Geometric Finite Element Discretization of Maxwell Equations in Primal and Dual Spaces
Abstract
Based on a geometric discretization scheme for Maxwell equations, we unveil a mathematical\textit{\}transformation between the electric field intensity and the magnetic field intensity , denoted as Galerkin duality. Using Galerkin duality and discrete Hodge operators, we construct two system matrices, (primal formulation) and (dual formulation) respectively, that discretize the second-order vector wave equations. We show that the primal formulation recovers the conventional (edge-element) finite element method (FEM) and suggests a geometric foundation for it. On the other hand, the dual formulation suggests a new (dual) type of FEM. Although both formulations give identical dynamical physical solutions, the dimensions of the null spaces are different.
Keywords
Cite
@article{arxiv.physics/0503013,
title = {Geometric Finite Element Discretization of Maxwell Equations in Primal and Dual Spaces},
author = {Bo He and F. L. Teixeira},
journal= {arXiv preprint arXiv:physics/0503013},
year = {2009}
}
Comments
22 pages and 4 figures