A Hierarchical Preconditioner within Edge Based BE-FE Coupling in Electromagnetism

Abstract

In this paper, a numerical algorithm solving large sparse linear systems that arise in electromagnetic field computation will be presented. It is based on hierarchical partitioning of the matrix and uses block-wise low-rank approximation in combination with element dropping in order to construct a preconditioner for iterative solution. Within the BE-FE coupling, this approximate factorisation is applied as preconditioner for the FE system. The treatment of multiply connected domains will also be described. The efficiency of the presented solver will be shown by means of an electromagnetic valve.