Parallel boundary element solutions of block circulant linear systems for acoustic radiation problems with rotationally symmetric boundary surfaces

Kenneth D. Czuprynski, John Brian Fahnline, Suzanne M. Shontz

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

Abstract

We propose a distributed parallel algorithm for the solution of block circulant linear systems arising from acoustic radiation problems with rotationally symmetric boundary surfaces. When large structural acoustics problems are solved using a coupling finite element / boundary element formulation, the most time consuming part of the analysis is the solution of the linear system of equations for the boundary element computation. In general, the problem is solved frequency by frequency, and the coefficient matrix for the boundary element analysis is fully populated and exhibits no exploitable structure. This typically limits the number of acoustic degrees of freedom to 10-20 thousand. Because acoustic boundary element calculations require approximately six elements per wavelength to produce accurate solutions, the formation is limited to relatively low frequencies. However, when the outer surface of the structure is rotationally symmetric, the system of linear equations becomes block circulant. Building upon a known inversion formula for block circulant matrices, a parallel algorithm for the efficient solution of linear systems arising from acoustic radiation problems with rotationally symmetric boundary surfaces is developed. We show through a runtime, speedup, and efficiency analysis that the reductions in computation time are significant for an increasing number of processors.

Original languageEnglish (US)
Title of host publication41st International Congress and Exposition on Noise Control Engineering 2012, INTER-NOISE 2012
Pages4115-4126
Number of pages12
StatePublished - Dec 1 2012
Event41st International Congress and Exposition on Noise Control Engineering 2012, INTER-NOISE 2012 - New York, NY, United States
Duration: Aug 19 2012Aug 22 2012

Publication series

Name41st International Congress and Exposition on Noise Control Engineering 2012, INTER-NOISE 2012
Volume5

Other

Other41st International Congress and Exposition on Noise Control Engineering 2012, INTER-NOISE 2012
CountryUnited States
CityNew York, NY
Period8/19/128/22/12

Fingerprint

linear systems
sound waves
acoustics
linear equations
central processing units
degrees of freedom
inversions
low frequencies
formulations
coefficients
matrices
wavelengths

All Science Journal Classification (ASJC) codes

  • Acoustics and Ultrasonics

Cite this

Czuprynski, K. D., Fahnline, J. B., & Shontz, S. M. (2012). Parallel boundary element solutions of block circulant linear systems for acoustic radiation problems with rotationally symmetric boundary surfaces. In 41st International Congress and Exposition on Noise Control Engineering 2012, INTER-NOISE 2012 (pp. 4115-4126). (41st International Congress and Exposition on Noise Control Engineering 2012, INTER-NOISE 2012; Vol. 5).
Czuprynski, Kenneth D. ; Fahnline, John Brian ; Shontz, Suzanne M. / Parallel boundary element solutions of block circulant linear systems for acoustic radiation problems with rotationally symmetric boundary surfaces. 41st International Congress and Exposition on Noise Control Engineering 2012, INTER-NOISE 2012. 2012. pp. 4115-4126 (41st International Congress and Exposition on Noise Control Engineering 2012, INTER-NOISE 2012).
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Czuprynski, KD, Fahnline, JB & Shontz, SM 2012, Parallel boundary element solutions of block circulant linear systems for acoustic radiation problems with rotationally symmetric boundary surfaces. in 41st International Congress and Exposition on Noise Control Engineering 2012, INTER-NOISE 2012. 41st International Congress and Exposition on Noise Control Engineering 2012, INTER-NOISE 2012, vol. 5, pp. 4115-4126, 41st International Congress and Exposition on Noise Control Engineering 2012, INTER-NOISE 2012, New York, NY, United States, 8/19/12.

Parallel boundary element solutions of block circulant linear systems for acoustic radiation problems with rotationally symmetric boundary surfaces. / Czuprynski, Kenneth D.; Fahnline, John Brian; Shontz, Suzanne M.

41st International Congress and Exposition on Noise Control Engineering 2012, INTER-NOISE 2012. 2012. p. 4115-4126 (41st International Congress and Exposition on Noise Control Engineering 2012, INTER-NOISE 2012; Vol. 5).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Czuprynski KD, Fahnline JB, Shontz SM. Parallel boundary element solutions of block circulant linear systems for acoustic radiation problems with rotationally symmetric boundary surfaces. In 41st International Congress and Exposition on Noise Control Engineering 2012, INTER-NOISE 2012. 2012. p. 4115-4126. (41st International Congress and Exposition on Noise Control Engineering 2012, INTER-NOISE 2012).