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Title: Iterative solution of multiple radiation and scattering problems in structural acoustics using the BL-QMR algorithm

Abstract

Finite-element discretizations of time-harmonic acoustic wave problems in exterior domains result in large sparse systems of linear equations with complex symmetric coefficient matrices. In many situations, these matrix problems need to be solved repeatedly for different right-hand sides, but with the same coefficient matrix. For instance, multiple right-hand sides arise in radiation problems due to multiple load cases, and also in scattering problems when multiple angles of incidence of an incoming plane wave need to be considered. In this talk, we discuss the iterative solution of multiple linear systems arising in radiation and scattering problems in structural acoustics by means of a complex symmetric variant of the BL-QMR method. First, we summarize the governing partial differential equations for time-harmonic structural acoustics, the finite-element discretization of these equations, and the resulting complex symmetric matrix problem. Next, we sketch the special version of BL-QMR method that exploits complex symmetry, and we describe the preconditioners we have used in conjunction with BL-QMR. Finally, we report some typical results of our extensive numerical tests to illustrate the typical convergence behavior of BL-QMR method for multiple radiation and scattering problems in structural acoustics, to identify appropriate preconditioners for these problems, and to demonstrate the importancemore » of deflation in block Krylov-subspace methods. Our numerical results show that the multiple systems arising in structural acoustics can be solved very efficiently with the preconditioned BL-QMR method. In fact, for multiple systems with up to 40 and more different right-hand sides we get consistent and significant speed-ups over solving the systems individually.« less

Authors:
 [1]
  1. Stanford Univ., CA (United States)
Publication Date:
Research Org.:
Front Range Scientific Computations, Inc., Lakewood, CO (United States)
OSTI Identifier:
440719
Report Number(s):
CONF-9604167-Vol.2
ON: DE96015307; TRN: 97:000721-0041
Resource Type:
Conference
Resource Relation:
Conference: Copper Mountain conference on iterative methods, Copper Mountain, CO (United States), 9-13 Apr 1996; Other Information: PBD: [1996]; Related Information: Is Part Of Copper Mountain conference on iterative methods: Proceedings: Volume 2; PB: 242 p.
Country of Publication:
United States
Language:
English
Subject:
99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; ACOUSTICS; MATHEMATICAL MODELS; SCATTERING; CONVERGENCE; ITERATIVE METHODS; MATRICES; PARTIAL DIFFERENTIAL EQUATIONS; SOUND WAVES

Citation Formats

Malhotra, M. Iterative solution of multiple radiation and scattering problems in structural acoustics using the BL-QMR algorithm. United States: N. p., 1996. Web.
Malhotra, M. Iterative solution of multiple radiation and scattering problems in structural acoustics using the BL-QMR algorithm. United States.
Malhotra, M. Tue . "Iterative solution of multiple radiation and scattering problems in structural acoustics using the BL-QMR algorithm". United States. https://www.osti.gov/servlets/purl/440719.
@article{osti_440719,
title = {Iterative solution of multiple radiation and scattering problems in structural acoustics using the BL-QMR algorithm},
author = {Malhotra, M},
abstractNote = {Finite-element discretizations of time-harmonic acoustic wave problems in exterior domains result in large sparse systems of linear equations with complex symmetric coefficient matrices. In many situations, these matrix problems need to be solved repeatedly for different right-hand sides, but with the same coefficient matrix. For instance, multiple right-hand sides arise in radiation problems due to multiple load cases, and also in scattering problems when multiple angles of incidence of an incoming plane wave need to be considered. In this talk, we discuss the iterative solution of multiple linear systems arising in radiation and scattering problems in structural acoustics by means of a complex symmetric variant of the BL-QMR method. First, we summarize the governing partial differential equations for time-harmonic structural acoustics, the finite-element discretization of these equations, and the resulting complex symmetric matrix problem. Next, we sketch the special version of BL-QMR method that exploits complex symmetry, and we describe the preconditioners we have used in conjunction with BL-QMR. Finally, we report some typical results of our extensive numerical tests to illustrate the typical convergence behavior of BL-QMR method for multiple radiation and scattering problems in structural acoustics, to identify appropriate preconditioners for these problems, and to demonstrate the importance of deflation in block Krylov-subspace methods. Our numerical results show that the multiple systems arising in structural acoustics can be solved very efficiently with the preconditioned BL-QMR method. In fact, for multiple systems with up to 40 and more different right-hand sides we get consistent and significant speed-ups over solving the systems individually.},
doi = {},
url = {https://www.osti.gov/biblio/440719}, journal = {},
number = ,
volume = ,
place = {United States},
year = {1996},
month = {12}
}

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