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

作者：Schmitz Phillip G^*; Ying Lexing

来源：Journal of Computational Physics, 2012, 231(4): 1314-1338.

DOI：10.1016/j.jcp.2011.10.013

• Elliptic equations
• Fast algorithms
• Multifrontal methods
• Hierarchical matrices
• Sparse matrix

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.

• 出版日期2012-2-20