Application of Collocation BEM for Axisymmetric Transmission Problems in Electro- and Magnetostatics

• Published in: Mathematical modelling and analysis Vol. 21; no. 1; pp. 16 - 34
• Main Authors: Lavrova, Olga, Polevikov, Viktor
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 02.01.2016; Vilnius Gediminas Technical University
• Subjects: Approximation; Axisymmetric; axisymmetric collocation; Boundaries; Boundary element method; Collocation; Integral equations; Interpolation; Kernels; Laplace equation; Mathematical models; Mathematical research; polygonal boundary; Symmetry; transmission problem; weakly singular integral equation; transmission problem; Laplace equation; boundary element method; polygonal boundary; axisymmetric collocation; weakly singular integral equation
• ISSN: 1392-6292; 1648-3510
• DOI: 10.3846/13926292.2016.1128488

This paper considers the numerical solution of boundary integral equations for an exterior transmission problem in a three-dimensional axisymmetric domain. The resulting potential problem is formulated in a meridian plane as the second kind integral equation for a boundary potential and the first kind integral equation for a boundary flux. The numerical method is an axisymmetric collocation with equal order approximations of the boundary unknowns on a polygonal boundary. The complete elliptic integrals of the kernels are approximated by polynomials. An asymptotic kernels behavior is analyzed for accurate numerical evaluation of integrals. A piecewise-constant midpoint collocation and a piecewise-linear nodal collocation on a circular arc and on its polygonal interpolation are used for test computations on uniform meshes. We analyze empirically the influence of the polygonal boundary interpolation to the accuracy and the convergence of the presented method. We have found that the polygonal boundary interpolation does not change the convergence behavior on the smooth boundary for the piecewise-constant and the piecewise-linear collocation.