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

TL;DR

This paper develops and analyzes an optimized Schwarz waveform relaxation algorithm with advanced transmission conditions for heterogeneous advection-diffusion-reaction problems, incorporating discontinuous Galerkin time-stepping and mortar finite elements for improved accuracy and efficiency.

Contribution

It introduces a novel domain decomposition method with optimized interface conditions and semi-discretization analysis tailored for complex heterogeneous problems.

Findings

Effective convergence with optimized Robin and Ventcell conditions

Successful implementation of DG time-stepping in the algorithm

Numerical results demonstrate improved accuracy in 2D heterogeneous problems

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.