A Galerkin formulation of the boundary element method for two-dimensional and axi-symmetric problems in electrostatics

• Published in: IEEE transactions on electrical insulation Vol. 27; no. 1; pp. 135 - 143
• Main Authors: Beatovic, D., Levin, P.L., Sadovic, S., Hutnak, R.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.02.1992; Institute of Electrical and Electronics Engineers
• Subjects: Boundary conditions; Boundary element methods; Classical and quantum physics: mechanics and fields; Classical electromagnetism, maxwell equations; Classical field theories; Conductors; Differential equations; Electrostatics; Exact sciences and technology; Geometry; Integral equations; Kernel; Moment methods; Physics; Solid modeling; Theoretical study; Two dimensional space; Galerkin method; Electrostatics; Axial symmetry; Boundary element method
• ISSN: 0018-9367; 1557-962X
• DOI: 10.1109/14.123449

The authors propose to process the Fredholm integral equation relating potential to an unknown source density function by the Galerkin weighted residual technique. In essence, this allows them to optimally satisfy the Dirichlet condition over the entire conductor surface. Solving the resulting equations requires evaluation of a second surface integration over weakly singular kernels, and the increased accuracy comes at some computational expense. The singularity issue is addressed analytically for 2-D problems and semi-analytically for axi-symmetric problems. The authors describe how the integrals are evaluated for both the standard and Galerkin boundary element functions using zero, first, and second order interpolation functions. They demonstrate that the Galerkin solution is superior to the standard collocation procedure for some canonical problems, including one in which analytical charge density becomes singular.< >