Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parallel-in-Time Multi-Level Integration of the Shallow-Water Equations
  on the Rotating Sphere   The modeling of atmospheric processes in the context of weather and climate
simulations is an important and computationally expensive challenge. The
temporal integration of the underlying PDEs requires a very large number of
time steps, even when the terms accounting for the propagation of fast
atmospheric waves are treated implicitly. Therefore, the use of
parallel-in-time integration schemes to reduce the time-to-solution is of
increasing interest, particularly in the numerical weather forecasting field.
We present a multi-level parallel-in-time integration method combining the
Parallel Full Approximation Scheme in Space and Time (PFASST) with a spatial
discretization based on Spherical Harmonics (SH). The iterative algorithm
computes multiple time steps concurrently by interweaving parallel high-order
fine corrections and serial corrections performed on a coarsened problem. To do
that, we design a methodology relying on the spectral basis of the SH to
coarsen and interpolate the problem in space. The methods are evaluated on the
shallow-water equations on the sphere using a set of tests commonly used in the
atmospheric flow community. We assess the convergence of PFASST-SH upon
refinement in time. We also investigate the impact of the coarsening strategy
on the accuracy of the scheme, and specifically on its ability to capture the
high-frequency modes accumulating in the solution. Finally, we study the
computational cost of PFASST-SH to demonstrate that our scheme resolves the
main features of the solution multiple times faster than the serial schemes.

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The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: adap-org