An Efficient Algorithm Of The Nearly Singular Integrals In Non-singular Boundary Element Method

On account of the difficulty of evaluating the nearly singular integrals in boundary element method (BEM), the application range of BEM is reduced in engineering for a long time. This paper proposes a new efficient transformation for nearly singular integrals. The proposed transformation can remove the nearly singularity efficiently and improve the accuracy of numerical results of the nearly singular integrals greatly. Thus, the nearly singular integrals are successfully calculated.In this paper, the new transformation algorithm is applied to the potential problems and the elastic problems. During the application to potential problems, the equivalent regularized boundary integral equations (BIEs) with indirect unknowns and the conventional BIEs with direct variables are introduced. The nearly singular integrals in the BIEs for interior point are handled with the proposed transformation, and extremely high accuracy of numerical results of the potentials and potential gradients at interior points close to the boundary is achieved even when the distance of the interior point to the boundary reaches 10?6 or smaller. In addition, for the deficiencies lied in the applications in practical problems, the modification for the conventional BIEs is given by this paper. Basing on a kind of new nonsingular BIEs for elastic plane problems, the suggested transformation is applied to the computation of mechanical parameters at interior point close to the boundary and eliminates successfully the boundary layer effect in BEM. Typical numerical examples in which the conventional method using standard Gaussian quadrature directly is also employed for purpose of comparison show the new algorithm can effectively evaluate the variables at interior points very close to the boundary and has satisfactory convergence.Finally, the perfected transformation project is given based on the experience of applications in practical problems.