A fast direct solver for elliptic problems on general meshes in 2D

Authors:
Phillip G. Schmitz;Lexing Ying
Affiliations:
Department of Mathematics, The University of Texas at Austin, 1 University Station, C1200, Austin, Texas 78712, United States;Department of Mathematics and ICES, The University of Texas at Austin, 1 University Station, C1200, Austin, Texas 78712, United States
Venue:
Journal of Computational Physics
Year:
2012

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Abstract

We present a fast direct algorithm for solutions to linear systems arising from 2D elliptic equations. We follow the approach in Xia et al. (2009) on combining the multifrontal method with hierarchical matrices. We present a variant of that approach with additional hierarchical structure, extend it to quasi-uniform meshes, and detail an adaptive decomposition procedure for general meshes. Linear time complexity is shown for a quasi-regular grid and demonstrated via numerical results for the adaptive algorithm.