Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solving hyperbolic-elliptic problems on singular mapped disk-like
  domains with the method of characteristics and spline finite elements   A common strategy in the numerical solution of partial differential equations
is to define a uniform discretization of a tensor-product multi-dimensional
logical domain, which is mapped to a physical domain through a given coordinate
transformation. By extending this concept to a multi-patch setting, simple and
efficient numerical algorithms can be employed on relatively complex
geometries. The main drawback of such an approach is the inherent difficulty in
dealing with singularities of the coordinate transformation. This work suggests
a comprehensive numerical strategy for the common situation of disk-like
domains with a singularity at a unique pole, where one edge of the rectangular
logical domain collapses to one point of the physical domain (for example, a
circle). We present robust numerical methods for the solution of Vlasov-like
hyperbolic equations coupled to Poisson-like elliptic equations in such
geometries. We describe a semi-Lagrangian advection solver that employs a novel
set of coordinates, named pseudo-Cartesian coordinates, to integrate the
characteristic equations in the whole domain, including the pole, and a finite
element elliptic solver based on globally $C^1$ smooth splines (Toshniwal et
al., 2017). The two solvers are tested both independently and on a coupled
model, namely the 2D guiding-center model for magnetized plasmas, equivalent to
a vorticity model for incompressible inviscid Euler fluids. The numerical
methods presented show high-order convergence in the space discretization
parameters, uniformly across the computational domain, without effects of order
reduction due to the singularity. Dedicated tests show that the numerical
techniques described can be applied straightforwardly also in the presence of
point charges (equivalently, point-like vortices), within the context of
particle-in-cell methods.

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The categories of this paper are: econ
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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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: solv-int
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The categories of this paper are: astro-ph
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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: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph