Solver Interface Research Articles

A semi-explicit parallel solver for viscous incompressible flows

An incompressible viscous flow solver is parallelized using a database management program GPAR developed for parallel/domain decomposition. The approach presented involves subdivision of the flow domain into sub-domains called solution blocks and distribution of the solution blocks to network of computers. The equations for each block are solved in block solvers, while the information exchange between neighboring blocks is achieved via interface solvers. The data structure for communication between block and interface solvers are provided by GPAR. The incompressible flow solver is based on the fractional step method in which the momentum equations are solved explicitly while the pressure equation is solved implicitly. Results are presented illustrating the performance of the algorithms with increasing number of blocks and processors.

Fast computations with the harmonic Poincaré–Steklov operators on nested refined meshes

In this paper we develop asymptotically optimal algorithms for fast computations with the discrete harmonic Poincare–Steklov operators (Dirichlet–Neumann mapping) for interior and exterior problems in the presence of a nested mesh refinement. Our approach is based on the multilevel interface solver applied to the Schur complement reduction onto the nested refined interface associated with a nonmatching decomposition of a polygon by rectangular substructures. This paper extends methods from Khoromskij and Prossdorf (1995), where the finite element approximations of interior problems on quasi‐uniform grids have been considered. For both interior and exterior problems, the matrix–vector multiplication with the compressed Schur complement matrix on the interface is shown to have a complexity of the order O(Nr log3Nu), where Nr = O((1 + pr) Nu) is the number of degrees of freedom on the polygonal boundary under consideration, Nu is the boundary dimension of a finest quasi‐uniform level and pr ⩾ 0 defines the refinement depth. The corresponding memory needs are estimated by O(Nr logqNu), where q = 2 or q = 3 in the case of interior and exterior problems, respectively.