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479 results on '"Halpern, Laurence"'

1. Piece-wise Constant, Linear and Oscillatory: a Historical Introduction to Spectral Coarse Spaces with Focus on Schwarz Methods

Author

Gander, Martin J., Halpern, Laurence, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Dostál, Zdeněk, editor, Kozubek, Tomáš, editor, Klawonn, Axel, editor, Langer, Ulrich, editor, Pavarino, Luca F., editor, Šístek, Jakub, editor, and Widlund, Olof B., editor

Published
2024
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2. Optimized Schwarz Method in Time for Transport Control

Author

Bui, Duc-Quang, Delourme, Berangere, Halpern, Laurence, Kwok, Felix, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Dostál, Zdeněk, editor, Kozubek, Tomáš, editor, Klawonn, Axel, editor, Langer, Ulrich, editor, Pavarino, Luca F., editor, Šístek, Jakub, editor, and Widlund, Olof B., editor

Published
2024
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3. Optimized Robin Transmission Conditions for Anisotropic Diffusion on Arbitrary Meshes

Author

Gander, Martin J., Halpern, Laurence, Hubert, Florence, Krell, Stella, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Dostál, Zdeněk, editor, Kozubek, Tomáš, editor, Klawonn, Axel, editor, Langer, Ulrich, editor, Pavarino, Luca F., editor, Šístek, Jakub, editor, and Widlund, Olof B., editor

Published
2024
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5. Perfectly Matched Layers on Cubic Domains forPauli's Equations

Author

Halpern, Laurence and Rauch, Jeffrey

Subjects
Mathematics - Analysis of PDEs, Mathematics - Numerical Analysis
Abstract

This article proves the well posedness of the boundary value problemthat arises when PML algorithms are applied to Pauli's equationswith a three dimensional rectangle as computational domain. The absorptionsare positive near the boundary and zero far from the boundary so are always x-dependent. At the flat parts of the boundary of the rectangle, the natural absorbing boundary conditions are imposed.The difficulty addressed is the analysis of the resulting variable coeffi-cient problem on the rectanglar solid with its edges and corners. TheLaplace transform is analysed. It turns on the analysis of a boundaryvalue problem formally obtained by complex stretching. Existence isproved by deriving a boundary value problems for a complex stretchedHelmholtz equation on smoothed domains. This is the first stabilityproof with x-dependent absorptions on a bounded domain whoseboundary is not smooth.

Published
2020

6. Overlapping DDFV Schwarz Algorithms on Non-Matching Grids

Author

Gander, Martin J., Halpern, Laurence, Hubert, Florence, Krell, Stella, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Brenner, Susanne C., editor, Chung, Eric, editor, Klawonn, Axel, editor, Kwok, Felix, editor, Xu, Jinchao, editor, and Zou, Jun, editor

Published
2022
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7. A Simple Finite Difference Discretization for Ventcell Transmission Conditions at Cross Points

Author

Gander, Martin J., Halpern, Laurence, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Brenner, Susanne C., editor, Chung, Eric, editor, Klawonn, Axel, editor, Kwok, Felix, editor, Xu, Jinchao, editor, and Zou, Jun, editor

Published
2022
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8. Fundamental Coarse Space Components for Schwarz Methods with Crosspoints

Author

Cuvelier, François, Gander, Martin J., Halpern, Laurence, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Brenner, Susanne C., editor, Chung, Eric, editor, Klawonn, Axel, editor, Kwok, Felix, editor, Xu, Jinchao, editor, and Zou, Jun, editor

Published
2022
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9. Comparison of Continuous and Discrete Techniques to Apply Coarse Corrections

Author

Gander, Martin J., Halpern, Laurence, Santugini-Repiquet, Kévin, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Haynes, Ronald, editor, MacLachlan, Scott, editor, Cai, Xiao-Chuan, editor, Halpern, Laurence, editor, Kim, Hyea Hyun, editor, Klawonn, Axel, editor, and Widlund, Olof, editor

Published
2020
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15. Optimized Schwarz methods with general Ventcell transmission conditions for fully anisotropic diffusion with discrete duality finite volume discretizations

Author

Gander Martin J., Halpern Laurence, Hubert Florence, and Krell Stella

Subjects
non-overlapping optimized schwarz method, ventell transmission condition, ddfv finite volume scheme, anistropic diffusion, 65n55, 65n08, 35a35, 65f10, Mathematics, QA1-939
Abstract

We introduce a new non-overlapping optimized Schwarz method for fully anisotropic diffusion problems. Optimized Schwarz methods take into account the underlying physical properties of the problem at hand in the transmission conditions, and are thus ideally suited for solving anisotropic diffusion problems. We first study the new method at the continuous level for two subdomains, prove its convergence for general transmission conditions of Ventcell type using energy estimates, and also derive convergence factors to determine the optimal choice of parameters in the transmission conditions. We then derive optimized Robin and Ventcell parameters at the continuous level for fully anisotropic diffusion, both for the case of unbounded and bounded domains. We next present a discretization of the algorithm using discrete duality finite volumes, which are ideally suited for fully anisotropic diffusion on very general meshes. We prove a new convergence result for the discretized optimized Schwarz method with two subdomains using energy estimates for general Ventcell transmission conditions. We finally study the convergence of the new optimized Schwarz method numerically using parameters obtained from the continuous analysis. We find that the predicted optimized parameters work very well in practice, and that for certain anisotropies which we characterize, our new bounded domain analysis is important.

Published
2021
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16. A new Algorithm Based on Factorization for Heterogeneous Domain Decomposition

Author

Gander, Martin J., Halpern, Laurence, and Martin, Véronique

Subjects
Mathematics - Numerical Analysis
Abstract

Often computational models are too expensive to be solved in the entire domain of simulation, and a cheaper model would suffice away from the main zone of interest. We present for the concrete example of an evolution problem of advection reaction diffusion type a heterogeneous domain decomposition algorithm which allows us to recover a solution that is very close to the solution of the fully viscous problem, but solves only an inviscid problem in parts of the domain. Our new algorithm is based on the factorization of the underlying differential operator, and we therefore call it factorization algorithm. We give a detailed error analysis, and show that we can obtain approximations in the viscous region which are much closer to the viscous solution in the entire domain of simulation than approximations obtained by other heterogeneous domain decomposition algorithms from the literature., Comment: 23 pages

Published
2014

17. Optimized Schwarz Waveform Relaxation for Advection Reaction Diffusion Equations in Two Dimensions

Author

Bennequin, Daniel, Gander, Martin J., Gouarin, Loic, and Halpern, Laurence

Subjects
Mathematics - Numerical Analysis
Abstract

Optimized Schwarz Waveform Relaxation methods have been developed over the last decade for the parallel solution of evolution problems. They are based on a decomposition in space and an iteration, where only subproblems in space-time need to be solved. Each subproblem can be simulated using an adapted numerical method, for example with local time stepping, or one can even use a different model in different subdomains, which makes these methods very suitable also from a modeling point of view. For rapid convergence however, it is important to use effective transmission conditions between the space-time subdomains, and for best performance, these transmission conditions need to take the physics of the underlying evolution problem into account. The optimization of these transmission conditions leads to a mathematically hard best approximation problem of homographic type. We study in this paper in detail this problem for the case of linear advection reaction diffusion equations in two spatial dimensions. We prove comprehensively best approximation results for transmission conditions of Robin and Ventcel type. We give for each case closed form asymptotic values for the parameters, which guarantee asymptotically best performance of the iterative methods. We finally show extensive numerical experiments, and we measure performance corresponding to our analysis, Comment: 42 pages

Published
2014

18. On Optimal Coarse Spaces for Domain Decomposition and Their Approximation

Author

Gander, Martin J., Halpern, Laurence, Santugini-Repiquet, Kévin, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Bjørstad, Petter E., editor, Brenner, Susanne C., editor, Halpern, Lawrence, editor, Kim, Hyea Hyun, editor, Kornhuber, Ralf, editor, Rahman, Talal, editor, and Widlund, Olof B., editor

Published
2018
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19. Optimized Schwarz Methods for Elliptic Optimal Control Problems

Author

Delourme, Bérangère, Halpern, Laurence, Nguyen, Binh Thanh, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Bjørstad, Petter E., editor, Brenner, Susanne C., editor, Halpern, Lawrence, editor, Kim, Hyea Hyun, editor, Kornhuber, Ralf, editor, Rahman, Talal, editor, and Widlund, Olof B., editor

Published
2018
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20. The Analysis of Matched Layers

Author

Halpern, Laurence, Petit-Bergez, Sabrina, and Rauch, Jeffrey

Subjects
Mathematics - Numerical Analysis
Abstract

A systematic analysis of matched layers is undertaken with special attention to better understand the remarkable method of B\'erenger. We prove that the B\'erenger and closely related layers define well posed transmission problems in great generality. When the B\'erenger method or one of its close relatives is well posed, perfect matching is proved. The proofs use the energy method, Fourier-Laplace transform, and real coordinate changes for Laplace transformed equations. It is proved that the loss of derivatives associated with the B\'erenger method does not occur for elliptic generators. More generally, an essentially necessary and sufficient condition for loss of derivatives in B\'erenger's method is proved. The sufficiency relies on the energy method with pseudodifferential multiplier. Amplifying and nonamplifying layers are identified by a geometric optics computation. Among the various flavors of B\'erenger's algorithm for Maxwell's equations our favorite choice leads to a strongly well posed augmented system and is both perfect and nonamplifying in great generality. We construct by an extrapolation argument an alternative matched layer method which preserves the strong hyperbolicity of the original problem and though not perfectly matched has leading reflection coefficient equal to zero at all angles of incidence.

Published
2011

21. Optimized Schwarz waveform relaxation and discontinuous Galerkin time stepping for heterogeneous problems

Author

Halpern, Laurence, Szeftel, Jérémie, and Japhet, Caroline

Subjects
Mathematics - Numerical Analysis
Abstract

We design and analyze a Schwarz waveform relaxation algorithm for domain decomposition of advection-diffusion-reaction problems with strong heterogeneities. The interfaces are curved, and we use optimized Robin or Ventcell transmission conditions. We analyze the semi-discretization in time with Discontinuous Galerkin as well. We also show two-dimensional numerical results using generalized mortar finite elements in space.

Published
2010

22. DDFV Ventcell Schwarz Algorithms

Author

Gander, Martin J., Halpern, Laurence, Hubert, Florence, Krell, Stella, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Dickopf, Thomas, editor, Gander, Martin J., editor, Halpern, Laurence, editor, Krause, Rolf, editor, and Pavarino, Luca F., editor

Published
2016
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23. A Direct Solver for Time Parallelization

Author

Gander, Martin J., Halpern, Laurence, Ryan, Juliet, Tran, Thuy Thi Bich, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Dickopf, Thomas, editor, Gander, Martin J., editor, Halpern, Laurence, editor, Krause, Rolf, editor, and Pavarino, Luca F., editor

Published
2016
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24. Overlapping Domain Decomposition Applied to the Navier–Stokes Equations

Author

Ciobanu, Oana, Halpern, Laurence, Juvigny, Xavier, Ryan, Juliette, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Dickopf, Thomas, editor, Gander, Martin J., editor, Halpern, Laurence, editor, Krause, Rolf, editor, and Pavarino, Luca F., editor

Published
2016
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27. Nonlinear Nonoverlapping Schwarz Waveform Relaxation for Semilinear Wave Propagation

Author

Halpern, Laurence and Szeftel, Jérémie

Subjects
Mathematics - Numerical Analysis, 65M55, 35L70
Abstract

We introduce a non-overlapping variant of the Schwarz waveform relaxation algorithm for semilinear wave propagation in one dimension. Using the theory of absorbing boundary conditions, we derive a new nonlinear algorithm. We show that the algorithm is well-posed and we prove its convergence by energy estimates and a Galerkin method. We then introduce an explicit scheme. We prove the convergence of the discrete algorithm with suitable assumptions on the nonlinearity. We finally illustrate our analysis with numerical experiments., Comment: 20 pages

Published
2007

28. Time Parallelization for Nonlinear Problems Based on Diagonalization

Author

Gander, Martin J., Halpern, Laurence, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Lee, Chang-Ock, editor, Cai, Xiao-Chuan, editor, Kim, Hyea Hyun, editor, Klawonn, Axel, editor, Park, Eun-Jae, editor, and Widlund, Olof B., editor

Published
2017
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31. A Finite Volume Ventcell–Schwarz Algorithm for Advection-Diffusion Equations

Author

Halpern, Laurence, Hubert, Florence, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Erhel, Jocelyne, editor, Gander, Martin J., editor, Halpern, Laurence, editor, Pichot, Géraldine, editor, Sassi, Taoufik, editor, and Widlund, Olof, editor

Published
2014
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32. Discontinuous Coarse Spaces for DD-Methods with Discontinuous Iterates

Author

Gander, Martin J., Halpern, Laurence, Santugini Repiquet, Kévin, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Erhel, Jocelyne, editor, Gander, Martin J., editor, Halpern, Laurence, editor, Pichot, Géraldine, editor, Sassi, Taoufik, editor, and Widlund, Olof, editor

Published
2014
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33. A New Coarse Grid Correction for RAS/AS

Author

Gander, Martin J., Halpern, Laurence, Repiquet, Kévin Santugini, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Erhel, Jocelyne, editor, Gander, Martin J., editor, Halpern, Laurence, editor, Pichot, Géraldine, editor, Sassi, Taoufik, editor, and Widlund, Olof, editor

Published
2014
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34. Optimized Schwarz Waveform Relaxation for Nonlinear Systems of Parabolic Type

Author

Häberlein, Florian, Halpern, Laurence, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Erhel, Jocelyne, editor, Gander, Martin J., editor, Halpern, Laurence, editor, Pichot, Géraldine, editor, Sassi, Taoufik, editor, and Widlund, Olof, editor

Published
2014
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47. An Optimized Schwarz Waveform Relaxation Algorithm for Micro-Magnetics

Author

Gander, Martin J., Halpern, Laurence, Labbé, Stéphane, Santugini-Repiquet, Kévin, Barth, Timothy J., editor, Griebel, Michael, editor, Keyes, David E., editor, Nieminen, Risto M., editor, Roose, Dirk, editor, Schlick, Tamar, editor, Langer, Ulrich, editor, Discacciati, Marco, editor, Widlund, Olof B., editor, and Zulehner, Walter, editor

Published
2008
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50. Schwarz Waveform Relaxation Algorithms

Author

Halpern, Laurence, Barth, Timothy J., editor, Griebel, Michael, editor, Keyes, David E., editor, Nieminen, Risto M., editor, Roose, Dirk, editor, Schlick, Tamar, editor, Langer, Ulrich, editor, Discacciati, Marco, editor, Widlund, Olof B., editor, and Zulehner, Walter, editor

Published
2008
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