COMMON COMPACT ANALYTICAL FORMULAS FOR COMPUTATION OF GEOMETRY INTEGRALS ON A BASIC CONIC SUBDOMAIN IN BOUNDARY AND VOLUME INTEGRAL METHODS

In both the boundary element (BEM) and the volume integral method (VIM), the discretization of the material medium and the ansatz for the source function always lead to corresponding integrals on the basic subdomain. The types of these integrals are classified. It is shown that these integrals on a basic conic element (volume or boundary element) consist of the same few simple contour integrals multiplied by the model (ansatz) dependent coefficients of the source fields. These contour integrals are pure geometry integrals and involve an algebraic combination of only ten line integrals on the basic conic sub-domain. The line integrals consist of elliptic integrals of three kinds and/or simple transcendental functions. Their computation can be performed analytically in a compact package of subroutines. As this computation depends only on the geometry, it can be effectively used to analyse a very wide range of field problems involving either vector or scalar fields and potentials, since the complex mathematics is relegated mainly to the subroutines of the package. Moreover, the analytical integration package can be casily incorporated into existing BIM/BEM and VIM algorithms, and thus permit time-saving computations. Some examples of practical applications are given. © 1990 Springer-Verlag.