### 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 | 41st International Congress and Exposition on Noise Control Engineering 2012, INTER-NOISE 2012 |

Pages | 4115-4126 |

Number of pages | 12 |

State | Published - Dec 1 2012 |

Event | 41st International Congress and Exposition on Noise Control Engineering 2012, INTER-NOISE 2012 - New York, NY, United States Duration: Aug 19 2012 → Aug 22 2012 |

### Publication series

Name | 41st International Congress and Exposition on Noise Control Engineering 2012, INTER-NOISE 2012 |
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Volume | 5 |

### Other

Other | 41st International Congress and Exposition on Noise Control Engineering 2012, INTER-NOISE 2012 |
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Country | United States |

City | New York, NY |

Period | 8/19/12 → 8/22/12 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Acoustics and Ultrasonics

### Cite this

*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).

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*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.

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=84883585042&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84883585042&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84883585042

SN - 9781627485609

T3 - 41st International Congress and Exposition on Noise Control Engineering 2012, INTER-NOISE 2012

SP - 4115

EP - 4126

BT - 41st International Congress and Exposition on Noise Control Engineering 2012, INTER-NOISE 2012

ER -