Iterative solution of multiple radiation and scattering problems in structural acoustics using the BLQMR algorithm
Abstract
Finiteelement discretizations of timeharmonic 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 righthand sides, but with the same coefficient matrix. For instance, multiple righthand 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 BLQMR method. First, we summarize the governing partial differential equations for timeharmonic structural acoustics, the finiteelement discretization of these equations, and the resulting complex symmetric matrix problem. Next, we sketch the special version of BLQMR method that exploits complex symmetry, and we describe the preconditioners we have used in conjunction with BLQMR. Finally, we report some typical results of our extensive numerical tests to illustrate the typical convergence behavior of BLQMR method for multiple radiation and scattering problems in structural acoustics, to identify appropriate preconditioners for these problems, and to demonstrate the importancemore »
 Authors:

 Stanford Univ., CA (United States)
 Publication Date:
 Research Org.:
 Front Range Scientific Computations, Inc., Lakewood, CO (United States)
 OSTI Identifier:
 440719
 Report Number(s):
 CONF9604167Vol.2
ON: DE96015307; TRN: 97:0007210041
 Resource Type:
 Conference
 Resource Relation:
 Conference: Copper Mountain conference on iterative methods, Copper Mountain, CO (United States), 913 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 BLQMR algorithm. United States: N. p., 1996.
Web.
Malhotra, M. Iterative solution of multiple radiation and scattering problems in structural acoustics using the BLQMR algorithm. United States.
Malhotra, M. Tue .
"Iterative solution of multiple radiation and scattering problems in structural acoustics using the BLQMR 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 BLQMR algorithm},
author = {Malhotra, M},
abstractNote = {Finiteelement discretizations of timeharmonic 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 righthand sides, but with the same coefficient matrix. For instance, multiple righthand 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 BLQMR method. First, we summarize the governing partial differential equations for timeharmonic structural acoustics, the finiteelement discretization of these equations, and the resulting complex symmetric matrix problem. Next, we sketch the special version of BLQMR method that exploits complex symmetry, and we describe the preconditioners we have used in conjunction with BLQMR. Finally, we report some typical results of our extensive numerical tests to illustrate the typical convergence behavior of BLQMR 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 Krylovsubspace methods. Our numerical results show that the multiple systems arising in structural acoustics can be solved very efficiently with the preconditioned BLQMR method. In fact, for multiple systems with up to 40 and more different righthand sides we get consistent and significant speedups over solving the systems individually.},
doi = {},
url = {https://www.osti.gov/biblio/440719},
journal = {},
number = ,
volume = ,
place = {United States},
year = {1996},
month = {12}
}