Parallelized iterative domain decomposition boundary element method for thermoelasticity in piecewise non-homogeneous media

The boundary element method (BEM) requires only a surface mesh to solve thermoelasticity problems, however, the resulting matrix is fully populated and non-diagonally dominant. Solution of non-homogeneous media by BEM is also problematic due to the lack of a general non-homogeneous fundamental solution. BEM solution of large-scale problems also pose serious challenges due to both storage requirements and the solution of large sets of non-symmetric systems of equations. In this article, we propose an effective and efficient iterative domain decomposition, or artificial sub-sectioning technique, along with a region-by-region iteration algorithm particularly tailored for parallel computation to address these issues. The domain decomposition approach effectively reduces the condition numbers of the resulting algebraic systems, while increasing efficiency of the solution process and decreasing memory requirements. Moreover, the approach lends itself to solving problems with piecewise non-homogeneities. The iterative process converges very efficiently while offering substantial savings in memory. The iterative domain decomposition technique is ideally suited for parallel computation. Results demonstrate the validity of the approach by providing solutions that compare closely to single-region BEM solutions and benchmark analytical solutions.