In vortex-like spin arrangements, multiple spins can combine into emergent multipole moments. Such multipole moments have broken space-inversion and time-reversal symmetries, and can therefore exhibit linear magnetoelectric (ME) activity. Three types of such multipole moments are known: toroidal; monopole; and quadrupole moments. So far, however, the ME activity of these multipole moments has o...

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,...

A novel technique to accelerate the aggregation and disaggregation stages in evanescent plane wave methods is presented. The new method calculates the six plane wave radiation patterns from a multipole expansion (aggregation) and calculates the multipole expansion of an incoming field from the six plane wave incoming field patterns. It is faster than the direct approach for multipole orders lar...

A new technique is presented for accelerating the fast multipole method, allowing rapid solution of surface integral equations for wave scattering problems. A non-nested, ray propagation approach is used to compute a matrix-vector multiply in O(N 4=3) operations, where N is the number of unknowns in the discretized integral equation.

We present an adaptive fast multipole method for solving the Poisson equation in two dimensions. The algorithm is direct, assumes that the source distribution is discretized using an adaptive quad-tree, and allows for Dirichlet, Neumann, periodic, and free-space conditions to be imposed on the boundary of a square. The amount of work per grid point is comparable to that of classical fast solver...