Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The mimetic finite difference method for the Landau-Lifshitz equation   The Landau-Lifshitz equation describes the dynamics of the magnetization
inside ferromagnetic materials. This equation is highly nonlinear and has a
non-convex constraint (the magnitude of the magnetization is constant) which
pose interesting challenges in developing numerical methods. We develop and
analyze explicit and implicit mimetic finite difference schemes for this
equation. These schemes work on general polytopal meshes which provide enormous
flexibility to model magnetic devices with various shapes. A projection on the
unit sphere is used to preserve the magnitude of the magnetization. We also
provide a proof that shows the exchange energy is decreasing in certain
conditions. The developed schemes are tested on general meshes that include
distorted and randomized meshes. The numerical experiments include a test
proposed by the National Institute of Standard and Technology and a test
showing formation of domain wall structures in a thin film.

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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org