This paper aims to simulate and analyze scenarios involving obstacles and parasitic
organisms during the growth of biological structures. We introduce an innovative model of …

This article presents a high-order accurate numerical method for the evaluation of singular
volume integral operators, with attention focused on operators associated with the Poisson …

We describe a new, adaptive solver for the two-dimensional Poisson equation in
complicated geometries. Using classical potential theory, we represent the solution as the …

Over the last two decades, several fast, robust, and high-order accurate methods have been
developed for solving the Poisson equation in complicated geometry using potential theory …

The accurate and efficient evaluation of Newtonian potentials over general two-dimensional
domains is important for the numerical solution of Poisson's equation and volume integral …

The accurate and efficient evaluation of potentials is of great importance for the numerical
solution of partial differential equations. When the integration domain of the potential is …

We consider the model problem of mixing of passive tracers by an incompressible viscous
fluid. Addressing questions of optimal control in realistic geometric settings or alternatively …