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| An efficient method for numerically evaluating singular integrals in high order boundary element method |
| Received:September 16, 2013 Revised:February 27, 2014 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx201501001 |
| KeyWord:boundary element methods high order singular integration high order Nyström method elastodynamics acoustics |
| Author | Institution |
| 姚厚朴 |
西北工业大学 航天学院, 西安 |
| 校金友 |
西北工业大学 航天学院, 西安 |
| 文立华 |
西北工业大学 航天学院, 西安 |
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| Abstract: |
| A general and efficient method for numerically evaluating singular integrals of various orders in boundary element method (BEM) is presented in this paper.The method is based on Taylor expansions of the integrands in polar coordinate system.Since the singular terms are extracted numerically rather than analytically as in existing methods,the present method is capable of treating various orders of singularities in a general form,independent on the explicit expressions of integrands.Nearly singularities caused by the large aspect ratio of the physical elements and the closeness of the singular points to the element boundary are circumvented by a conformal transformation and a sigmoidal transformation,respectively.Numerical results show that our method could maintain high accuracy with few quadrature points regardless the shape of the element being distorted or not.Performance of this method is further verified by incorporating into a Nyström BEM to solve elastodynamic problems.Our method is implemented in C language and is freely available. |