The co-volume integration method, Yee’s scheme, generalized to unstructured mesh is considered and compared with time domain finite element method (TDFE). In order to generate the meshes for which a good quality dual mesh is ensured, a new point placing method for the generation of meshes appropriate for the use of the co-volume method is proposed. Numerical examples are presented which demonst...

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...

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 ...

Successful design and operation of hydraulic structures require more effective and reliable tools to be used in a variety of practical problems, including bottom outlets, intakes and/or spillways. Until recently, physical modeling has been the principal approach in studying the flow pattern and behavior of such structures. The main concerns might generally be related to estimating of discharge ...

Finite-difference time-domain (FDTD) grids are often described as being divergence-free in a source-free region of space. However, in the presence of a source, the continuity equation states that charges may be deposited in the grid, while Gauss’s law dictates that the fields must diverge from any deposited charge. The FDTD method will accurately predict the (diverging) fields associated with c...

The paper presents a convergence analysis of a multigrid solver for a system of linear algebraic equations resulting from the disretization of a convection-diffusion problem using a finite element method. We consider piecewise linear finite elements in combination with a streamline diffusion stabilization . We analyze a multigrid method that is based on canonical inter-grid transfer operators, ...

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...

We consider the problem of constructing spatial finite difference approximations on an arbitrary fixed grid which preserve any number of integrals of the partial differential equation and preserve some of its symmetries. A basis for the space of of such finite difference operators is constructed; most cases of interest involve a single such basis element. (The “Arakawa” Jacobian is such an elem...