Boundary element domain decomposition method and its parallelization for the problem exhibiting nonlinear boundary conditions

The problem with nonlinear mixed boundary condition, using boundary element method (BEM), results in the problem for solving nonlinear algebraic equations. We usually treat with the nonlinear algebraic equations by applying iterative scheme such as the Newton-Raphson method, which is generally not computationally efficient. Here, we propose more efficient scheme compared with conventional methods, by applying domain decomposition which we previously introduced to BEM analysis with help of parallel computing. The entire domain is decomposed into subdomains with fictitious boundaries taken inside and therefore, each subdomain becomes smaller. The size of resulting nonlinear equation is smaller, which can be solved more effectively. Radiation condition in the heat conduction problem is thought as the nonlinear boundary condition in this paper. We investigate relations between total computing times and size of the subdomain with nonlinear boundary conditions for the two-dimensional steady-state problem. Serial and parallel computations are tested. Computational experiments suggest high utility of the domain decomposition for the stated problem.