Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Second-kind integral equations for the Laplace-Beltrami problem on
  surfaces in three dimensions   The Laplace-Beltrami problem $\Delta_\Gamma \psi = f$ has several
applications in mathematical physics, differential geometry, machine learning,
and topology. In this work, we present novel second-kind integral equations for
its solution which obviate the need for constructing a suitable parametrix to
approximate the in-surface Green's function. The resulting integral equations
are well-conditioned and compatible with standard fast multipole methods and
iterative linear algebraic solvers, as well as more modern fast direct solvers.
Using layer-potential identities known as Calder\'on projectors, the
Laplace-Beltrami operator can be pre-conditioned from the left and/or right to
obtain second-kind integral equations. We demonstrate the accuracy and
stability of the scheme in several numerical examples along surfaces described
by curvilinear triangles.

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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph