Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Cylindrical Basis Function for Solving Partial Differential Equations
  on Manifolds   Numerical solutions of partial differential equations (PDEs) on manifolds
continues to generate a lot of interest among scientists in the natural and
applied sciences. On the other hand, recent developments of 3D scanning and
computer vision technologies have produced a large number of 3D surface models
represented as point clouds. Herein, we develop a simple and efficient method
for solving PDEs on closed surfaces represented as point clouds. By projecting
the radial vector of standard radial basis function(RBF) kernels onto the local
tangent plane, we are able to produce a representation of functions that
permits the replacement of surface differential operators with their Cartesian
equivalent. We demonstrate, numerically, the efficiency of the method in
discretizing the Laplace Beltrami operator.

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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th