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

2 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 publicationASME 2012 Noise Control and Acoustics Division Conference at InterNoise 2012, NCAD 2012
Pages147-158
Number of pages12
DOIs
StatePublished - Dec 1 2012
EventASME 2012 Noise Control and Acoustics Division Conference at InterNoise 2012, NCAD 2012 - New York City, NY, United States
Duration: Aug 19 2012Aug 22 2012

Other

OtherASME 2012 Noise Control and Acoustics Division Conference at InterNoise 2012, NCAD 2012
CountryUnited States
CityNew York City, NY
Period8/19/128/22/12

Fingerprint

linear systems
sound waves
Linear systems
Acoustics
Radiation
Parallel algorithms
acoustics
Linear equations
linear equations
central processing units
degrees of freedom
Wavelength
inversions
low frequencies
formulations
coefficients
matrices
wavelengths

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering
  • 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 ASME 2012 Noise Control and Acoustics Division Conference at InterNoise 2012, NCAD 2012 (pp. 147-158) https://doi.org/10.1115/NCAD2012-0445
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. ASME 2012 Noise Control and Acoustics Division Conference at InterNoise 2012, NCAD 2012. 2012. pp. 147-158
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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 ASME 2012 Noise Control and Acoustics Division Conference at InterNoise 2012, NCAD 2012. pp. 147-158, ASME 2012 Noise Control and Acoustics Division Conference at InterNoise 2012, NCAD 2012, New York City, NY, United States, 8/19/12. https://doi.org/10.1115/NCAD2012-0445

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.

ASME 2012 Noise Control and Acoustics Division Conference at InterNoise 2012, NCAD 2012. 2012. p. 147-158.

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 ASME 2012 Noise Control and Acoustics Division Conference at InterNoise 2012, NCAD 2012. 2012. p. 147-158 https://doi.org/10.1115/NCAD2012-0445