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A New Approach to Singular Kernel Integration for General Curved Elements

  • M. Koizumi
  • M. Utamura
Conference paper
Part of the Boundary Elements book series (BOUNDARY, volume 8)

Abstract

Numerical accuracy in boundary element method depends on the errors appearing in the approximation of geometry, interpolation of functions and integration scheme except loss of digits inherent in computer hardware. Among them, the integration scheme takes an essential part and may significantly deteriorate numerical accuracy in ordinary boundary element formulation because integration in Cartesian coordinate includes singular kernel. It is known that direct application of numerical quadratures fails to predict the value of unknown function near the integration points. To overcome this difficulty, analytical integration method (Kuwabara and Takeda1), double exponential numerical integration method (Higashimachi et al.2) and Robmerg numerical integration method (Takahashi et al.3) have been attempted. However, in analytical method not only an element shape is limited to a piecewise plane element but also applicable integrand is limited to 1/r or log r type function. Thus it cannot be in general usage.

Keywords

Boundary Element Observation Point Boundary Element Method Integration Point Potential Gradient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    T. Kuwabara and T. Takeda (1985) Calculation of Potential and Potential Gradient for 3-Dimensional Field by B. E. M using Analytical Integration, pp 73 to 82 Proceeding of Conf. on Rotary Machines and Stational Apparatus, SA-85–47, JECGoogle Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • M. Koizumi
    • 1
  • M. Utamura
    • 1
  1. 1.Energy Research LaboratoryHitachi Ltd.Hitachi-shi, Ibaraki-ken 316Japan

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