A parallel implementation of the boundary element method for heat conduction analysis in heterogeneous media

Abstract

A direct boundary element formulation is implemented on a parallel computer using MPI (message passing interface). This implementation solves potential problems, specifically heat conduction problems in heterogeneous media. Single-zone problems, where at least one boundary condition is known at every node on the boundary, produce dense, asymmetric coefficient matrices which are relatively easy to distribute and solve in parallel. Multi-zone problems, where no boundary conditions are specified at nodes on the heterogeneity interfaces, produce coefficient matrices which contain some unpopulated blocks. The parallel data distribution of the coefficient matrix for the multi-zone case is performed so that the populated blocks are evenly distributed across the processors to balance the computational load. Several application problems are solved to find the effect of various input parameters on the effective thermal conductivity. The numerical results agree well with experimental data and analytical models over the volume fractions and thermal conductivity ratios considered.