Numerical aspects of the boundary residual method

Abstract

SUMMARYThe boundary residual method is a powerful technique for solving EM boundary-value problems. This technique produces matrices difficult to solve using many of the standard numerical techniques. This paper discusses lesser-known numerical aspects of this method, and it shows efficient and well-conditioned methods to solve both the homogeneous' and non-homogeneous boundary residual problem.

A High Order Numerical Investigation of Electromagnetic Scattering From a Torus and a Circular Loop

“…2). The NRE, which was motivated by the Boundary Residual Method [21], [22], measures the residual error in the satisfaction of Eq. 1(a) and (b).…”

Cavity resonances by the boundary residual method versus experiment

“…Resonances of the cavity solved by the boundary residual method for the geometries given in Table I where SI' ... , Sm are the sampling locations along the boundary S, and W" ... , W m are weighting values of a numerical integration method (Bunch and Grow 1990). This approach eliminates the need to calculate the matrix of integrals given by (5).…”

“…This approach eliminates the need to calculate the matrix of integrals given by (5). Now the minimum residual solution corresponds to the minimum singular value of the matrix M (Bunch and Grow 1990). The geometry of the cavity boundary is shown in Fig.…”

“…Thus resonances of the spherical cavity have been solved previously using the boundary residual method (Bunch and Grow 1990), and an example of the results is shown in Fig. 2.…”