Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A fourth-order accurate compact difference scheme for solving the
  three-dimensional Poisson equation with arbitrary boundaries   This paper presents an efficient high-order sharp-interface method for
solving the three-dimensional (3D) Poisson equation with Dirichlet boundary
conditions on a nonuniform Cartesian grid with irregular domain boundaries. The
new approach is based on the combination of the fourth-order compact finite
difference scheme and the preconditioned stabilized biconjugate-gradient
(BiCGSTAB) method. Contrary to the original immersed interface method by
LeVeque and Li [1], the new method does not require jump corrections, instead,
the (regular) compact finite difference stencil is adjusted at the irregular
grid points (in the vicinity of the interfaces of the immersed bodies) to
obtain a solution that is sharp across the interface while keeping the
fourth-order global accuracy. The contribution of the present work is the
design of a fourth-order-accurate 3D Poisson solver whose accuracy and
efficiency does not deteriorate in the presence of an immersed boundary. This
is attributed to (i) the modification of the discrete operators near immersed
boundaries does not lead to a wide grid stencil due to the compact nature of
the discretization and (ii) a preconditioning technique whose efficiency and
cost are independent of the complexity of the geometry and the presence or not
of an immersed boundary. The accuracy and computational efficiency of the
proposed algorithm is demonstrated and validated over a range of problems
including smooth and irregular boundaries. The test cases show that the new
method is fourth-order accurate in the maximum norm whether an immersed
boundary is present or not, on uniform or nonuniform grids. Furthermore, the
efficiency of the preconditioned BiCGSTAB is demonstrated with regard to
convergence rate and `extra' floating-point operation ($FLOP_{extra}$) which is
due to the presence of immersed boundaries.

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The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
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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: econ
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The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph