Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Dissipation Theory for Three-Dimensional FDTD with Application to
  Stability Analysis and Subgridding   The finite-difference time-domain (FDTD) algorithm is a popular numerical
method for solving electromagnetic problems. FDTD simulations can suffer from
instability due to the explicit nature of the method. Stability enforcement can
be particularly challenging in scenarios where a setup is composed of multiple
components, such as grids of different resolution, advanced boundary
conditions, reduced-order models, and lumped elements. We propose a dissipation
theory for 3-D FDTD inspired by the principle of energy conservation. We view
the FDTD update equations for a 3-D region as a dynamical system, and show
under which conditions the system is dissipative. By requiring each component
of an FDTD-like scheme to be dissipative, the stability of the overall coupled
scheme follows by construction. The proposed framework enables the creation of
provably stable schemes in an easy and modular fashion, since conditions are
imposed on the individual components, rather than on the overall coupled scheme
as in existing approaches. With the proposed framework, we derive a new
subgridding scheme with guaranteed stability, low reflections, support for
material traverse and arbitrary (odd) grid refinement ratio.

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The categories of this paper are: q-alg
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg