We describe a multipole method for calculating the modes of microstructured optical fibers. The method uses a multipole expansion centered on each hole to enforce boundary conditions accurately and matches expansions with different origins by use of addition theorems. We also validate the method and give representative results. © 2002 Optical Society of America OCIS codes: 060.2280, 060.2400, 0...

Article history: Received 27 January 2012 Received in revised form 3 October 2012 Accepted 16 January 2013 Available online 1 February 2013

A new two-dimensional panel technique has been developed to solve Laplacian flows, which eliminates the edge effect present in traditional panel methods. Such a method is very useful for applications where the velocity induced by the panels is required at arbitrary locations. Particle based flow solvers are a prime example. The method, however, requires considerably more computational effort. I...

Reconstructing neuronal activity from MEG and EEG measurements requires the accurate calculation of the electromagnetic field inside the head. The boundary element formulation of this problem leads to a dense linear system which is too large to be solved directly. We propose to accelerate the computations via the fast multipole method. This method approximates the electromagnetic interaction be...

A fast multipole boundary element method (BEM) for solving large-scale thin plate bending problems is presented in this paper. The method is based on the Kirchhoff thin plate bending theory and the biharmonic equation governing the deflection of the plate. First, the direct boundary integral equations and the conventional BEM for thin plate bending problems are reviewed. Second, the complex not...

Article history: Received 3 May 2017 Received in revised form 24 October 2017 Accepted 11 November 2017 Available online 15 November 2017

We present a novel stabilization procedure for accurate surface formulations of electromagnetic scattering problems involving three-dimensional dielectric objects with arbitrarily low contrasts. Conventional surface integral equations provide inaccurate results for the scattered fields when the contrast of the object is low, i.e., when the electromagnetic material parameters of the scatterer an...

Fast multipole methods (FMM) were originally developed for accelerating N body problems for particle-based methods. FMM is more than an N -body solver, however. Recent efforts to view the FMM as an elliptic Partial Differential Equation (PDE) solver have opened the possibility to use it as a preconditioner for a broader range of applications. FMM can solve Helmholtz problems with optimal O(N lo...

The multi-level fast multipole algorithm (MLFMA) is applied to the analysis of planewave scattering from multiple conducting and/or dielectric targets, of arbitrary shape, situated in the presence of a dielectric half space. The multiple-target scattering problem is solved in an iterative fashion. In particular, the fields exciting each target are represented as the incident fields plus the sca...

In this series of lectures, we describe the analytic and computational foundations of fast multipole methods, as well as some of their applications. They are most easily understood, perhaps, in the case of particle simulations, where they reduce the cost of computing all pairwise interactions in a system of N particles from O(N) to O(N) or O(N logN) operations. They are equally useful, however,...