Parallel ELLPACK for shared memory multiprocessors

Abstract

This paper describes a parallel version of ELLPACK for shared memory multiprocessors. ELLPACK is a system for numerically solving elliptic PDEs. It consists of a very high level language for defining PDE problems and selecting methods of solution, and a library of approximately 50 problem solving modules. Each of the modules performs one of the basic steps in solving an elliptic PDE: discretization, reordering of equations and unknowns, linear system solution, etc. ELLPACK may be used to solve linear elliptic PDEs posed on general two-dimensional domains or in three-dimensional boxes, nonlinear problems, time-dependent problems and systems of elliptic equations. Earlier work considered three discretization modules ( five point star, hodie and hermite collocation), two linear system solution modules ( linpack spd band and jacobi cg) and a triple module ( hodie fft), which includes both discretization and solution, all for rectangular domains and simple boundary conditions. Here we describe parallel versions of six additional modules ( hermite collocation, hodie helmholtz, five point star, band ge, sor, symmetric sor cg) for general boundary conditions and domains, and discuss modifications to the ELLPACK preprocessor, the tool that translates an ELLPACK “program” into FORTRAN. The parallelization strategy is based on kernels, with the machine-dependent and performance critical code located in a relatively small number of kernels. We report performance of these parallel ELLPACK modules on a Sequent Symmetry S81 shared memory multiprocessor with 26 processors for two simple test problems, and a problem involving a composite laminate with spatially varying fiber orientations.