Discretization of boundary integral equations by discrete differential forms on dual grids

S. Kurz, Firma Bosch, Stuttgart, Germany

Wednesday, January 22
at 16.30
in HG E1.1

In the recent years, a remarkable amount of papers has been published that treat continuous and discrete electromagnetics in terms of differential forms. However, most of these papers focus on (generalised) finite difference and finite element methods. There are only rare contributions that deal with the boundary element method. The aim of the present talk is to show how the integral equations of electromagnetics can be expressed in the language 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 discretisation. As an example, a boundary integral equation for the double curl operator is considered. The discretisation scheme generalises the well-known collocation technique by using de Rham maps.