The main focus of this paper is the numerical solution of the Boltzmann transport equation for neutral particles through mixed material media in a spherically symmetric geometry. Standard solution strategies, like the Discrete Ordinates Method (DOM), may lead to nonphysical approximate solutions. In particular, a point source at the center of the sphere yields undesirable ray effects. Posing th...

An adaptive unstructured grid generation scheme is introduced to use finite volume (FV) and finite element (FE) formulation to solve the heat equation with singular boundary conditions. Regular grids could not acheive accurate solution to this problem. The grid generation scheme uses an optimal time complexity frontal method for the automatic generation and delaunay triangulation of the grid po...

In this paper, we propose a numerical method to approximate the solution of partial differential equations in irregular domains with no-flux boundary conditions by means of spectral methods. The main features of this method are its capability to deal with domains of arbitrary shape and its easy implementation via Fast Fourier Transform routines. We discuss several examples of practical interest...

We develop a finite element method for convection diffusion problems on a given time dependent surface, for instance modeling the evolution of a surfactant. The method is based on a characteristic-Galerkin formulation combined with a piecewise linear cut finite element method in space. The cut finite element method is constructed by embedding the surface in a background grid and then using the ...

Plant tissue has a complex cellular structure which is an aggregate of individual cells bonded by middle lamella. During drying processes, plant tissue undergoes extreme deformations which are mainly driven by moisture removal and turgor loss. Numerical modelling of this problem becomes challenging when conventional grid-based modelling techniques such as finite element and finite difference me...

In this article we introduce a fast iterative solver for sparse matrices arising from the finite element discretization of elliptic PDEs. The solver uses a fast direct multi-frontal solver as a preconditioner to a simple fixed point iterative scheme. This approach combines the advantages of direct and iterative schemes to arrive at a fast, robust and accurate solver. We will show that this solv...