Generalized Extrapolation for Computation of Hypersingular Integrals in Boundary Element Methods

The trapezoidal rule for the computation of Hadamard finite-part integrals in boundary element methods is discussed, and the asymptotic expansion of error function is obtained. A series to approach the singular point is constructed and the convergence rate is proved. Based on the asymptotic expansion of the error functional, algorithm with theoretical analysis of the generalized extrapolation are given. Some examples show that the numerical results coincide with the theoretic analysis very well.

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