Parallel penalty combinations for singularity problems

Abstract

Listen

Translate article

An embedding technique is presented in this paper to implement penalty combinations into parallel by the iterative substructuring method. Penalty combinations using a penalty integral are much simpler than the direct nonconforming constraints to match different admissible functions. In the penalty combinations, the Ritz-Galerkin method is used in the singular subdomains Ω + where there exist solution singularities. The singular particular solutions are chosen to be admissible functions so that only a few of them are needed, to cope well with the difference grids in the finite difference methods used in the rest of the solution domain. Consequently, while applying the iterative substructuring methods, we may attain the singular domain Ω + to the interface of two subregions in the domain decomposition methods, and regard Ω + as a ‘fat’ interface or call an interface ‘zone’. The matrix contribution resulting from Ω + can be included in the preconditioner matrix due to a few of unknown coefficients to be sought. The new embedding technique may reform penalty combinations easily into parallel computing by the existing, domain decomposition methods. Such a technique has been proven to be effective, by a brief analysis and numerical experiments of Motz's problem given in this paper.