A stabilized local integral method using RBFs for Helmholtz problems arising from electrodynamics

Abstract

In this paper we present the Stabilized Local Boundary Domain Integral Method (SLBDIM), which is a local integral boundary element technique with stable computation based on Radial Basis Function (RBF) approximations, applied to Helmholtz problems. We present numerical results for small shape parameters of the RBF that stabilize the errors. We also discuss accuracy, conditioning and comparisons with other methods for various case studies. The virtues of the method are demonstrated through its application to problems arising in wave chaos, acoustics, and dielectric microresonators. The SLBDIM is computationally efficient and well suited to geometries with arbitrarily shaped domains, including those with corners.