The FEniCS Project set out in 2003 with an idea to automate the solution of mathematical
models based on differential equations. Initially, the FEniCS Project consisted of two …

Hierarchical matrices present an efficient way of treating dense matrices that arise in the
context of integral equations, elliptic partial differential equations, and control theory. While a …

In this paper we consider numerical solution methods for two dimensional Fredholm integral
equation of the second kind where a (x, y, u, v) is smooth and g (x, y) is in L2 [− 1, 1] 2. We …

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 …

Low-cost airlines have significantly increased air transport, thus an increase in aviation
noise. Therefore, predicting aircraft noise is an important component for designing an aircraft …

In this paper, we develop a Taylor expansion (TE) based fast multipole method (FMM) for
low frequency 3D Helmholtz Green's function in layered media. Two forms of Taylor …

Abstract The Poisson-Boltzmann model is an effective and popular approach for modeling
solvated biomolecules in continuum solvent with dissolved electrolytes. In this paper, we …

Abstract The Poisson‐Boltzmann equation offers an efficient way to study electrostatics in
molecular settings. Its numerical solution with the boundary element method is widely used …

When the Fast Multipole Method is implemented with Taylor instead of multipole expansions
a large class of Green's functions can be treated in a unified manner. If in addition the order …

Abstract The Fast Multipole Method was introduced by Greengard and Rokhlin in a seminal
paper appeared in 1987 for studying large systems of particle interactions with reduced …