Calculation of fields and force densities from finite element approximations of potentials (abstract)

Abstract

Problems of electrostatics and magnetostatics are usually formulated such that fields and force densities are related by some differential operator to a potential. Because of the necessity of finding potentials numerically, and difficulties inherent in numerical differentiation, fields forces and other expressions involving derivatives of the potential are seldom determined accurately. For the case of a particle situated in a field whose potential is a harmonic function, Bui avoided this difficulty by considering an analytic expression for the potential in a neighborhood of a point, and relating expressions involving the derivatives of the potential at that point to the potential in a neighborhood by an integral operator. In this paper, Bui’s approach is extended to fields whose potentials are harmonic functions or vectors fields whose components in Cartesian coordinates are harmonic functions. In this way, field and force density vectors as well as other expressions involving derivatives of the potential can be estimated from finite element approximations to the potential. The paper contains a derivation of the method from the Green’s function for a sphere, the justification of the particular choice of integral operator among possible variants, and a discussion of the fortran programs used to implement the method.