Multi-Level Boundary Element Methods for Steady Heat Diffusion in Three-Dimensions

Abstract

We have recently developed a novel multi-level boundary element method (MLBEM) for steady heat diffusion in irregular two-dimensional domains (Numerical Heat Transfer Part B: Fundamentals, 46: 329–356, 2004). This presentation extends the MLBEM methodology to three-dimensional problems. First, we outline a 3-D MLBEM formulation for steady heat diffusion and discuss the differences between multi-level algorithms for two and three dimensions. Then, we consider an example problem that involves heat conduction in a semi-infinite three-dimensional domain. We investigate the performance of the MLBEM formulation using a single-patch approach. The MLBEM algorithms are shown facilitate fast and accurate numerical solutions with no loss of the solution accuracy. More dramatic speed-ups can be achieved provided that patch-edge corrections are also evaluated using multi-level technique.