Error Estimate of Numerical Integration in Boundary Element Method Analysis

概要

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Errors included in solutions obtained by the boundary element method analysis are generally larger than those by the finite element method analysis in the case that the number of discretized elements is small. One of the reasons is supposed to be attributable to the error which will be produced in the numerical integration of the singular functions of the type (1/γ)^n in a two dimensional elastic problem. In this report the distance r between a load point and an observation point on a boundary element was represented graphically by two parameters. Then the functions composing the fundamental solutions could be classified into seven basic ones and their tendencies along an element were characterized. The following results were obtained: (1) Errors of the numerical integration of the functions are small enough in the region γ_d/L>0.5 even if four points are chosen in the Gaussian quadrature formulas. (2) The higher the exponent, the more increase the errors in the integration of the functions γ^i_<,x>γ^j_<,y>ξ^k/γ^l. Then, the methods to reduce computing time and to decrease errors of the numerical integrations are proposed.
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