Computing Three-dimensional Acoustic Scattering Problems with Unique-solution Boundary Element Method
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摘要: 针对传统边界元法在求解外部声学问题时存在非唯一解的缺点,本文利用Burton-miller公式有效解决这一问题。对于Burton-miller公式引入的超奇异积分算子,采用奇异性减少技术进行弱奇异积分规划,有效避免了计算超奇异积分的困难,数值处理变得十分有效。此外,在算法中还采用有效的块对角预处理迭代求解器加速求解线性方程系统,全面提高算法的计算效率。数值算例验证了算法计算三维声散射问题的准确性、有效性及潜在的工程应用价值。
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关键词:
- 边界元法 /
- Burton-miller公式 /
- 声散射 /
- 前处理 /
- 算法
Abstract: We employ the Burton-Miller formula to overcome the non-unique problem of the conventional boundary element method for exterior acoustic scattering problems. We apply the effective singularity subtraction algorithm to implementing the hypersingular integral involved in the Burton-Miller formula, thus obtaining the improved weak form of the hypersingular integral, whose evaluation is no longer difficult. Furthermore, our algorithm adopts the ef-fective block diagonal pre-conditioner and the iterative solver to solve the matrix equation, thus improving its overall computational efficiency. Several numerical examples demonstrate the accuracy, efficiency and potential engineer-ing application of our algorithm.-
Key words:
- boundary element method /
- algorithms /
- computational efficiency /
- efficiency /
- iterative methods
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[1] Ciskowski R D,Brebbia C A.Boundary Element Methods in Acoustics[M].Computational Mechanics Publications and Elsevier Applied Science,Southampton,1991 [2] Schenck H A.Improved integral formulation for acoustic radiation problems[J]. Journal of the Acoustical Society of America,1968,44:41~58 [3] Burton A J,Miller G F.The application of integral equation methods to the numerical solution of some exterior boundary val-ue problems[A]. Proceedings of the R oyal Society of Lon-don[C],Series A,1971,323:201~210 [4] 闫再友,姜楫,严明.利用边界元法计算无界声场中结构体声 辐射[J].上海交通大学学报,2000,34: 520~523 [5] Engleder S,Steinbach O.Stabilized boundary element methods for exterior Helmholtz problems[J].Numerische Mathematik,2008,110:145~160 [6] Yan Z Y,Cui F S,Hung K C.Investigation on the normal deriv-ative equation of Helmholtz integral equation in acoustics[J].Computer Modeling in Engineering and Sciences,2005,7:97~106 [7] Saad Y,Schultz M H.GMR ES: a generalized minimal residual algorithm for solving nonsymmetric linear systems[J]. SIAM Journal on Scientific Computing,1986,7:856~869 [8] Chen K,Harris P J.Efficient preconditioners for iterative solu-tion of the boundary element equations for the three-dimensional Helmholtz equation[J]. Applied Numerical Mathematics,2001,36:475~489 [9] Yasuda Y,Higuchi K.Efficient technique in low-frequency fast multipole boundary element method for plane-symmetric acoustic problems[J]. Engineering Analysis with Boundary Ele-ments,2012,36:1493~1501 [10] Chien C C,R ajiyah H,Atluri S N.An effective method for sol-ving the hypersingular integral equations in 3D acoustics[J].Journal of the Acoustical Society of America,1990,88:918~937
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