Parallel implementation of a least-squares spectral element solver for incompressible flow problems

Abstract

Least-squares spectral element methods are based on two important and successful numerical methods: spectral/hp element methods and least-squares finite element methods. Least-squares methods lead to symmetric and positive definite algebraic systems which circumvent the Ladyzhenskaya-Babuska-Brezzi stability condition and consequently allow the use of equal order interpolation polynomials for all variables. In this paper, we present results obtained with a parallel implementation of the least-squares spectral element solver on a distributed memory machine (Cray T3E) and on a virtual shared memory machine (SGI Origin 3800). © 2002 Springer-Verlag Berlin Heidelberg.