The paper deals with the efficient parallelization of least-squares spectral element methods for incompressible flows. The parallelization of this sort of problems requires two different strategies. On the one hand, the spectral element discretization benefits from an element-by-element parallelization strategy. On the other hand, an efficient strategy to solve the large sparse global systems benefits from a row-wise distribution of data. This requires two different kinds of data distributions and the conversion between them is rather complicated. In the present paper, the different strategies together with its conversion are discussed. Moreover, some results obtained on a distributed memory machine (Cray T3E) are presented.

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Springer
Lecture Notes in Computer Science
Parallel implementation of a sparse grid method for time-dependent advection-diffusion reaction problems
International Meeting on High Performance Computing for Computational Science
Scientific Computing

Nool, M., & Proot, M. M. J. (2003). A parallel, state-of-the-art, least-squares spectral element solver for incompressible flow problems. In Lecture Notes in Computer Science (pp. 39–52). Springer.