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| Analytical algorithm of the nearly singular integrals in boundary element method to anisotropic potential problems |
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| DOI：10.7511/jslx20083064 |
| KeyWord:BEM,nearly singular integrals,analytical integral,anisotropy,potential problems |
| ZHOU Huan-lin NIU Zhong-rong CHENG Chang-zheng WANG Xiu-xi |
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| Abstract: |
| A new analytical integral algorithm is proposed and applied to the evaluation of the nearly singular integrals in the Boundary Element Method for 2D anisotropic potential problems.The nearly singular integrals over the linear elements are accurately computed by new analytical formulas.For quadratic element,after it is subdivided into several linear elements,the nearly singular integrals can be approximately computed by the analytical formulas.When an interior point is far away from an element,the conventional Gaussian numerical quadrature scheme is kept.Otherwise if the point is very close to the element,the Gaussian numerical quadrature is replaced by the new analytical formulas due to the invalidation of the Gaussian quadrature.The numerical results of two examples demonstrate the effectiveness and accuracy of the algorithm.The results of quadratic elements are more accurate than those of linear elements. |
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