We extend previous work and present a general approach for solving partial differential
equations in complex, stationary, or moving geometries with Dirichlet, Neumann, and Robin …

We improve upon a method introduced in Bertalmio et al. 4 for solving evolution PDEs on
codimension-one surfaces in R^ N. As in the original method, by representing the surface as …

Reaction-diffusion systems have been widely studied in developmental biology, chemistry
and more recently in financial mathematics. Most of these systems comprise nonlinear …

We develop an algorithm for the evolution of interfaces whose normal velocity is given by the
normal derivative of a solution to an interior Poisson equation with curvature-dependent …

We present a numerical method for solving Poisson's equation, with variable coefficients
and Dirichlet boundary conditions, on two-dimensional regions. The approach uses a finite …

In this article we propose models and a numerical method for pattern formation on evolving
curved surfaces. We formulate reaction-diffusion equations on evolving surfaces using the …

We introduce a new approach to deal with the numerical solution of partial differential
equations on surfaces. Thereby we reformulate the problem on a larger domain in one …

Biomembranes consisting of multiple lipids may involve phase separation phenomena
leading to coexisting domains of different lipid compositions. The modeling of such …

We present finite difference schemes for solving the variable coefficient Poisson and heat
equations on irregular domains with Dirichlet boundary conditions. The computational …

Moving interface problems are ubiquitous in science and engineering. To develop an
accurate and efficient methodology for this class of problems, we present algorithms for local …