Least-squares spectral element methods are based on two important and successful numerical methods: spectral/{\em hp} element methods and least-squares finite element methods. Least-squares methods lead to symmetric and positive definite algebraic systems which circumvent the Ladyzhenskaya-Babu\v{s}ka-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).

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Springer
P.M.A. Sloot (Peter) , C.J. Kenneth Tan , J.J. Dongarra , A.G. Hoekstra (Alfons)
Lecture Notes in Computer Science
Parallel implementation of a sparse grid method for time-dependent advection-diffusion reaction problems
International Conference on Computational Science
Scientific Computing

Nool, M., & Proot, M. M. J. (2002). Parallel Implementation of a Least-Squares Spectral Element Solver for Incomressible Flow Problems. In P. Sloot, C. J. Kenneth Tan, J. J. Dongarra, & A. Hoekstra (Eds.), The 2002 International Conference on Computational Science (pp. 900–909). Springer.