Solving the Helmholtz Equation At High-Wave Numbers On a Parallel Computer With a Shared Virtual Memory

Abstract

In this paper, we address the implementation of finite element codes on a parallel computer providing a shared virtual memory. We solve the Helmholtz equa tion at high-wave numbers by a method combining the least-squares formulation and finite-element dis cretization. Numerical experiments concerning the scattering of planar waves by nonconvex obstacles show the efficiency of the new algorithm. Parallelism relies heavily on shared variables and parallel loops; performances are enhanced by considering local ver sus global nodes and by renumbering the mesh. Ex periments are implemented on a KSR computer with up to 20 processors.