Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: MGM: A meshfree geometric multilevel method for systems arising from
  elliptic equations on point cloud surfaces   We develop a new meshfree geometric multilevel (MGM) method for solving
linear systems that arise from discretizing elliptic PDEs on surfaces
represented by point clouds. The method uses a Poisson disk sampling-type
technique for coarsening the point clouds and new meshfree
restriction/interpolation operators based on polyharmonic splines for
transferring information between the coarsened point clouds. These are then
combined with standard smoothing and operator coarsening methods in a V-cycle
iteration. MGM is applicable to discretizations of elliptic PDEs based on
various localized meshfree methods, including RBF finite differences (RBF-FD)
and generalized finite differences (GFD). We test MGM both as a standalone
solver and preconditioner for Krylov subspace methods on several test problems
using RBF-FD and GFD, and numerically analyze convergence rates, efficiency,
and scaling with increasing point cloud sizes. We also perform a side-by-side
comparison to algebraic multigrid (AMG) methods for solving the same systems.
Finally, we further demonstrate the effectiveness of MGM by applying it to
three challenging applications on complicated surfaces: pattern formation,
surface harmonics, and geodesic distance.

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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-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
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci