A Parallel Domain Decomposition Method For Parabolic Partial Differential Equations
Free (open access)
M S Ingber, C C Schmidt, J A Tanski & J Phillips
A parallel domain decomposition method is developed for the solution of three-dimensional parabolic partial differential equations. Within each subdomain, time is discretized using the generalized trapezoidal rule. The resulting modified Helmholtz equation is solved using the particular solution boundary element method which is a variant of the dual reciprocity method. Interfacial conditions between subdomains are satisfied using a Schwarz Neumann-Neumam iteration scheme. Outside of the first time step where zero initial flux is assumed on all interfacial boundaries, the initial estimates for the interfacial flux is given from the converged solutions from the previous step. This significantly reduces the number of iterations required to meet the convergence criterion.