We introduce the continuous fast multipole method (CFMM), a generalization of the fast multipole method for calculating Coulomb interaction of point charges. The CFMM calculates Coulomb interactions between charge distributions, represented by continuous functions, in work scaling linearly with their number for constant density systems. Model calculations suggest that for errors in the potentia...

We present a method for the rankwise distributed multipole analysis of an arbitrary distribution of charge and its surrounding field. Using the superposition principle, the electrostatic field created by a distribution of charge can be resolved recursively into the contributions of a set of intrinsic multipole moments "tied to" their rank-specific multipole centers. The positions of the multipo...

Nilsson, M. 2003. Fast Numerical Techniques for Electromagnetic Problems in Frequency Domain. Acta Universitatis Upsaliensis. Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 916. 38 pp. Uppsala. ISBN 91-554-5827-0 The Method of Moments is a numerical technique for solving electromagnetic problems with integral equations. The method discretizes a surfa...

This article reviews several fast algorithms for boundary integral equations. After a brief introduction of the boundary integral equations for the Laplace and Helmholtz equations, we discuss in order the fast multipole method and its kernel independent variant, the hierarchical matrix framework, the wavelet based method, the high frequency fast multipole method, and the recently proposed multi...

Highly accurate computations of surface plasmons in metallic nanostructures with various geometries are presented. Calculations for cylinders with irregular cross section, coupled structures, and periodic gratings are shown. These systems exhibit a resonant behavior with complex field distribution and strong field enhancement, and therefore their computation requires a very accurate numerical m...

Because of its practical significance, many different methods have been developed for the solution of the time-harmonic Maxwell equations in an exterior domain at higher frequency. Often methods with complimentary strengths can be combined to obtain an even better method. In this paper we provide a numerical study of a method for coupling of the Ultra-Weak Variational Formulation (UWVF) of Maxw...