Efficient Preconditioning of hp -FEM Matrices by Hierarchical Low-Rank Approximations
作者: P. GattoJ. S. Hesthaven
作者单位: 1RWTH Aachen University
2École Polytechnique Fédérale de Lausanne (EPFL)
刊名: Journal of Scientific Computing, 2017, Vol.72 (1), pp.49-80
来源数据库: Springer Journal
DOI: 10.1007/s10915-016-0347-x
关键词: Preconditioned GMRESInterpolative decompositionIndefinite operators
英文摘要: We introduce a preconditioner based on a hierarchical low-rank compression scheme of Schur complements. The construction is inspired by standard nested dissection, and relies on the assumption that the Schur complements can be approximated, to high precision, by Hierarchically-Semi-Separable matrices. We build the preconditioner as an approximate \(LDM^t\) factorization of a given matrix A , and no knowledge of A in assembled form is required by the construction. The \(LDM^t\) factorization is amenable to fast inversion, and the action of the inverse can be determined fast as well. We investigate the behavior of the preconditioner in the context of DG finite element approximations of elliptic and hyperbolic problems, with respect to both the mesh size and the order of approximation.
原始语种摘要: We introduce a preconditioner based on a hierarchical low-rank compression scheme of Schur complements. The construction is inspired by standard nested dissection, and relies on the assumption that the Schur complements can be approximated, to high precision, by Hierarchically-Semi-Separable matrices. We build the preconditioner as an approximate \(LDM^t\) factorization of a given matrix A , and no knowledge of A in assembled form is required by the construction. The \(LDM^t\) factorization is amenable to fast inversion, and the action of the inverse can be determined fast as well. We investigate the behavior of the preconditioner in the context of DG finite element approximations of elliptic and hyperbolic problems, with respect to both the mesh size and the order of approximation.
全文获取路径: Springer  (合作)
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来源刊物:
影响因子:1.71 (2012)

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关键词翻译
关键词翻译
  • factorization 因式分解
  • hierarchical 分级
  • compression 压缩
  • approximate 近似的
  • inspired 吸入的
  • complements 互补商品
  • construction 构造
  • action 行为
  • respect 珍视
  • elliptic 椭圆形的