A parallel domain decomposition boundary element method (BEM) was developed for the solution of 3-dimensional multi-species diffusion problems. The chemical species were uncoupled in the interior of the domain but couple at the boundary through a non-linear surface reaction equation. The method of lines was used whereby time was discretized using the finite difference method and space was discretized using the boundary element method. The original problem was transformed into a sequence of inhomogeneous modified Helmholtz equations. A Schwarz Neumann–Neumann iteration scheme was used to satisfy interfacial boundary conditions between sub-domains. A segregated solver based on a quasi-predictor–corrector time integrator was used to satisfy the non-linear boundary conditions on the reactive surfaces. The accuracy and parallel efficiency of the method was demonstrated through a benchmark problem.

A Parallel Domain Decomposition BEM for Diffusion Problems with Surface Reactions. M.S.Ingber, J.A.Tanskin: Engineering Analysis with Boundary Elements, 2005, 29[9], 878-85