A Projection Transformation Method for Nearly Singular Surface Boundary Element Integrals

1. Front Matter

   Pages I-X

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2. Theory and Algorithms

   1. Front Matter

      Pages 1-1

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   2. Introduction

      • Ken Hayami

      Pages 3-7

   3. Boundary Element Formulation of 3-D Potential Problems

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      Pages 8-28

   4. Nature of Integrals in 3-D Potential Problems

      • Ken Hayami

      Pages 29-71

   5. Survey of Quadrature Methods for 3-D Boundary Element Integrals

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      Pages 72-88

   6. The Projection and Angular & Radial Transformation (Part) Method

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      Pages 89-154

   7. Elementary Error Analysis

      • Ken Hayami

      Pages 155-203

   8. Error Analysis using Complex Function Theory

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      Pages 204-260

3. Applications and Numerical Results

   1. Front Matter

      Pages 261-261

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   2. Numerical Experiment Procedures and Element Geometry

      • Ken Hayami

      Pages 263-272

   3. Applications to Weakly Singular Integrals

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      Pages 273-330

   4. Applications to Nearly Singular Integrals

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      Pages 331-440

   5. Application to Hypersingular Integrals

      • Ken Hayami

      Pages 441-444

   6. Conclusions

      • Ken Hayami

      Pages 445-450

4. Back Matter

   Pages 451-457

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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
• fluid- and aerodynamics

• C & C Information Technology Research Laboratories, NEC Corporation, Miyamae, Kawasaki Kanagawa 213, Japan

  Ken Hayami

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