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.

In order to overcome the difficulties of low computational efficiency and high memory requirement in the conventional boundary element method for solving large-scale potential problems, a fast multipole boundary element method for the problems of Poisson equation is presented. First of all, through the multipole expansion and local expansion for the basic solution of the kernel function of the ...

An efficient scheme for solving boundary integral equations of the heat equation based on the Galerkin method is introduced. The parabolic fast multipole method (pFMM) is applied to accelerate the evaluation of the thermal layer potentials. In order to remain attractive for a wide range of applications, a key issue is to ensure efficiency for a big variety of temporal to spatial mesh ratios. Wi...

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 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...