A highly efficient multidomain BEM for multimillion subdomains

This paper presents a 2D multidomain boundary element method (BEM) for potential problems using mixed boundary elements. The aim of the paper is to test the developed numerical method for solving multimillion DOFs under extreme conditions: high element aspect ratios and high conductivity ratios. The double precision for the system matrix was found to be necessary for the solution for multimillion DOFs. The accuracy, robustness, and efficiency of the developed BEM are demonstrated by solving a nine million node mesh within a few days. A one million node mesh is solved in 1 h using a 3.4 GHz personal computer and 3 GB of memory in double precision. The main numerical example is heat diffusion in the intricate fractal geometry of the Koch snowflake.