A Strategy for BEM Modeling of Large-Scale Three-Dimensional Heat Transfer Problems

摘要

The boundary element method (BEM) only requires a surface mesh to solve heat conduction problems. However, the resulting matrix is full populated. For large-scale problems , this poses serious challenges due storage requirements and iterative solution of a large set of non-symmetric equations. The BEM community approaches this problem by: 1. artificial sub-sectioning of the 3-D model into a multi-region model in conjunction with block-solvers reminiscent of FEM frontal solvers, and 2. multipole methods in conjunction with GMRES non-symmetric iterative solver. We propose to adopt the first approach, however, we use region-by-region iteration. For linear problems, the process converges efficiently, offers substantial savings in memory, and does not require complex data-structure preparation. Several examples are presented and rectangular bar nd a 3-D thurst vector control vane geometries are considered.