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Numerical integration in the vicinity of a logarithmic singularity

par Migeot, Jean-Louis
Référence Engineering Analysis, 2, 2, page (92-94)
Publication Publié, 1985-06

Article révisé par les pairs

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Résumé :

This paper presents a study of the numerical integration of the (1n r) function in the vicinity of the singularity. This problem occurs for instance in the solution of field problems by the boundary element method. Two methods are considered, the Gauss-Legendre method and the analytical one. As a first step, the computing time of both methods are compared and an upper limit of the number of economic Gauss points is found. We then compute the error for various observation points and plot the iso-ε{lunate} curves from which we derive a rule giving the number of Gauss points necessary to obtain a given precision as a function of the relative distance to the mid-point of the element. More surprising is the occurrence of lines of vanishing error. This last point is of great importance, in the boundary integral equation method for instance, as it allows important time economy in the integration. © 1985.