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 B.

AU - Shontz, Suzanne M.

PY - 2012

Y1 - 2012

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.

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U2 - 10.1115/NCAD2012-0445

DO - 10.1115/NCAD2012-0445

M3 - Conference contribution

AN - SCOPUS:84884839873

SN - 9780791845325

T3 - American Society of Mechanical Engineers, Noise Control and Acoustics Division (Publication) NCAD

SP - 147

EP - 158

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

T2 - ASME 2012 Noise Control and Acoustics Division Conference at InterNoise 2012, NCAD 2012

Y2 - 19 August 2012 through 22 August 2012

ER -