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.
Cite
@article{arxiv.1703.09085,
title = {Hierarchical matrix arithmetic with accumulated updates},
author = {Steffen Börm},
journal= {arXiv preprint arXiv:1703.09085},
year = {2019}
}