Discretization of boundary integral equations by differential forms on dual grids

In this paper, some integral equations of electromagnetics are reformulated in terms of differential forms. The integral kernels become double forms. These are forms in one space with coefficients that are forms in another space. The results correspond closely to the usual treatment, but are clearer...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on magnetics 2004-03, Vol.40 (2), p.826-829
Main Authors: Kurz, S., Rain, O., Rischmuller, V., Rjasanow, S.
Format: Article
Language:English
Subjects:
Condensed matter: electronic structure, electrical, magnetic, and optical properties
Current density
Electromagnetic forces
Exact sciences and technology
Finite difference methods
Finite element methods
Integral equations
Kernel
Laplace equations
Magnetic fields
Magnetic properties and materials
Magnetism
Magnetostatics
Physics
Rain
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, some integral equations of electromagnetics are reformulated in terms of differential forms. The integral kernels become double forms. These are forms in one space with coefficients that are forms in another space. The results correspond closely to the usual treatment, but are clearer and more intuitive. Since differential forms possess discrete counterparts, the discrete differential forms, such schemes lend themselves naturally to discretization. As an example, a boundary integral equation for the double curl operator is considered. The discretization scheme generalizes the well-known collocation technique by using de Rham maps. Depending on the integral operator to be discretized, the 1-form valued residual is forced to be zero either over the 1-chains of the primal or the dual grid.
ISSN:0018-9464
1941-0069
DOI:10.1109/TMAG.2004.824902