A self-adaptive coordinate transformation for efficient numerical evluation of general boundary element integrals. (English) Zbl 0622.65014

The work discusses in detail the question of numerical quadrature schemes for singular or nearly singular integrals, currently found in two- dimensional, axisymmetric and three-dimensional applications of the boundary element method. The main idea is to use a suitable coordinate transformation whose Jacobian smoothes out the singularity. Some polynomial transformations (especially of third degree) are carried out. They improve the accuracy of Gaussian quadrature schemes within the near- singularity range. A lot of numerical examples clearly demonstrates the power of polynomial transformations of this kind of problems.
Reviewer: C.-I.Gheorghiu


65D32 Numerical quadrature and cubature formulas
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
41A55 Approximate quadratures
65R20 Numerical methods for integral equations
30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane
41A63 Multidimensional problems


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