Domain Decomposition Methods for Solving Stokes--Darcy Problems with Boundary Integrals

Abstract

We consider a coupled problem of Stokes and Darcy equations. This involves solving PDEs of different orders simultaneously. To overcome this difficulty, we apply a nonoverlapping domain decomposition method based on a Robin boundary condition obtained by combining the velocity and force interface conditions. The coupled system is then reduced to solving each problem separately by an iterative procedure using a Krylov subspace method. The numerical solution in each subdomain is based on the boundary integral formulation, where the kernels are regularized and correction terms are added to reduce the regularization error.