Algorithm and Implementation of Fast Multipole Boundary Element Method with Theoretical Analysis for Two-Dimensional Heat Conduction Problems

This paper presents the fast multipole boundary element method (FM-BEM) as a new BEM solution methodology that overcomes many disadvantages of conventional BEM. In conventional BEM, large-scale problems cannot be treated easily because the computation time increases rapidly with an increase in the number of boundary elements owing to the dense coefficient matrix. Analysis results are obtained to compare FM-BEM with conventional BEM in terms of computation time and accuracy for a simple two-dimensional steady-state heat conduction problem. It is confirmed that the FM-BEM solution methodology greatly enhances the computation speed while maintaining solution accuracy similar to that of conventional BEM. As a result, the theory and implementation algorithm of FM-BEM are discussed in this study.