Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hierarchical multigrid approaches for the finite cell method on uniform
  and multi-level hp-refined grids   This contribution presents a hierarchical multigrid approach for the solution
of large-scale finite cell problems on both uniform grids and multi-level
hp-discretizations. The proposed scheme leverages the hierarchical nature of
the basis functions utilized in the finite cell method and the multi-level
hp-method, which is attributed to the use of high-order integrated Legendre
basis functions and overlay meshes, to yield a simple and elegant multigrid
scheme. This simplicity is reflected in the fact that all restriction and
prolongation operators reduce to binary matrices that do not need to be
explicitly constructed. The coarse spaces are constructed over the different
polynomial orders and refinement levels of the immersed discretization.
Elementwise and patchwise additive Schwarz smoothing techniques are used to
mitigate the influence of the cut cells leading to convergence rates that are
independent of the cut configuration, mesh size and in certain scenarios even
the polynomial order. The multigrid approach is applied to second-order
problems arising from the Poisson equation and linear elasticity. A series of
numerical examples demonstrate the applicability of the scheme for solving
large immersed systems with multiple millions and even billions of unknowns on
massively parallel machines.

19
The categories of this paper are: eess
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn