|
|
 |
| |
|
|
|
A Hermite Method for Maxwell’s Equations |
|
|
|
PP: 271-283 |
|
|
|
doi:10.18576/amis/120201
|
|
|
|
Author(s) |
|
|
|
Vitoriano Ruas,
Marco Antonio Silva Ramos,
|
|
|
|
Abstract |
|
|
| A mathematical formulation suitable for the application of a novel Hermite finite element method, to solve electromagnetic
field problems in two- and three-dimensional domains is studied. This approach offers the possibility to generate accurate
approximations of Maxwell’s equations in smooth domains, with a rather rough interpolation and without curved elements. Method’s
degrees of freedom are the normal derivative mean values of the electric field across the edges or the faces of a mesh consisting of
N-simplices, in addition to the mean value in the mesh elements of the field itself. Second-order convergence of the electric field in
the mean-square sense and first-order convergence of the magnetic field in the same sense are rigorously established, if the domain is a
convex polytope. Numerical results for two-dimensional problems suggest however that second-order convergence can also be expected
of the magnetic field. Both behaviors are shown to apply to the case of curved domains as well, provided a simple interpolated boundary
condition technique is employed. |
|
|
|
|
|
|
|
