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...

A symmetric Galerkin boundary-element method is used for the solution of boundary-value problems with mixed boundary conditions of Dirichlet and Neumann type. As a model problem we consider the Laplace equation. When an iterative scheme is employed for solving the resulting linear system, the discrete boundary integral operators are realized by the fast multipole method. While the single-layer ...

In this thesis we study multipole moments of axisymmetric spacetimes. Using the recursive definition of the multipole moments of Geroch and Hansen we develop a method for computing all multipole moments of a stationary axisymmetric spacetime without the use of a recursion. This is a generalisation of a method developed by Herberthson for the static case. Using Herberthson’s method we also devel...

This paper proposes a finite mixture model (FMM) to model the behavioral transition of calorie consumption with an assumption that nutrition consumption is a mixture of two different behavioral stages: a poor stage and an affluent stage. Based on 387 calorie-income elasticities collected from 90 primary studies, our results identify that the threshold income for calorie demand transition is 459...

Talk Abstract We present an efficient integral equation method approach to solve the forced heat equation, ut(x) − ∆u(x) = F (x, u, t), in a two dimensional, multiply connected domain, with Dirichlet boundary conditions. We first discretize in time, which is known as Rothe’s method, resulting in a non-homogeneous modified Helmholtz equation that is solved at each time step. We formulate the sol...

We report the integration of a FMM (Fast Multipole Method) template library “FMMTL” into the discrete circulation-preserving vortex sheets method to accelerate the Biot-Savart integral. We measure the speed-up on a bubble oscillation test with varying mesh resolution. We also report a few examples with higher complexity than previously achieved.

This paper describes a simple version of the Fast Multipole Method (FMM) for the Helmholtz equation in two dimensions. We discuss both the underlying theory and some of the practical aspects of its implementation to allow for stability and high accuracy at all wavelengths.

We consider the problem of interpolating scattered data using spline methods and present a general framework of using the multipole method to accelerate the evaluation of splines. The method depends on a tree-data structure and two hierarchical approximations: an upward multipole expansion approximation and a downward local Taylor series approximation. We also illustrate the performance of the ...