Deflated BiCG with an Application to Model Reduction

Most calculations in model reduction involve the solutions of a sequence of dual linear systems with multiple right-hand sides. To solve such systems efficiently, a new deflated BiCG method is explored in this paper. The proposed algorithm uses harmonic Ritz vectors to approximate left and right inv...

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Main Authors:	Jing Meng, Pei-Yong Zhu, Hou-Biao Li
Format:	Article
Language:	English
Published:	Hindawi Limited 2015-01-01
Series:	Mathematical Problems in Engineering
Online Access:	http://dx.doi.org/10.1155/2015/372109

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record_format	Article
spelling	doaj-40e5f909d26543ee930dc1b04dc2d0cb2020-11-25T01:02:23ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472015-01-01201510.1155/2015/372109372109Deflated BiCG with an Application to Model ReductionJing Meng0Pei-Yong Zhu1Hou-Biao Li2School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, ChinaSchool of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, ChinaSchool of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, ChinaMost calculations in model reduction involve the solutions of a sequence of dual linear systems with multiple right-hand sides. To solve such systems efficiently, a new deflated BiCG method is explored in this paper. The proposed algorithm uses harmonic Ritz vectors to approximate left and right invariant subspaces inexpensively via small descenting direction vectors found by subsequent runs of deflated BiCG and then derives the deflated subspaces for the next pair of dual linear systems. This process leads to faster convergence for the next pair of systems. Numerical examples illustrate the effectiveness of the proposed method.http://dx.doi.org/10.1155/2015/372109
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Jing Meng Pei-Yong Zhu Hou-Biao Li
spellingShingle	Jing Meng Pei-Yong Zhu Hou-Biao Li Deflated BiCG with an Application to Model Reduction Mathematical Problems in Engineering
author_facet	Jing Meng Pei-Yong Zhu Hou-Biao Li
author_sort	Jing Meng
title	Deflated BiCG with an Application to Model Reduction
title_short	Deflated BiCG with an Application to Model Reduction
title_full	Deflated BiCG with an Application to Model Reduction
title_fullStr	Deflated BiCG with an Application to Model Reduction
title_full_unstemmed	Deflated BiCG with an Application to Model Reduction
title_sort	deflated bicg with an application to model reduction
publisher	Hindawi Limited
series	Mathematical Problems in Engineering
issn	1024-123X 1563-5147
publishDate	2015-01-01
description	Most calculations in model reduction involve the solutions of a sequence of dual linear systems with multiple right-hand sides. To solve such systems efficiently, a new deflated BiCG method is explored in this paper. The proposed algorithm uses harmonic Ritz vectors to approximate left and right invariant subspaces inexpensively via small descenting direction vectors found by subsequent runs of deflated BiCG and then derives the deflated subspaces for the next pair of dual linear systems. This process leads to faster convergence for the next pair of systems. Numerical examples illustrate the effectiveness of the proposed method.
url	http://dx.doi.org/10.1155/2015/372109
work_keys_str_mv	AT jingmeng deflatedbicgwithanapplicationtomodelreduction AT peiyongzhu deflatedbicgwithanapplicationtomodelreduction AT houbiaoli deflatedbicgwithanapplicationtomodelreduction
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Deflated BiCG with an Application to Model Reduction

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