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-Babuška-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).
Funding for this work was provided by the National Computing Facilities Foundation (NCF), under project numbers NRG-2000.07
and MP-068. Computing time was also provided by HPαC, Centre for High Performance Applied Computing at the Delft University
of Technology.