Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adaptive radial basis function generated finite-difference (RBF-FD) on
  non-uniform nodes using $p$-refinement   Radial basis functions-generated finite difference methods (RBF-FDs) have
been gaining popularity recently. In particular, the RBF-FD based on
polyharmonic splines (PHS) augmented with multivariate polynomials (PHS+poly)
has been found significantly effective. For the approximation order of RBF-FDs'
weights on scattered nodes, one can already find mathematical theories in the
literature. Many practical problems in numerical analysis, however, do not
require a uniform node-distribution. Instead, they would be better suited if
specific areas of the domain, where complicated physics needed to be resolved,
had a relatively higher node-density compared to the rest of the domain. In
this work, we proposed a practical adaptive RBF-FD with a user-defined order of
convergence with respect to the total number of (possibly scattered and
non-uniform) data points $N$. Our algorithm outputs a sparse differentiation
matrix with the desired approximation order. Numerical examples are provided to
show that the proposed adaptive RBF-FD method yields the expected
$N$-convergence even for highly non-uniform node-distributions. The proposed
method also reduces the number of non-zero elements in the linear system
without sacrificing accuracy.

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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
31
The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org