A parallel domain decomposition BEM for diffusion problems with surface reactions

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