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Hierarchical matrix arithmetic with accumulated updates

Numerical Analysis 2019-06-13 v3 Numerical Analysis

Abstract

Hierarchical matrices can be used to construct efficient preconditioners for partial differential and integral equations by taking advantage of low-rank structures in triangular factorizations and inverses of the corresponding stiffness matrices. The setup phase of these preconditioners relies heavily on low-rank updates that are responsible for a large part of the algorithm's total run-time, particularly for matrices resulting from three-dimensional problems. This article presents a new algorithm that significantly reduces the number of low-rank updates and can reduce the setup time by 50 percent or more.

Keywords

Cite

@article{arxiv.1703.09085,
  title  = {Hierarchical matrix arithmetic with accumulated updates},
  author = {Steffen Börm},
  journal= {arXiv preprint arXiv:1703.09085},
  year   = {2019}
}
R2 v1 2026-06-22T18:57:56.590Z