Hierarchical matrix arithmetic with accumulated updates

2017/03/27 by Steffen Börm, Börm, Steffen
Computer Science · Engineering · Physics and Astronomy · #65F05 #65F08 #65F30 #65N22 #65N38 #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1703.09085

openalex publication_date 2017/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Die Berechnung optischer und elektrostatischer Gitterpotentiale

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