A discrete exterior calculus and electromagnetic theory on alattice
Forgy, E.A.
Chew, W.C.
Dept. of Electr. & Comput. Eng., Illinois Univ., Urbana, IL;
This paper appears in: Antennas and Propagation Society International Symposium, 2000. IEEE
Publication Date: 2000
Volume: 2,
On page(s): 880-883 vol.2
Meeting Date: 07/16/2000 - 07/21/2000
Location: Salt Lake City, UT, USA
ISBN: 0-7803-6369-8
References Cited: 2
INSPEC Accession Number: 6819677
Digital Object Identifier: 10.1109/APS.2000.875358
Current Version Published: 2002-08-06
Abstract
A highly accurate FDTD formulation was developed on an overlapped
cubic grid that greatly reduces numerical dispersion errors. However,
errors in in the FDTD method arise not only from numerical dispersion,
but from geometrical modelling as well. Although representing a
significant progress in addressing the numerical dispersion problem, it
is still confined to a cubic grid with the subsequent
“stair-casing” geometric approximations that it entails. The
material presented represents a fundamentally new paradigm for
finite-difference methods which hopes to address both issues of
numerical dispersion and geometrical modelling. It involves a rigorous
mathematical framework based on concepts from topology and differential
geometry. Particularly, it involves a construction of a discrete analog
to the calculus of differential forms. It should be noted that the use
of differential forms, and their lattice counterparts, is well known
within the field of algebraic topology. However, the original
contribution here lies in the introduction of a metric onto the lattice.
It is with the metric that the adjoint exterior derivative may be
defined, which is required for most physical systems not the least of
importance being Maxwell's equations
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