© 1992

A Projection Transformation Method for Nearly Singular Surface Boundary Element Integrals


Part of the Lecture Notes in Engineering book series (LNENG, volume 73)

Table of contents

  1. Front Matter
    Pages I-X
  2. Theory and Algorithms

  3. Applications and Numerical Results

    1. Front Matter
      Pages 261-261
    2. Ken Hayami
      Pages 441-444
    3. Ken Hayami
      Pages 445-450
  4. Back Matter
    Pages 451-457

About this book


In three dimensional boundary element analysis, computation of integrals is an important aspect since it governs the accuracy of the analysis and also because it usually takes the major part of the CPU time. The integrals which determine the influence matrices, the internal field and its gradients contain (nearly) singular kernels of order lIr a (0:= 1,2,3,4,.··) where r is the distance between the source point and the integration point on the boundary element. For planar elements, analytical integration may be possible 1,2,6. However, it is becoming increasingly important in practical boundary element codes to use curved elements, such as the isoparametric elements, to model general curved surfaces. Since analytical integration is not possible for general isoparametric curved elements, one has to rely on numerical integration. When the distance d between the source point and the element over which the integration is performed is sufficiently large compared to the element size (d> 1), the standard Gauss-Legendre quadrature formula 1,3 works efficiently. However, when the source is actually on the element (d=O), the kernel 1I~ becomes singular and the straight forward application of the Gauss-Legendre quadrature formula breaks down. These integrals will be called singular integrals. Singular integrals occur when calculating the diagonals of the influence matrices.


Integral equation Natur Randelementmethode Transformation algorithm boundary element method calculus error analysis geometry model nearly singular integral numerische Analysis

Authors and affiliations

  1. 1.C & C Information Technology Research LaboratoriesNEC CorporationMiyamae, Kawasaki Kanagawa 213Japan

Bibliographic information