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

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.