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Title: Improvement of Hierarchical Matrices with Adaptive Cross Approximation for Large-scale Simulation
Authors: Ida, Akihiro
Iwashita, Takeshi
Ohtani, Makiko
Hirahara, Kazuro
Author's alias: 伊田, 明弘
Keywords: low-rank approximation
hierarchical matrices
adaptive cross approximation
integral equation method
earthquake cycle simulation
Issue Date: 2015
Publisher: Information Processing Society of Japan
Journal title: Journal of Information Processing
Volume: 23
Issue: 3
Start page: 366
End page: 372
Abstract: We propose an improved method for hierarchical-matrices (H-matrices) using adaptive cross approximation (ACA) as the low-rank approximation. The improvement consists of a kind of normalization and a new stopping criterion for the ACA. By using the proposed method, we can avoid the trouble that ranks of approximated matrices increase rapidly as the matrix size increases when the conventional H-matrices with ACA are employed to an integral equation whose kernel function has high-order singularities. In particular, application of the proposed method enables us to perform large-scale simulations such that the conventional H-matrices with ACA fail to construct the low-rank approximation. Applicability of the proposed method is confirmed through numerical experiments on an earthquake cycle simulation.
Rights: Notice for the use of this material The copyright of this material is retained by the Information Processing Society of Japan (IPSJ). This material is published on this web site with the agreement of the author (s) and the IPSJ. Please be complied with Copyright Law of Japan and the Code of Ethics of the IPSJ if any users wish to reproduce, make derivative work, distribute or make available to the public any part or whole thereof. All Rights Reserved, Copyright (C) Information Processing Society of Japan.
DOI(Published Version): 10.2197/ipsjjip.23.366
Appears in Collections:Journal Articles

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