Parallel decomposition methods in trace spaces

Two-level iterative Krylov's conjugate direction methods are proposed for the traces of solutions on the internal boundaries of subdomains in the case of spatial decomposition of multidimensional boundary value problems. The global iterative process consists in solving the Poincare–Steklov equation with overlapping and without overlapping of subdomains. The local iterative process consists in solving independent auxiliary problems in the subdomains. The effect of the subdomain overlapping size, the types of iterated internal boundary conditions, and the accuracy of the solutions to the auxiliary boundary value problems on the convergence rate of the decomposition methods is experimentally studied. Some results of solving a number of representative model boundary value problems are discussed. These results confirm the efficiency of parallelization of the decomposition methods on multiprocessor computing system with distributed and shared memory, depending on the chosen values of computational parameters of the iterative processes.