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.
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