An efficient direct parallel spectral-element solver for separable elliptic problems

Authors:
Yuen-Yick Kwan;Jie Shen
Affiliations:
Department of Mathematics, Purdue University West Lafayette, IN 47907, USA;Department of Mathematics, Purdue University West Lafayette, IN 47907, USA
Venue:
Journal of Computational Physics
Year:
2007

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Abstract

An efficient direct parallel elliptic solver based on the spectral element discretization is developed. The direct solver is based on a matrix decomposition approach which reduces multi-dimensional separable problems to a sequence of one-dimensional problems that can be efficiently handled by a static condensation process. Thanks to the spectral accuracy and the localized nature of a spectral element discretization, this elliptic solver is spectrally accurate and can be efficiently parallelized, and it can serve as an essential building block for large scale high-performance solvers in computational fluid dynamics and computational materials science.