### 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 language | English (US) |
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Title of host publication | ASME 2012 Noise Control and Acoustics Division Conference at InterNoise 2012, NCAD 2012 |

Pages | 147-158 |

Number of pages | 12 |

DOIs | |

State | Published - Dec 1 2012 |

Event | ASME 2012 Noise Control and Acoustics Division Conference at InterNoise 2012, NCAD 2012 - New York City, NY, United States Duration: Aug 19 2012 → Aug 22 2012 |

### Other

Other | ASME 2012 Noise Control and Acoustics Division Conference at InterNoise 2012, NCAD 2012 |
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Country | United States |

City | New York City, NY |

Period | 8/19/12 → 8/22/12 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mechanical Engineering
- Acoustics and Ultrasonics

### Cite this

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

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*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Parallel boundary element solutions of block circulant linear systems for acoustic radiation problems with rotationally symmetric boundary surfaces

AU - Czuprynski, Kenneth D.

AU - Fahnline, John Brian

AU - Shontz, Suzanne M.

PY - 2012/12/1

Y1 - 2012/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84884839873&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84884839873&partnerID=8YFLogxK

U2 - 10.1115/NCAD2012-0445

DO - 10.1115/NCAD2012-0445

M3 - Conference contribution

SN - 9780791845325

SP - 147

EP - 158

BT - ASME 2012 Noise Control and Acoustics Division Conference at InterNoise 2012, NCAD 2012

ER -