Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Dissipative Systems Theory for FDTD with Application to Stability
  Analysis and Subgridding   This paper establishes a far-reaching connection between the
Finite-Difference Time-Domain method (FDTD) and the theory of dissipative
systems. The FDTD equations for a rectangular region are written as a dynamical
system having the magnetic and electric fields on the boundary as inputs and
outputs. Suitable expressions for the energy stored in the region and the
energy absorbed from the boundaries are introduced, and used to show that the
FDTD system is dissipative under a generalized Courant-Friedrichs-Lewy
condition. Based on the concept of dissipation, a powerful theoretical
framework to investigate the stability of FDTD methods is devised. The new
method makes FDTD stability proofs simpler, more intuitive, and modular.
Stability conditions can indeed be given on the individual components (e.g.
boundary conditions, meshes, embedded models) instead of the whole coupled
setup. As an example of application, we derive a new subgridding method with
material traverse, arbitrary grid refinement, and guaranteed stability. The
method is easy to implement and has a straightforward stability proof.
Numerical results confirm its stability, low reflections, and ability to handle
material traverse.

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The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin