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 ...

The notion of well-separated sets is crucial in fast multipole methods as the main idea is to approximate the interaction between such sets via cluster expansions. We revisit the one-parameter multipole acceptance criterion in a general setting and derive a relative error estimate. This analysis benefits asymmetric versions of the method, where the division of the multipole boxes is more libera...

The conformational flexibility of carbohydrates is challenging within the field of computational chemistry. This flexibility causes the electron density to change, which leads to fluctuating atomic multipole moments. Quantum Chemical Topology (QCT) allows for the partitioning of an "atom in a molecule," thus localizing electron density to finite atomic domains, which permits the unambiguous eva...

The fast multipole method (FMM) has been regarded as one of the top 10 algorithms in scientific computing that were developed in the 20th century. Combined with the FMM, the boundary element method (BEM) can now solve large-scale problems with several million degrees of freedom on a desktop computer within hours. This opened up a wide range of applications for the BEM that has been hindered for...