DD17 Strobl
Schwarz waveform relaxation algorithms : theory and applications

Speaker: Laurence Halpern

Abstract

To solve evolution problems in parallel, many strategies are available: amongst them, implicit time schemes with domain decomposition in space or explicit time schemes with interpolation on the boundary. These two methods have several limitations: in the first case a common time step must be used in each subdomain, while the second case exhibits a lack of stability for hyperbolic problems.

Schwarz Waveform relaxation algorithms develop a completely different strategy: on the continuous level, they compute a solution on each subdomain in space, over the whole time interval, or over time windows. Transmission conditions of differential or integral type on the boundary then transmit the information to the neighbours at the end of the time interval. They are optimized so as to minimize the convergence rate for the interface problem. These algorithms can be used with or without overlap, and thus the discretization can be made independently in the subdomains. This allows for a large versatility: one can deal with large discontinuities in the coefficients, adapt the time step locally, use different numerical methods in different parts of the computational domain, and even different equations and different codes.

In this presentation, I shall give an overview of the algorithms we use, for hyperbolic or parabolic problems. In the parabolic case, a skillful choice of the transmission conditions will allow the convergence rates to be almost independent of the mesh size. In the hyperbolic case, we use absorbing boundary conditions with overlap, and optimize the coefficients. I shall also show how this method produces a "natural" mesh refinement in time and space. Each case is illustrated with numerical experiments.


< Back | ^ Top
URL: www.ricam.oeaw.ac.at/events/conferences/dd17/invited_speakers/abstracts/abstract_halpern.php

This page was made with 100% valid HTML & CSS - Send comments to Webmaster
Today's date and time is 03/28/24 - 12:24 CEST and this file (/events/conferences/dd17/invited_speakers/abstracts/abstract_halpern.php) was last modified on 06/21/06 - 10:00 CEST