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| Indirect computation of singular integrals in Helmholtz boundary integral equation |
| Received:September 10, 2018 Revised:October 22, 2018 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20180910003 |
| KeyWord:Burton-Miller formulation hyper singular integral Cauchy principal value integral the characteristic function method |
| Author | Institution |
| 周琪 |
北京大学 工学院 力学与工程科学系, 北京 |
| 陈永强 |
北京大学 工学院 力学与工程科学系, 北京 |
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| Abstract: |
| A new particular solution method is proposed to indirectly calculate the strong singular integrals and free terms in conventional Helmholtz boundary integral equation (CBIE) and hyper-strong singular integrals in Burton-Miller boundary integral equation (BMBIE).For the acoustic problem of interior field,the particular solution satisfying Helmholtz governing equation is given,and the strong singular integral and free terms in CBIE are obtained indirectly.For an exterior field problem,however,calculation of its Cauchy principal value (CPV) for hyper-strong singular integral needs higher-order approximation of the kernel function through Taylor series expansion,which makes numerical implementation quite complex.In this paper,the particular solution satisfying Helmholtz governing equation and Sommerfeld radiation condition is given,and the hyper-strong singular integrals are obtained using a proposed new particular solution method.Also,the CPV of the strongly singular integral for an axisymmetric structure is derived.The high efficiency of the method is demonstrated with axisymmetric examples.The numerical results show that for the interior domain problem,the accuracy obtained by the proposed particular solution method is superior to that of directly calculating the strongly singular integral and the free term coefficient.Furthermore,the particular solution method can avoid calculating the free term with consideration of specific geometric information,and thus is of more general applicability.For an exterior domain problem,both methods provide almost the same accuracy,however,the proposed particular method can avoid expanding the kernel function to higher order and is easier to implement numerically. |
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