We present a numerically improved multipole formulation for the calculation of resonances of multiple disks located at arbitrary positions in a 2-d plane, and suitable for the accurate computation of the resonances of large numbers of disks and of high-wavenumber eigenstates. Using a simple reformulation of the field expansions and boundary conditions, we are able to transform the multipole for...

The simulation code COMBI has been developed to enable the study of coherent beam-beam effects in the full collision scenario of the LHC, with multiple bunches interacting at multiple crossing points over many turns. The parallel version of COMBI was first implemented using a soft-Gaussian collision model which entails minimal communication between worker processes. Recently we have extended th...

This article introduces a new fast direct solver for linear systems arising out of wide range of applications, integral equations, multivariate statistics, radial basis interpolation, etc., to name a few. The highlight of this new fast direct solver is that the solver scales linearly in the number of unknowns in all dimensions. The solver, termed as Inverse Fast Multipole Method (abbreviated as...

We present the optimization of a transmission grating to be used as a phase mask in photolithography. The electromagnetic fields diffracted by the structure are computed with MMP (Multiple Multipole Method). With this simple procedure a high accuracy and low computation time are achieved.

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...

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...