We present a novel approach for high-order accurate numerical differentiation on unstructured meshes of quadrilateral elements. To differentiate given function, an auxiliary function with greater smoothness properties is defined which when differentiated provides the derivatives original function. The method generalises traditional finite difference methods to arbitrary topology in any number d...

In this paper we generalize a new type of limiters based on the weighted essentially nonoscillatory (WENO) finite volume methodology for the Runge-Kutta discontinuous Galerkin (RKDG) methods solving nonlinear hyperbolic conservation laws, which were recently developed in [31] for structured meshes, to two-dimensional unstructured triangular meshes. The key idea of such limiters is to use the en...

In the recent years, there has been an increasing interest in discontinuous Galerkin time domain (DGTD) methods for the solution of the unsteady Maxwell equations modeling electromagnetic wave propagation. One of the main features of DGTD methods is their ability to deal with unstructured meshes which are particularly well suited to the discretization of the geometrical details and heterogeneou...

This paper describes an approach to construct unstructured tetrahedral and hexahedral meshes for a domain with multiple materials. In earlier works, we developed an octreebased isocontouring method to construct unstructured 3D meshes for a single-material domain. Based on this methodology, we introduce the notion of material change edge and use it to identify the interface between two or severa...