A New Approach to Singular Kernel Integration for General Curved Elements
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.
KeywordsBoundary Element Observation Point Boundary Element Method Integration Point Potential Gradient
Unable to display preview. Download preview PDF.
- 1.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
- 2.T. Higashimachi et al. (1983) Interactive Structure Analysis System Using the Advanced Boundary Element Method, Boundary Elements Procceding of 5th Int. Conf. Springer-VerlagGoogle Scholar
- 3.K. Takahashi et al. (1985) On the Evaluation of Various Numerical Integrations in Boundary Element Method, PP 91 to 99 Procceding of Conf. on Rotary Machines and Stational Apparatus, SA-85–49, JECGoogle Scholar
- 4.J. V. Cox and T. A. Shugar (1985) A Recursive Integration Technique for Boundary Element Method in Elastoatatics, Advanced Topics in Boundary Element Analysis AMD-Vol. 72, The winter meeting of ASMEGoogle Scholar