Efficiency of boundary integral equation techniques for internal resonance problem

Abstract

The major problem encountered by the solution of boundary integral equations is related to the nonuniqueness of its solution. The problem is also known as internal resonance problem. As a remedy the combined-field integral equation (CFIE) technique is widely used which contains a linear combination of the magnetic and electric field integral equation to provide a unique stable solution. A second effective technique is the constrained conjugate gradient method (CCG) that minimizes a cost functional consisting of two terms. The first term is the error norm with respect to boundary integral equation, while the second term is the error norm with respect to the interior equation over a closed interior surface. This paper presents the efficiency of both approaches. The results are compared for the solution of a sphere.