کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1864827 | 1530666 | 2006 | 14 صفحه PDF | دانلود رایگان |
Based on a geometric discretization scheme for Maxwell equations, we unveil a mathematical transformation between the electric field intensity E and the magnetic field intensity H , denoted as Galerkin duality. Using Galerkin duality and discrete Hodge operators, we construct two system matrices, [XE][XE] (primal formulation) and [XH][XH] (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.
Journal: Physics Letters A - Volume 349, Issues 1–4, 9 January 2006, Pages 1–14