values of both walls and windows suggested by the Italian Law; a stratified combined tank for both heating purposes and domestic hot water production was also used for storing heat. Simulations were performed considering the transient nature of the building and occupant driven loads as well as the part-load characteristics of the cogeneration unit. This system was described in detail and analyzed from an energy point of view in the companion paper. In this paper the simulation results were evaluated in terms of both carbon dioxide equivalent emissions and operating costs; detailed analyses were performed in order to estimate the influence of the most significant boundary conditions on both environmental and economic performance of the proposed system: in particular, three volumes of the hot water storage, four climatic zones corresponding to four Italian cities, two electric demand profiles, as well as two control strategies micro-cogeneration unit were considered. The assessment of environmental impact was performed by using the standard emission factors approach, neglecting the effects of local pollutants. The operating costs due to both natural gas and electric energy consumption were evaluated in detail, whereas both the capital and maintenance costs were
Explicit boundary form factors: The scaling Lee–Yang model
Energy Technology Data Exchange (ETDEWEB)
Hollo, L. [MTA Lendület Holographic QFT Group, Wigner Research Centre for Physics, P.O.B. 49, H-1525 Budapest 114 (Hungary); Laczko, Z.B. [Roland Eötvös University, Pázmány Péter sétány 1/A, 1117 Budapest (Hungary); Bajnok, Z. [MTA Lendület Holographic QFT Group, Wigner Research Centre for Physics, P.O.B. 49, H-1525 Budapest 114 (Hungary)
2014-09-15
We provide explicit expressions for boundary form factors in the boundary scaling Lee–Yang model for operators with the mildest ultraviolet behavior for all integrable boundary conditions. The form factors of the boundary stress tensor take a determinant form, while the form factors of the boundary primary field contain additional explicit polynomials.
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
Bridging Boundaries in Networked Military Organizations
Kleij, R. van der; Broek, J. van den; Cornelissen, M.; Essens, P.J.D.M.
2010-01-01
One of the challenges facing networked military organizations is to coordinate and integrate activities of organization components. Several studies have demonstrated the importance of boundary spanning as integrative mechanism, and, more specifically, individual communication holes within
Mirinejad, Hossein; Gaweda, Adam E; Brier, Michael E; Zurada, Jacek M; Inanc, Tamer
2017-09-01
Anemia is a common comorbidity in patients with chronic kidney disease (CKD) and is frequently associated with decreased physical component of quality of life, as well as adverse cardiovascular events. Current treatment methods for renal anemia are mostly population-based approaches treating individual patients with a one-size-fits-all model. However, FDA recommendations stipulate individualized anemia treatment with precise control of the hemoglobin concentration and minimal drug utilization. In accordance with these recommendations, this work presents an individualized drug dosing approach to anemia management by leveraging the theory of optimal control. A Multiple Receding Horizon Control (MRHC) approach based on the RBF-Galerkin optimization method is proposed for individualized anemia management in CKD patients. Recently developed by the authors, the RBF-Galerkin method uses the radial basis function approximation along with the Galerkin error projection to solve constrained optimal control problems numerically. The proposed approach is applied to generate optimal dosing recommendations for individual patients. Performance of the proposed approach (MRHC) is compared in silico to that of a population-based anemia management protocol and an individualized multiple model predictive control method for two case scenarios: hemoglobin measurement with and without observational errors. In silico comparison indicates that hemoglobin concentration with MRHC method has less variation among the methods, especially in presence of measurement errors. In addition, the average achieved hemoglobin level from the MRHC is significantly closer to the target hemoglobin than that of the other two methods, according to the analysis of variance (ANOVA) statistical test. Furthermore, drug dosages recommended by the MRHC are more stable and accurate and reach the steady-state value notably faster than those generated by the other two methods. The proposed method is highly efficient for
An HP Adaptive Discontinuous Galerkin Method for Hyperbolic Conservation Laws. Ph.D. Thesis
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.
DEFF Research Database (Denmark)
Jørgensen, Kristian Møller; Petersen, Michael Nebeling
2018-01-01
Hook-up apps such as Grindr and Scruff have become important sites for the negotiation of sex between men, in that they shape the ways intimacy cultures are practised and become visible (Mowlabocus, 2010; Race, 2014; Duguay et al., 2016). While such apps enable different intimacy cultures......, they also come paired with anxieties. In the epigraph the interview participant James1 expresses concerns about the how the hook-up app Scruff might restructure the boundaries of privacy and make him vulnerable to exposure. Such technological ambivalence is central to domestication theory, which focuses...
DEFF Research Database (Denmark)
. As a fundamental human experience, liminality transmits cultural practices, codes, rituals, and meanings in-between aggregate structures and uncertain outcomes. As a methodological tool it is well placed to overcome disciplinary boundaries, which often direct attention to specific structures or sectors of society....... Its capacity to provide explanatory accounts of seemingly unstructured situations provides an opportunity to link experience-based and culture-oriented approaches not only to contemporary problems but also to undertake comparisons across historical periods. From a perspective of liminality...
Townsend, Alan R.; Porder, Stephen
2011-03-01
What is our point of no return? Caesar proclaimed 'the die is cast' while crossing the Rubicon, but rarely does modern society find so visible a threshold in our continued degradation of ecosystems and the services they provide. Humans have always used their surroundings to make a living— sometimes successfully, sometimes not (Diamond 2005)—and we intuitively know that there are boundaries to our exploitation. But defining these boundaries has been a challenge since Malthus first prophesied that nature would limit the human population (Malthus 1798). In 2009, Rockström and colleagues tried to quantify what the 6.8 billion (and counting) of us could continue to get away with, and what we couldn't (Rockström et al 2009). In selecting ten 'planetary boundaries', the authors contend that a sustainable human enterprise requires treating a number of environmental thresholds as points of no return. They suggest we breach these Rubicons at our own peril, and that we've already crossed three: biodiversity loss, atmospheric CO2, and disruption of the global nitrogen (N) cycle. As they clearly hoped, the very act of setting targets has provoked scientific inquiry about their accuracy, and about the value of hard targets in the first place (Schlesinger 2009). Such debate is a good thing. Despite recent emphasis on the science of human-ecosystem interactions, understanding of our planetary boundaries is still in its infancy, and controversy can speed scientific progress (Engelhardt and Caplan 1987). A few weeks ago in this journal, Carpenter and Bennett (2011) took aim at one of the more controversial boundaries in the Rockström analysis: that for human alteration of the global phosphorus (P) cycle. Rockström's group chose riverine P export as the key indicator, suggesting that humans should not exceed a value that could trigger widespread marine anoxic events—and asserting that we have not yet crossed this threshold. There are defensible reasons for a marine
Numerical modelling of MPA-CVD reactors with the discontinuous Galerkin finite element method
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.
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.
Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients
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.
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.
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
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.
Discontinuous Galerkin time-domain analysis of power/ground plate pairs with wave port excitation
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.
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.
A discontinuous Galerkin method for two-dimensional PDE models of Asian options
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.
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.
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.
A new operational matrix of fractional order integration for the ...
Indian Academy of Sciences (India)
49
M. H. Heydari1, M. R. Hooshmandasl2, C. Cattani3. 1,2Faculty of ... (CWs) together with spectral Galerkin method is proposed for solving a class of nonlinear multi-order fractional differential equations .... with their operational matrix of fractional integration is proposed for solving the following NMFDE: Dα. ∗ u(x) + s. ∑ i=1.
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.
Shapkalijevski, M.; Ouwersloot, Huug; Moene, A.F.; Vilà-Guerau De Arellano, J.
2017-01-01
By characterizing the dynamics of a convective boundary layer above a relatively sparse and uniform orchard canopy, we investigated the impact of the roughness-sublayer (RSL) representation on the predicted diurnal variability of surface fluxes and state variables. Our approach combined numerical
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.
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.
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.
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.
Hybridizable discontinuous Galerkin method for the 2-D frequency-domain elastic wave equations
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.
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.
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.
DEFF Research Database (Denmark)
Emerek, Ruth
2004-01-01
Bidraget diskuterer de forskellige intergrationsopfattelse i Danmark - og hvad der kan forstås ved vellykket integration......Bidraget diskuterer de forskellige intergrationsopfattelse i Danmark - og hvad der kan forstås ved vellykket integration...
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.
DEFF Research Database (Denmark)
Marhadi, Kun Saptohartyadi; Evgrafov, Anton; Sørensen, Mads Peter
2011-01-01
We demonstrate the use of a C0 discontinuous Galerkin method for topology optimization of nano-mechanical sensors, namely temperature, surface stress, and mass sensors. The sensors are modeled using classical thin plate theory, which requires C1 basis functions in the standard finite element method...
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
Error Analysis of p-Version Discontinuous Galerkin Method for Heat Transfer in Built-up Structures
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.
Berdyshev, Abdumauvlen S.; Karimov, Erkinjon T.; Akhtaeva, Nazgul S.
2014-08-01
The main aim of the present work is an investigation of the analogue of the Tricomi problem with the integral sewing condition for parabolic-hyperbolic equation with the fractional derivative. The uniqueness of the solution for considered problem we prove by the method of energy integrals. The existence of the solution have been proved by reducing the considered problem to the Fredholm integral equation. We represent solution in an explicit form using Green's function.
A discontinuous Galerkin method for studying elasticity and variable viscosity Stokes problems
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
Working with boundaries in systems psychodynamic consulting
Directory of Open Access Journals (Sweden)
Henk Struwig
2012-03-01
Research purpose: The purpose of the research was to produce a set of theoretical assumptions about organisational boundaries and boundary management in organisations and, from these, to develop a set of hypotheses as a thinking framework for practising consulting psychologists when they work with boundaries from a systems psychodynamic stance. Motivation for the study: The researcher used the belief that organisational boundaries reflect the essence of organisations. Consulting to boundary managers could facilitate a deep understanding of organisational dynamics. Research design, approach and method: The researcher followed a case study design. He used systems psychodynamic discourse analysis. It led to six working hypotheses. Main findings: The primary task of boundary management is to hold the polarities of integration and differentiation and not allow the system to become fragmented or overly integrated. Boundary management is a primary task and an ongoing activity of entire organisations. Practical/managerial implications: Organisations should work actively at effective boundary management and at balancing integration and differentiation. Leaders should become aware of how effective boundary management leads to good holding environments that, in turn, lead to containing difficult emotions in organisations. Contribution/value-add: The researcher provided a boundary-consulting framework in order to assist consultants to balance the conceptual with the practical when they consult.
To the boundary value problem of ordinary differential equations
Directory of Open Access Journals (Sweden)
Serikbai Aisagaliev
2015-09-01
Full Text Available Method for solving of a boundary value problem for ordinary differential equations with boundary conditions at phase and integral constraints is proposed. The base of the method is an immersion principle based on the general solution of the first order Fredholm integral equation which allows to reduce the original boundary value problem to the special problem of the optimal equation.
Microlocal methods in the analysis of the boundary element method
DEFF Research Database (Denmark)
Pedersen, Michael
1993-01-01
The application of the boundary element method in numerical analysis is based upon the use of boundary integral operators stemming from multiple layer potentials. The regularity properties of these operators are vital in the development of boundary integral equations and error estimates. We show...
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 ...
hp-version discontinuous Galerkin methods on polygonal and polyhedral meshes
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...
The use of Galerkin finite-element methods to solve mass-transport equations
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)
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.
A spectral multiscale hybridizable discontinuous Galerkin method for second order elliptic problems
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.
A numerical investigation of the GRLW equation using lumped Galerkin approach with cubic B-spline.
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.
Directory of Open Access Journals (Sweden)
Hiroyuki Asada
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.
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
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.
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.
Directory of Open Access Journals (Sweden)
Fakhrodin Mohammadi
2017-10-01
Full Text Available Stochastic fractional differential equations (SFDEs have been used for modeling many physical problems in the fields of turbulance, heterogeneous, flows and matrials, viscoelasticity and electromagnetic theory. In this paper, an efficient wavelet Galerkin method based on the second kind Chebyshev wavelets are proposed for approximate solution of SFDEs. In this approach, operational matrices of the second kind Chebyshev wavelets are used for reducing SFDEs to a linear system of algebraic equations that can be solved easily. Convergence and error analysis of the proposed method is considered. Some numerical examples are performed to confirm the applicability and efficiency of the proposed method.
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.
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.
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.
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.
A class of discontinuous Petrov–Galerkin methods. Part III: Adaptivity
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.
A High Order Filter with Galerkin Finite Element Method for the Spherical Local domain Model
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.
Recent advances in boundary element methods
Manolis, GD
2009-01-01
Addresses the needs of the computational mechanics research community in terms of information on boundary integral equation-based methods and techniques applied to a variety of fields. This book collects both original and review articles on contemporary Boundary Element Methods (BEM) as well as on the Mesh Reduction Methods (MRM).
Wu, Fu-Chun; Shao, Yun-Chuan; Chen, Yu-Chen
2011-09-01
The forcing effect of channel width variations on free bars is investigated in this study using a two-dimensional depth-averaged morphodynamic model. The novel feature of the model is the incorporation of a characteristic dissipative Galerkin (CDG) upwinding scheme in the bed evolution module. A correction for the secondary flows induced by streamline curvature is also included, allowing for simulations of bar growth and migration in channels with width variations beyond the small-amplitude regimes. The model is tested against a variety of experimental data ranging from purely forced and free bars to coexisting bed forms in the variable-width channel. The CDG scheme effectively dissipates local bed oscillations, thus sustains numerical stabilities. The results show that the global effect of width variations on bar height is invariably suppressive. Such effect increases with the dimensionless amplitude AC and wave number λC of width variations. For small AC, λC has little effects on bar height; for AC beyond small amplitudes, however, the suppressing effect depends on both AC and λC. The suppressing effect on bar length increases also with both AC and λC, but is much weaker than that on bar height. The global effect of width variations on bar celerity can be suppressive or enhancive, depending on the combination of AC and λC. For smaller λC, the effect on bar celerity is enhancive; for larger λC, bar celerity tends to increase at small AC but decreases for AC beyond small amplitudes. We present herein an unprecedented data set verifying the theoretical prediction on celerity enhancement. Full suppression of bar growth above the theoretically predicted threshold AC was not observed, regardless of the adopted amplitude of initial bed perturbation A. The global effects of width variations on free bars can be quantified using a forcing factor FC that integrates the effects of AC and λC. The suppressing effects on bar height and length are both proportional to FC
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
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.
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.
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.
DEFF Research Database (Denmark)
Olwig, Karen Fog
2011-01-01
, while the countries have adopted disparate policies and ideologies, differences in the actual treatment and attitudes towards immigrants and refugees in everyday life are less clear, due to parallel integration programmes based on strong similarities in the welfare systems and in cultural notions...
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.
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.
Time-integration methods for finite element discretisations of the second-order Maxwell equation
Sarmany, D.; Bochev, Mikhail A.; van der Vegt, Jacobus J.W.
This article deals with time integration for the second-order Maxwell equations with possibly non-zero conductivity in the context of the discontinuous Galerkin finite element method (DG-FEM) and the H(curl)-conforming FEM. For the spatial discretisation, hierarchic H(curl)-conforming basis
Time-integration methods for finite element discretisations of the second-order Maxwell equation
Sarmany, D.; Bochev, Mikhail A.; van der Vegt, Jacobus J.W.
This article deals with time integration for the second-order Maxwell equations with possibly non-zero conductivity in the context of the discontinuous Galerkin finite element method DG-FEM) and the $H(\\mathrm{curl})$-conforming FEM. For the spatial discretisation, hierarchic
A simple finite element method for boundary value problems with a Riemann–Liouville derivative
Jin, Bangti
2016-02-01
© 2015 Elsevier B.V. All rights reserved. We consider a boundary value problem involving a Riemann-Liouville fractional derivative of order α∈(3/2,2) on the unit interval (0,1). The standard Galerkin finite element approximation converges slowly due to the presence of singularity term xα-^{1} in the solution representation. In this work, we develop a simple technique, by transforming it into a second-order two-point boundary value problem with nonlocal low order terms, whose solution can reconstruct directly the solution to the original problem. The stability of the variational formulation, and the optimal regularity pickup of the solution are analyzed. A novel Galerkin finite element method with piecewise linear or quadratic finite elements is developed, and ^{L2}(D) error estimates are provided. The approach is then applied to the corresponding fractional Sturm-Liouville problem, and error estimates of the eigenvalue approximations are given. Extensive numerical results fully confirm our theoretical study.
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
Stoykova, Kristalina; Idakieva, Vyara; Ivanov, Marin; Reháková, Daniela
2018-04-01
Calcareous nannofossil, calpionellid and ammonite occurrences have been directly constrained across the Jurassic-Cretaceous boundary interval in the section of Kopanitsa, SW Bulgaria. This section reveals a continuous and expanded sedimentary record through the Upper Tithonian and Lower Berriasian, besides an excellent calcareous nannofossil and ammonite record. The topmost part of the NJT 16b and the base of NJT 17a nannofossil Subzones correspond to the ammonite Microcanthum / Transitorius Subzone. The major part of the NJT 17a Subzone equates to the Durangites spp. ammonite Zone, whereas the NJT 17b Subzone correlates to the lower part of the B. jacobi ammonite Zone. The NKT nannofossil Zone approximately corresponds to the upper part of the B. jacobi Zone and the NK-1 nannofossil Zone correlates at least to the lowest part of the T. occitanica Zone. The FOs of Nannoconus globulus minor, N. wintereri, N. kamptneri minor, N. steinmannii minor, N. kamptneri kamptneri and N. steinmannii steinmannii are confirmed as reliable bio-horizons for correlations in the Mediterranean Tethys area. The first occurrence of Nannoconus wintereri is regarded as an almost concomitant event with the first occurrence of Berriasella jacobi. We suggest it could be the most useful nannofossil proxy for approximating the base of the B. jacobi Zone. Rare, but relatively well preserved calpionellids and calcareous dinoflagellates together with microfacies analysis were used additionally for stratigraphical and palaeoenvironmental interpretations. The investigated sediments are typical for the steep slope of a steepened ramp, with accumulation of hemipelagic and gravitational deposits.
Directory of Open Access Journals (Sweden)
Stoykova Kristalina
2018-04-01
Full Text Available Calcareous nannofossil, calpionellid and ammonite occurrences have been directly constrained across the Jurassic–Cretaceous boundary interval in the section of Kopanitsa, SW Bulgaria. This section reveals a continuous and expanded sedimentary record through the Upper Tithonian and Lower Berriasian, besides an excellent calcareous nannofossil and ammonite record. The topmost part of the NJT 16b and the base of NJT 17a nannofossil Subzones correspond to the ammonite Microcanthum / Transitorius Subzone. The major part of the NJT 17a Subzone equates to the Durangites spp. ammonite Zone, whereas the NJT 17b Subzone correlates to the lower part of the B. jacobi ammonite Zone. The NKT nannofossil Zone approximately corresponds to the upper part of the B. jacobi Zone and the NK-1 nannofossil Zone correlates at least to the lowest part of the T. occitanica Zone. The FOs of Nannoconus globulus minor, N. wintereri, N. kamptneri minor, N. steinmannii minor, N. kamptneri kamptneri and N. steinmannii steinmannii are confirmed as reliable bio-horizons for correlations in the Mediterranean Tethys area. The first occurrence of Nannoconus wintereri is regarded as an almost concomitant event with the first occurrence of Berriasella jacobi. We suggest it could be the most useful nannofossil proxy for approximating the base of the B. jacobi Zone. Rare, but relatively well preserved calpionellids and calcareous dinoflagellates together with microfacies analysis were used additionally for stratigraphical and palaeoenvironmental interpretations. The investigated sediments are typical for the steep slope of a steepened ramp, with accumulation of hemipelagic and gravitational deposits.
Rigid supersymmetry with boundaries
Energy Technology Data Exchange (ETDEWEB)
Belyaev, D.V. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Van Nieuwenhuizen, P. [State Univ. of New York, Stony Brook, NY (United States). C.N. Yang Inst. for Theoretical Physics
2008-01-15
We construct rigidly supersymmetric bulk-plus-boundary actions, both in x-space and in superspace. For each standard supersymmetric bulk action a minimal supersymmetric bulk-plus-boundary action follows from an extended F- or D-term formula. Additional separately supersymmetric boundary actions can be systematically constructed using co-dimension one multiplets (boundary superfields). We also discuss the orbit of boundary conditions which follow from the Euler-Lagrange variational principle. (orig.)
Rigid supersymmetry with boundaries
International Nuclear Information System (INIS)
Belyaev, D.V.; Van Nieuwenhuizen, P.
2008-01-01
We construct rigidly supersymmetric bulk-plus-boundary actions, both in x-space and in superspace. For each standard supersymmetric bulk action a minimal supersymmetric bulk-plus-boundary action follows from an extended F- or D-term formula. Additional separately supersymmetric boundary actions can be systematically constructed using co-dimension one multiplets (boundary superfields). We also discuss the orbit of boundary conditions which follow from the Euler-Lagrange variational principle. (orig.)
Distributed Tuning of Boundary Resources
DEFF Research Database (Denmark)
Eaton, Ben; Elaluf-Calderwood, Silvia; Sørensen, Carsten
2015-01-01
The digital age has seen the rise of service systems involving highly distributed, heterogeneous, and resource-integrating actors whose relationships are governed by shared institutional logics, standards, and digital technology. The cocreation of service within these service systems takes place...... in the context of a paradoxical tension between the logic of generative and democratic innovations and the logic of infrastructural control. Boundary resources play a critical role in managing the tension as a firm that owns the infrastructure can secure its control over the service system while independent...... firms can participate in the service system. In this study, we explore the evolution of boundary resources. Drawing on Pickering’s (1993) and Barrett et al.’s (2012) conceptualizations of tuning, the paper seeks to forward our understanding of how heterogeneous actors engage in the tuning of boundary...
Directory of Open Access Journals (Sweden)
Tatyana Darienko
Full Text Available Integrative taxonomy is an approach for defining species and genera by taking phylogenetic, morphological, physiological, and ecological data into account. This approach is appropriate for microalgae, where morphological convergence and high levels of morphological plasticity complicate the application of the traditional classification. Although DNA barcode markers are well-established for animals, fungi, and higher plants, there is an ongoing discussion about suitable markers for microalgae and protists because these organisms are genetically more diverse compared to the former groups. To solve these problems, we assess the usage of a polyphasic approach combining phenotypic and genetic parameters for species and generic characterization. The application of barcode markers for database queries further allows conclusions about the 'coverage' of culture-based approaches in biodiversity studies and integrates additional aspects into modern taxonomic concepts. Although the culture-dependent approach revealed three new lineages, which are described as new species in this paper, the culture-independent analyses discovered additional putative new species. We evaluated three barcode markers (V4, V9 and ITS-2 regions, nuclear ribosomal operon and studied the morphological and physiological plasticity of Coccomyxa, which became a model organism because its whole genome sequence has been published. In addition, several biotechnological patents have been registered for Coccomyxa. Coccomyxa representatives are distributed worldwide, are free-living or in symbioses, and colonize terrestrial and aquatic habitats. We investigated more than 40 strains and reviewed the biodiversity and biogeographical distribution of Coccomyxa species using DNA barcoding. The genus Coccomyxa formed a monophyletic group within the Trebouxiophyceae separated into seven independent phylogenetic lineages representing species. Summarizing, the combination of different characteristics
Müller, Inigo A; Fernandez, Alvaro; Radke, Jens; van Dijk, Joep; Bowen, Devon; Schwieters, Johannes; Bernasconi, Stefano M
2017-06-30
Clumped isotope analyses (Δ 47 ) of carbonates by dual inlet (DI) mass spectrometry require long integration times to reach the necessary high precision due to the low abundance of the rare isotopologue 13 C 18 O 16 O. Traditional DI protocols reach this only with large amounts of sample and/or a large number of replicates as a large portion of the analyte gas is wasted. We tested an improved analytical workflow that significantly reduces the sample sizes and total analysis time per sample while preserving precision and accuracy. We implemented the LIDI (long-integration dual-inlet) protocol to measure carbonates in micro-volume mode using a Kiel IV carbonate device coupled to a Thermo Scientific 253 Plus isotope ratio mass spectrometer without the new 10 13 ohm amplifier technology. The LIDI protocol includes a single measurement of the sample gas (600 s integration) followed by a single measurement of the working gas (WG) with the same integration time. The Δ 47 measurements of four calcite standards over a period of 5 weeks demonstrate excellent long-term stability with a standard deviation of ±0.021 to ±0.025 ‰ for the final values of the individual aliquots. The Δ 47 analyses of a coral, four foraminifera and a calcite precipitated in the laboratory demonstrate that 14 replicates of 90 to 120 μg are sufficient to achieve an external precision of ±0.007 ‰ (1SE) or of ±0.013 ‰ at the 95% confidence level. This study demonstrates that by using a Kiel IV-253 Plus system with LIDI it is possible to achieve the same analytical precision as conventional DI measurements with at least a factor of 40 less sample material. With the new 10 13 ohm resistor technology there is the potential to reduce the required sample material even more. This opens new avenues of research in paleoceanography, paleoclimatology, low-temperature diagenesis and other currently sample size limited applications. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John
A Newton--Galerkin Method for Fluid Flow Exhibiting Uncertain Periodic Dynamics
Schick, M.
2014-01-01
The determination of stable limit-cycles plays an important role in quantifying the characteristics of dynamical systems. In practice, exact knowledge of model parameters is rarely available leading to parameter uncertainties, which can be modeled as an input of random variables. This has the effect that the limit-cycles become stochastic themselves, resulting in almost surely time-periodic solutions with a stochastic period. In this paper we introduce a novel numerical method for the computation of stable stochastic limit-cycles based on the spectral stochastic finite element method using polynomial chaos (PC). We are able to overcome the difficulties of PC regarding its well-known convergence breakdown for long term integration. To this end, we introduce a stochastic time scaling which treats the stochastic period as an additional random variable and controls the phase-drift of the stochastic trajectories, keeping the necessary PC order low. Based on the rescaled governing equations, we aim at determining an initial condition and a period such that the trajectories close after completion of one stochastic cycle. Furthermore, we verify the numerical method by computation of a vortex shedding of a flow around a circular domain with stochastic inflow boundary conditions as a benchmark problem. The results are verified by comparison to purely deterministic reference problems and demonstrate high accuracy up to machine precision in capturing the stochastic variations of the limit-cycle.
Directory of Open Access Journals (Sweden)
Mario J Juha
2012-12-01
Full Text Available The Reproducing Kernel Element Method (RKEM is a relatively new techniquedeveloped to have two distinguished features: arbitrary high ordersmoothness and arbitrary interpolation order of the shape functions. This paper provides a tutorial on the derivation and computational implementationof RKEM for Galerkin discretizations of linear elastostatic problems forone and two dimensional space. A key characteristic of RKEM is that it donot require mid-side nodes in the elements to increase the interpolatory powerof its shape functions, and contrary to meshless methods, the same mesh usedto construct the shape functions is used for integration of the stiffness matrix. Furthermore, some issues about the quadrature used for integration arediscussed in this paper. Its hopes that this may attracts the attention ofmathematicians.El Método del Elemento Reproductor del Núcleo (RKEM es una técnica relativamente nueva desarrollada para tener dos propiedades distinguidas: suavidad de orden arbitrario y funciones de interpolación de orden arbitrario. Este artículo provee un tutorial acerca de la deducción e implementación de RKEM en discretizaciones de Galerkin en problemas elasto-estáticos en una y dos dimensiones. Una característica clave de RKEM es que no requiere de nodos intermedios en los lados de los elementos para incrementar el poder de interpolación de sus funciones de forma, y contrario a los métodos sin malla, la misma malla usada para construir las funciones de forma es usada para la integración de la matriz de rigidez. Además, algunas cuestiones acerca de la cuadratura usada para integración son discutidas en el artículo. Se espera que esto pueda atraer la atención de matemáticos.
Sequential limiting in continuous and discontinuous Galerkin methods for the Euler equations
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.
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.
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.
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.
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.
A discontinuous Galerkin method for P-wave modeling in tilted TI media
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.
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.
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.
On the optimal polynomial approximation of stochastic PDEs by galerkin and collocation methods
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.
A nodal discontinuous Galerkin finite element method for nonlinear elastic wave propagation.
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.
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.
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.
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.
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.
Approximate tensor-product preconditioners for very high order discontinuous Galerkin methods
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.
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
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.
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.
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.
Beauchamp, Catherine; Beauchamp, Miriam H.
2013-01-01
Within the emerging field of educational neuroscience, concerns exist that the impact of neuroscience research on education has been less effective than hoped. In seeking a way forward, it may be useful to consider the problems of integrating two complex fields in the context of disciplinary boundaries. Here, a boundary perspective is used as a…
Allegheny County Municipal Boundaries
Allegheny County / City of Pittsburgh / Western PA Regional Data Center — This dataset demarcates the municipal boundaries in Allegheny County. Data was created to portray the boundaries of the 130 Municipalities in Allegheny County the...
Department of Housing and Urban Development — The HUD GIS Boundary Files are intended to supplement boundary files available from the U.S. Census Bureau. The files are for community planners interested in...
State Agency Administrative Boundaries
Kansas Data Access and Support Center — This database comprises 28 State agency boundaries and point of contact. The Kansas Geological Survey collected legal descriptions of the boundaries for various...
Political State Boundary (National)
Department of Transportation — State boundaries with political limit - boundaries extending into the ocean (NTAD). The TIGER/Line Files are shapefiles and related database files (.dbf) that are an...
A new approach to implement absorbing boundary condition in biomolecular electrostatics.
Goni, Md Osman
2013-01-01
This paper discusses a novel approach to employ the absorbing boundary condition in conjunction with the finite-element method (FEM) in biomolecular electrostatics. The introduction of Bayliss-Turkel absorbing boundary operators in electromagnetic scattering problem has been incorporated by few researchers. However, in the area of biomolecular electrostatics, this boundary condition has not been investigated yet. The objective of this paper is twofold. First, to solve nonlinear Poisson-Boltzmann equation using Newton's method and second, to find an efficient and acceptable solution with minimum number of unknowns. In this work, a Galerkin finite-element formulation is used along with a Bayliss-Turkel absorbing boundary operator that explicitly accounts for the open field problem by mapping the Sommerfeld radiation condition from the far field to near field. While the Bayliss-Turkel condition works well when the artificial boundary is far from the scatterer, an acceptable tolerance of error can be achieved with the second order operator. Numerical results on test case with simple sphere show that the treatment is able to reach the same level of accuracy achieved by the analytical method while using a lower grid density. Bayliss-Turkel absorbing boundary condition (BTABC) combined with the FEM converges to the exact solution of scattering problems to within discretization error.
Deckers, Jef; Van Noten, Koen; Schiltz, Marco; Lecocq, Thomas; Vanneste, Kris
2018-01-01
The Grote Brogel Fault (GBF) is a major WNW-ESE striking normal fault in Belgium that diverges westward from the NW-SE striking western border fault system of the Roer Valley Graben. The GBF delimits the topographically higher Campine Block from the subsiding Roer Valley Graben, and is expressed in the Digital Terrain Model (DTM) by relief gradients or scarps. By integrating DTM, Electrical Resistivity Tomography (ERT), Cone Penetration Test (CPT) and borehole data, we studied the Quaternary activity of the GBF and its effects on local hydrogeology. In the shallow subsurface (elevated footwall towards the hangingwall, resulting in hydraulic head differences of up to 12.7 m. For the two investigation sites, the hydraulic head changes correlate with the relief gradient, which in turn correlates with the Quaternary vertical offset of the GBF. ERT profiles at the eastern site also revealed a local soft-linked stepover in the shallow subsurface, which affects groundwater levels in the different fault blocks, and illustrates the complex small-scale geometry of the GBF.
Environmentalists without Boundaries
African Journals Online (AJOL)
GREGORY
2009-03-16
Mar 16, 2009 ... Environmentalists without Boundaries. Setting Boundaries is a popular strategy in child development programs. But as children mature into young adults, it dawns on many that certain boundaries must be crossed to explore rich opportunities outside the safe closet of their teachers or parents' watchful eyes.
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
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
Honti, Mark; Schuwirth, Nele; Rieckermann, Jörg; Ghielmetti, Nico; Stamm, Christian
2014-05-01
Catchments are complex systems where water quantity, quality and the ecological services provided are determined by interacting physical, chemical, biological, economical and social factors. The realization of these interactions led to the prevailing catchment management paradigm: Integrated Water Resources Management (IWRM). IWRM requires considering all these aspects during the design of sustainable resource utilization. Due to the complexity of this task, mathematical modeling plays a key role in IWRM, namely in the evaluation of the impacts of hypothetical scenarios and management measures. Toxicity is a key determinant of the ecological state and as such a focal point in IWRM, but we still have significant knowledge gaps about the diffuse loads of organic micropollutants (OMP) that leak from both urban and agricultural areas. Most European catchments possess mixed land use, containing rural (natural and agricultural) landscapes and settlements in varying proportions. Thus, a catchment model supporting IWRM must be able to cope with both classes. However, the majority of existing catchment models is dedicated to either rural or urban areas, while the minority capable of simulating both contain overly simplified descriptions for either land use category. We applied a conceptual model that describes all major land use classes for assessing the impacts of climate change, socio-economic development and management alternatives on diffuse OMP loads. We simulated the loads of 12 compounds (agricultural and urban pesticides and urban biocides) with daily resolution at 11 locations in the stream network of a small catchment (46 km2) in Switzerland. The model considers all important diffuse transport pathways separately, but each with a simple empirical process rate. Consequently, some site-specific observations were required to calibrate rate parameters. We assessed uncertainty during both calibration and prediction phases. Predictions indicated that future OMP loads
DEFF Research Database (Denmark)
Bødker, Susanne; Kristensen, Jannie Friis; Nielsen, Christina
2003-01-01
This paper presents a study of an organisation, which is undergoing a process transforming organisational and technological boundaries. In particular, we shall look at three kinds of boundaries: the work to maintain and change the boundary between the organisation and its customers; boundaries...... between competencies within the organisation; and boundaries between various physical locations of work, in particular between what is done in the office and what is done on site. Maintaining and changing boundaries are the processes through which a particular community sustains its identity and practice...... on the one hand, and where it is confronted with the identity and practices on the other.The organisation being studied employs a multitude of IT systems that support and maintain these boundaries in a particular manner that are in many ways inappropriate to the current needs of the organisation...
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.
Discontinuous Galerkin modeling of the Columbia River's coupled estuary-plume dynamics
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.
Spanning organizational boundaries to manage creative processes:
DEFF Research Database (Denmark)
Andersen, Poul Houman; Kragh, Hanne; Lettl, Christopher
2013-01-01
In order to continue to be innovative in the current fast-paced and competitive environment, organizations are increasingly dependent on creative inputs developed outside their boundaries. The paper addresses the boundary spanning activities that managers undertake to a) select and mobilize...... creative talent, b) create shared identity, and c) combine and integrate knowledge in innovation projects involving external actors. We study boundary spanning activities in two creative projects in the LEGO group. One involves identifying and integrating deep, specialized knowledge, the other focuses...... on the use of external actors as a source of broad, not necessarily fully developed ideas. We find that the boundary spanning activities in these two projects differ in respect, among other things, of how the firm selects participants, formulates problems, and aligns the expectations of internal and external...
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.
Czech Academy of Sciences Publication Activity Database
Kosík, Adam; Feistauer, M.; Hadrava, Martin; Horáček, Jaromír
2015-01-01
Roč. 267, September (2015), s. 382-396 ISSN 0096-3003 R&D Projects: GA ČR(CZ) GAP101/11/0207 Institutional support: RVO:61388998 Keywords : discontinuous Galerkin method * nonlinear elasticity * compressible viscous flow * fluid–structure interaction Subject RIV: BI - Acoustics Impact factor: 1.345, year: 2015 http://www. science direct.com/ science /article/pii/S0096300315002453/pdfft?md5=02d46bc730e3a7fb8a5008aaab1da786&pid=1-s2.0-S0096300315002453-main.pdf
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.
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.
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.
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)
Characterizations of boundary pluripolar hulls
Djire, I.K.; Wiegerinck, J.
2016-01-01
We present some basic properties of the so-called boundary relative extremal function and discuss boundary pluripolar sets and boundary pluripolar hulls. We show that for B-regular domains the boundary pluripolar hull is always trivial on the boundary of the domain and present a “boundary version”
On the boundary conditions in cylindrical cell approximation
International Nuclear Information System (INIS)
Altiparmakov, D.V.
1980-01-01
A solution of the integral transport equation for an arbitrary boundary condition is obtained by solving the integral transport equation for homogeneous (vacuum) boundary condition and using the neutron balance condition. An effective boundary condition satisfying the zero gradient of the neutron flux on the cell boundary is assumed. The numerical solution is obtained by using a pointwise approximation based on a polynomial flux approximation. Disadvantage factor calculations of the Thie lattice cells are carried out. Comparisons are performed with the results obtained for the actual cells by two-dimensional methods as well as their cylindrical approximations applying various boundary conditions. It is obvious from the results shown here that the proposed boundary condition has advantages in respect to others. The errors introduced by the proposed boundary condition are of the lower order in respect to the inaccuracy of the existing transport methods. Thus, the applications of the two-dimensional methods for regular lattice calculations is unnecessary. (author)
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.
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.
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.
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.
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.
Isogeometric Analysis of Boundary Integral Equations
2015-04-21
needs to modify the construction. This issue has been addressed by introducing “2-ring” collocation points [54] for discontinuous cubic T- splines . In...methods, IgA relies on Non-Uniform Rational B- splines (NURBS) [43, 46], T- splines [55, 53] or subdivision surfaces [21, 48, 51] rather than piece- wise...polynomials for approximating the geometry and field variables. Thus, by replacing piecewise polynomials with NURBS or T- splines , one can develop
Steeneveld, G.J.
2012-01-01
Understanding and prediction of the stable atmospheric boundary layer is a challenging task. Many physical processes are relevant in the stable boundary layer, i.e. turbulence, radiation, land surface coupling, orographic turbulent and gravity wave drag, and land surface heterogeneity. The
Development of boundary layers
International Nuclear Information System (INIS)
Herbst, R.
1980-01-01
Boundary layers develop along the blade surfaces on both the pressure and the suction side in a non-stationary flow field. This is due to the fact that there is a strongly fluctuating flow on the downstream blade row, especially as a result of the wakes of the upstream blade row. The author investigates the formation of boundary layers under non-stationary flow conditions and tries to establish a model describing the non-stationary boundary layer. For this purpose, plate boundary layers are measured, at constant flow rates but different interferent frequency and variable pressure gradients. By introducing the sample technique, measurements of the non-stationary boundary layer become possible, and the flow rate fluctuation can be divided in its components, i.e. stochastic turbulence and periodical fluctuation. (GL) [de
Miyake, Y.; Noda, H.
2017-12-01
Earthquake sequences involve many processes in a wide range of time scales, from quasistatic loading to dynamic rupture. At a depth of brittle-plastic transitional and deeper, rock behaves as a viscous fluid in a long timescale, but as an elastic material in a short timescale. Viscoelastic stress relaxation may be important in the interseismic periods at the depth, near the deeper limit of the seismogenic layer or the region of slow slip events (SSEs) [Namiki et al., 2014 and references therein]. In the present study, we implemented the viscoelastic effect (Maxwell material) in fully-dynamic earthquake sequence simulations using a spectral boundary integral equation method (SBIEM) [e.g., Lapusta et al., 2000]. SBIEM is efficient in calculation of convolutional terms for dynamic stress transfer, and the problem size is limited by the amount of memory available. Linear viscoelasticity could be implemented by convolution of slip rate history and Green's function, but this method requires additional memory and thus not suitable for the implementation to the present code. Instead, we integrated the evolution of "effective slip" distribution, which gives static stress distribution when convolved with static elastic Green's function. This method works only for simple viscoelastic property distributions, but such models are suitable for numerical experiments aiming basic understanding of the system behavior because of the virtue of SBIEM, the ability of fine on-fault spatial resolution and efficient computation utilizing the fast Fourier transformation. In the present study, we examined the effect of viscoelasticity on earthquake sequences of a fault with a rate-weakening patch. A series of simulations with various relaxation time tc revealed that as decreasing tc, recurrence intervals of earthquakes increases and seismicity ultimately disappears. As long as studied, this transition to aseismic behavior is NOT associated with SSEs. In a case where the rate-weakening patch
DEFF Research Database (Denmark)
Mariegaard, Jesper Sandvig
equation: a linear finite element method (L-FEM) and a discontinuous Galerkin-FEM (DG-FEM). The controllability operator is discretized with both L-FEM and DG-FEM to obtain a HUM matrix. We show that formulating HUM in a sine basis is beneficial for several reasons: (i) separation of low and high frequency......We consider a control problem for the wave equation: Given the initial state, find a specific boundary condition, called a control, that steers the system to a desired final state. The Hilbert uniqueness method (HUM) is a mathematical method for the solution of such control problems. It builds...... on the duality between the control system and its adjoint system, and these systems are connected via a so-called controllability operator. In this project, we are concerned with the numerical approximation of HUM control for the one-dimensional wave equation. We study two semi-discretizations of the wave...
MHD boundary layer flow and heat transfer in an inclined porous square cavity filled with nanofluids
Directory of Open Access Journals (Sweden)
Chandra Shekar Balla
2017-06-01
Full Text Available The present paper deals with the magnetohydrodynamic boundary layer flow of a free convection heat transfer in an inclined square cavity filled with nanofluid-saturated porous medium. The effects of different nanoparticles Cu, Al2O3, TiO2 and SiO2 are considered. The top and bottom horizontal walls of cavity are considered adiabatic, while the vertical walls are kept at constant temperatures. The governing partial differential equations are solved by finite element method of Galerkin weighted residual scheme. Numerical results are obtained for different values of the Rayleigh number, angle of inclination, magnetic field and nanofluid volume fraction. The overall investigation of variation of streamlines, isotherms and Nusselt numbers is presented graphically. To examine the accuracy, the present results are compared with the available results.
Finite element fluid modeling of axisymmetric magnetized boundary plasma with recycling neutrals
International Nuclear Information System (INIS)
Zanino, R.
1992-01-01
Finite elements should provide a natural and flexible method for fluid modeling of the tokamak SOL, in particular when the SOL geometry is complex, and/or the poloidal magnetic field is very inclined to the limiter/divertor target. Here we present a Galerkin finite element code, FELS, for transport modeling of a 2-fluid magnetized boundary plasma in an axisymmetry domain, in the presence of recycling neutrals. The classical collisional plasma dynamics along magnetic field lines is taken into account, and a simple diffusive Ansatz is used for the fluxes across magnetic surfaces; electric currents and diamagnetic flows are neglected for the time being. An analytical fluid model is used for the recycling neutrals. Results are shown and discussed for the case of a simple geometry. (orig.)
Efficient spectral-Petrov-Galerkin methods for third- and fifth-order ...
African Journals Online (AJOL)
Two new families of general parameters generalized Jacobi polynomials are introduced. Some efficient and accurate algorithms based on these families are developed and implemented for solving third- and fifth-order differential equations in one variable subject to homogeneous and nonhomogeneous boundary ...
Xin, F X; Lu, T J
2009-03-01
The air-borne sound insulation performance of a rectangular double-panel partition clamp mounted on an infinite acoustic rigid baffle is investigated both analytically and experimentally and compared with that of a simply supported one. With the clamped (or simply supported) boundary accounted for by using the method of modal function, a double series solution for the sound transmission loss (STL) of the structure is obtained by employing the weighted residual (Galerkin) method. Experimental measurements with Al double-panel partitions having air cavity are subsequently carried out to validate the theoretical model for both types of the boundary condition, and good overall agreement is achieved. A consistency check of the two different models (based separately on clamped modal function and simply supported modal function) is performed by extending the panel dimensions to infinite where no boundaries exist. The significant discrepancies between the two different boundary conditions are demonstrated in terms of the STL versus frequency plots as well as the panel deflection mode shapes.
Dynamic stability analysis of fluid-filled cylindrical shells with top end-fixed boundary condition
International Nuclear Information System (INIS)
Xu, Y.H.; Tsukimori, K.
1995-01-01
This study is aimed at understanding the dynamic instability mechanism of fluid-filled cylindrical shells with top end-fixed boundary condition under seismic excitation. The fluid-structure interaction problem is formulated using the concept of added mass. The contribution of each individual fluid pressure components are identified. A Galerkin/Finite Element discretization is applied to obtain the governing matrix equations. The model coupling among the various combinations of axial and circumferential modes are identified. For dynamic stability analysis, the matrix equations are cast into a set of coupled Hill's equations by employing an orthogonality transformation. The application of this method and the discussion on dynamic buckling behaviors of different boundary conditions are presented. The following comments are found: (1) Strong effect of added mass to the first beam mode frequency is observed in the top end-fixed case and the effect depends on the level of filled fluid and the ratio of shall radius to height; (2) The static and dynamic pressure acting on the bottom plate increase the axial frequency for n=2... N and the critical instability parameter ε cr in the top end-fixed case, respectively; (3) Strong effect of shell top boundary, open or closed, to axial frequencies for mode (i,n) (n=2... N) and instability behaviors is observed for fluid-filled tanks with bottom-fixed boundary condition. (author)
International Nuclear Information System (INIS)
Mohammed, M.H.H.
2012-01-01
Radiation transfer problem for anisotropic scattering in a spherical homogeneous, turbid medium with angular dependent (specular) and diffuse reflecting boundary is considered. The angular dependent reflectivity of the boundary is considered as Fresnel's reflection probability function. The solution of the problem containing an energy source in a medium of specular and diffuse reflecting boundaries is given in terms of the solution of the source-free problem. The source-free problem for anisotropic scattering through a homogeneous solid sphere and two concentric spheres is solved by using the Pomraning- Eddington approximation method. This method transform the integro-differential equation into two differential equations for the radiance g (x) and net flux q (x) which has an analytical solution in terms of the modified Bessel function. Two different weight functions are used to verify the boundary conditions and so, find the solution constants. The partial heat fluxes at the boundaries of a solid sphere and spherical shell of transparent and reflecting boundaries are calculated. The media are taken with or without internal black-body radiation. The calculations are carried out for various values of refractive index and different radii. The results are compared with those of the Galerkin technique
Administrative Area Boundaries 2 (State Boundaries), Region 9, 2010, NAVTEQ
U.S. Environmental Protection Agency — NAVTEQ Administrative Area Boundaries 2 (State Boundaries) for Region 9. There are five Administrative Area Boundaries layers (1, 2, 3, 4, 5). These layers contain...
Administrative Area Boundaries 4 (City Boundaries), Region 9, 2010, NAVTEQ
U.S. Environmental Protection Agency — NAVTEQ Administrative Area Boundaries 4 (City Boundaries) for Region 9. There are five Administrative Area Boundaries layers (1, 2, 3, 4, 5). These layers contain...
DEFF Research Database (Denmark)
Gorm Hansen, Birgitte
2011-01-01
Whether celebratory or critical, STS research on science-industry relations has focused on the blurring of boundaries and hybridization of codes and practices. However, the vocabulary of boundary and hybrid tends to reify science and industry as separate in the attempt to map their relation...... as the negotiation of a preexisting science-industry boundary. Rather, viability is obtained through a strategy of "circumventing" the science-industry food chain and "sequestering" biotech components within the research center. Symbiosis allows academic scientists to do biology while at the same time demonstrating...
Riemann surfaces with boundaries and string theory
International Nuclear Information System (INIS)
Morozov, A.Yu.; Roslyj, A.A.
1989-01-01
A consideration of the cutting and joining operations for Riemann surfaces permits one to express the functional integral on a Riemann surface in terms of integrals over its pieces which are suarfaces with boundaries. This yields an expression for the determinant of the Laplacian on a Riemann surface in terms of Krichever maps for its pieces. Possible applications of the methods proposed to a study of the string perturbation theory in terms of an universal moduli space are mentioned
Secure Supply Chains : Design Restrictions & Organizational Boundaries
Ludema, M.W.
2009-01-01
An important issue in the design of secure supply chains is the understanding of the relation between supply chains and the organizational responsibility of specific parts of these supply chains. Organizational boundaries change over time by means of vertical and/or horizontal (des)-integration and
Allegheny County Parcel Boundaries
Allegheny County / City of Pittsburgh / Western PA Regional Data Center — This dataset contains parcel boundaries attributed with county block and lot number. Use the Property Information Extractor for more control downloading a filtered...
Allegheny County / City of Pittsburgh / Western PA Regional Data Center — This dataset contains the Allegheny County boundary. If viewing this description on the Western Pennsylvania Regional Data Center’s open data portal...
Boundary representation modelling techniques
2006-01-01
Provides the most complete presentation of boundary representation solid modelling yet publishedOffers basic reference information for software developers, application developers and users Includes a historical perspective as well as giving a background for modern research.
Earth Data Analysis Center, University of New Mexico — The dataset represents the boundaries of all public school districts in the state of New Mexico. The source for the data layer is the New Mexico Public Education...
U.S. Environmental Protection Agency — This dataset consists of site boundaries from multiple Superfund sites in U.S. EPA Region 8. These data were acquired from multiple sources at different times and...
Relationships, not boundaries.
Combs, Gene; Freedman, Jill
2002-01-01
The authors find it more useful to pay attention to relationships than to boundaries. By focusing attention on bounded, individual psychological issues, the metaphor of boundaries can distract helping professionals from thinking about inequities of power. It oversimplifies a complex issue, inviting us to ignore discourses around gender, race, class, culture, and the like that support injustice, abuse, and exploitation. Making boundaries a central metaphor for ethical practice can keep us from critically examining the effects of distance, withdrawal, and non-participation. The authors describe how it is possible to examine the practical, moral, and ethical effects of our participation in relationships by focusing on just relationships rather than on boundaries. They give illustrations and clinical examples of relationally-focused ethical practices that derive from a narrative approach to therapy.
Minnesota Department of Natural Resources — This theme shows the USFS national forest boundaries in the state. This data was acquired from the GIS coordinators at both the Chippewa National Forest and the...
Kansas Data Access and Support Center — This data set is a digital hydrologic unit boundary that is at the 4-digit, 6-digit, 8-digit, and 11-digit level. The data set was developed by delineating the...
U.S. Department of Health & Human Services — This city boundary shapefile was extracted from Esri Data and Maps for ArcGIS 2014 - U.S. Populated Place Areas. This shapefile can be joined to 500 Cities...
State Park Statutory Boundaries
Minnesota Department of Natural Resources — Legislative statutory boundaries for sixty six state parks, six state recreation areas, and eight state waysides. These data are derived principally from DNR's...
Directory of Open Access Journals (Sweden)
Pamuda Pudjisuryadi
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.
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.