6 papers
Perfectly Matched Layers on Cubic Domains forPauli's Equations
Laurence Halpern, Jeffrey Rauch
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 computatio…
A new Algorithm Based on Factorization for Heterogeneous Domain Decomposition
Martin J. Gander, Laurence Halpern, Véronique Martin
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…
Optimized Schwarz Waveform Relaxation for Advection Reaction Diffusion Equations in Two Dimensions
Daniel Bennequin, Martin J. Gander, Loic Gouarin +1
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 a…
The Analysis of Matched Layers
Laurence Halpern, Sabrina Petit-Bergez, Jeffrey Rauch
A systematic analysis of matched layers is undertaken with special attention to better understand the remarkable method of Bérenger. We prove that the Bérenger and closely related…
Optimized Schwarz waveform relaxation and discontinuous Galerkin time stepping for heterogeneous problems
Laurence Halpern, Jérémie Szeftel, Caroline Japhet
We design and analyze a Schwarz waveform relaxation algorithm for domain decomposition of advection-diffusion-reaction problems with strong heterogeneities. The interfaces are curv…
Nonlinear Nonoverlapping Schwarz Waveform Relaxation for Semilinear Wave Propagation
Laurence Halpern, Jérémie Szeftel
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 conditi…