Fast Domain Decomposition Algorithm Using Barycentric Interpolation and Overlapping Subdomains for 3D Multiscale Problems

Abstract

A robust data-transfer process for balanced domain decomposition is presented. This algorithm reduces the number of mesh elements required to solve certain 3D multiscale problems with the finite element method. In some examples, a reduction factor of up to 5 has been observed. The reduction is achieved by introducing an overlapping auxiliary domain to an originally non-overlapping domain decomposition scheme, allowing for individual meshing of the subdomains. The data transfer to couple the individually meshed subdomains is performed with the help of barycentric interpolation. Hence, the advantages of parallel solution of subdomain problems is combined with a stable inter-subdomain data transfer. The developed algorithm can be applied on problems with a scalar valued second order spatial elliptic differential operator in various fields of engineering, such as semiconductors, huge and complex biological cell clusters, heat conducting and pressure problems on multiple scales.