Sparse matrix and solver objects for parallel finite element simulation of multi-field problems

Abstract

In this paper, we present an object-oriented concept of sparse matrix and iterative linear solver for large scale parallel and sequential finite element analysis of multi-field problems. With the present concept, the partitioning and parallel solving of linear equation systems can be easily realized, and the memory usage to solve coupled multi-field problems is optimized. For the parallel computing, the present objects are tailored to the domain decomposition approach for both equation assembly and linear solver. With such approach, the assembly of a global equation system is thoroughly avoided. Parallelization is realized in the sparse matrix object by the means of (1) enable the constructor of the sparse matrix class to use domain decomposition data to establish the local domain sparse pattern and (2) introduce MPI calls into the member function of matrix-vector multiplication to collect local results and form global solutions. The performance of these objects in C++ is demonstrated by a geotechnical application of 3D thermal, hydraulic and mechanical (THM) coupled problem in parallel manner. © 2010 Springer-Verlag.