Publication

Rao-Wilton-Glisson basis functions and the electrostatics of triangles & polygons

Juan Ramon Mosig
2025

Abstract

Rao-Wilton-Glisson basis functions provide one of the most popular and versatile tools for the numerical solution of integral equations in Electromagnetics. They are deeply connected with the problem of calculating the electrostatic potential and field of uniform surface charge distributions existing on polygonal supports. This tutorial reviews the history and relevance of such a calculation, which has been attempted since the 19th century and continues to be the object of new developments, where frequently the physical properties of the problem are hidden by the mathematical complexity of the treatment. Here, a simple geometry-based strategy is used, leading to compact analytical expressions for both potentials and fields, which provide new insights on the singularities associated to the Rao-Wilton-Glisson basis functions.

Official source

https://infoscience.epfl.ch/entities/publication/a550003a-85d9-4777-8f70-bbca147d2738

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Juan Ramon Mosig
2025

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/a550003a-85d9-4777-8f70-bbca147d2738

About this result

Related concepts (32)

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.

Regular polygon

In Euclidean geometry, a regular polygon is a polygon that is direct equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may be either convex, star or skew. In the limit, a sequence of regular polygons with an increasing number of sides approximates a circle, if the perimeter or area is fixed, or a regular apeirogon (effectively a straight line), if the edge length is fixed. These properties apply to all regular polygons, whether convex or star.

Numerical integration

In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.

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Rao-Wilton-Glisson basis functions and the electrostatics of triangles & polygons

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