Geometrical representation and integration in BIE analysis

Abstract

AbstractBoundary representation by straight lines and circular arcs is described, and the error introduced through the common representation of circular arc boundaries by quadratic geometrical shape functions is investigated. This error is shown to be in some cases the major contributor to the total error. An even more significant advantage of exact boundary representation is that it permits many of the required integrations to be performed analytically, rather than by using Gaussian quadrature. For example, all integrations in any rectilinear domain can then be evaluated analytically. This generally produces an increase in accuracy, and a saving in the computing time required to assemble the coefficient matrices. In slender domains both this increase in accuracy and saving in computing time are very marked, as analytical integrations permit the use of very much coarser discretization than would be required for numerical quadrature.