Monika Eisenmann: A fully discretized domain decomposition approach for semi-linear SPDEs

Abstract:

In recent years, SPDEs have become a well-studied field in mathematics. With their increasing popularity, it has become important to efficiently approximate their solutions. Therefore, our goal is to develop a modern time-stepping method for SPDEs. We consider a fully discretized numerical scheme for parabolic stochastic partial differential equations. Our method is based on a non-iterative domain decomposition approach, which can help parallelize the code, leading to more efficient implementations.
 
The domain decomposition is integrated through an operator splitting approach, where each operator acts on a specific part of the domain. More precisely, we combine the implicit Euler method with the Douglas-Rachford splitting scheme. For an efficient space discretization of the underlying equation, we chose the discontinuous Galerkin method. We provide a strong space-time convergence result for this fully discretized scheme and verify our theoretical findings through numerical experiments.
 
This talk is based on a joint work with Eskil Hansen and Marvin Jans (both Lund University).