A Semi-analytic Algorithm For Nearly Singular Integrals In 3D Acoustic BEM With High Order Element

Because of nearly singular integrals of boundary element method(BEM),the wide application of BEM in engineering is confined.How to calculate the nearly singular integral of boundary element method accurately and efficiently is concerned by scholars for a long time.In this thesis,the current research status and background of three-dimensional acoustic BEM are introduced primarily.And then,the major research directions and the types of nearly singular integrals of BEM are introduced.Finally,a new semi-analytic algorithm of three-dimensional acoustic BEM based on high order element is proposed.The study on the nearly singular integral of three-dimensional acoustic boundary element method with higher order elements is major work component in this thesis.Based on the 6-noded triangular and the 8-noded quadrilateral iso-parametric element,a new semi-analytic algorithm with high order three-dimensional element is presented.The main contributions in this thesis can be shown in the follows.The semi-analytic algorithm based on the 8-noded quadrilateral iso-parametric element is proposed,which can be used to compute the nearly singular integrals.By analyzing the geometry features of high order elements,approximate geometric parameters are constructed.Then,the kernel function of nearly singular integral is decomposed into two parts using subtraction method.One is the regular part and the other is still singular part.The integral of the regular part is no singular,so it can be computed accurately using the conventional Gauss quadrature.As for the integral of the singular part,the semi-analytic algorithm presented in this paper can give exact result.In the end,some classical examples are given including 3D acoustic internal and external problems.The sound pressures at the points near the boundary are calculated with different methods in the examples,and the comparisons of the computed results demonstrate the accuracy and the effectiveness of the present algorithm.Compared with the 8-noded quadrilateral iso-parametric element,the 6-noded triangular iso-parametric element has many advantages,such as good structural adaptability,simple element division etc.Based on the idea of semi-analytic algorithm of 8-noded quadrilateral element,a new semi-analytic algorithm with the 6-noded triangular iso-parametric element is proposed in chapter four.Some examples are given in the last part of chapter four to show the accuracy and the effectiveness of the present algorithm.Both of the computed results demonstrate that the semi-analytic algorithm with 6-noded triangular isoparametric element presented in chapter four is more effective than linear regularization BEM to solve the problem of nearly singular integrals for 3D acoustic BEM.