Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: High-order partitioned spectral deferred correction solvers for
  multiphysics problems   We present an arbitrarily high-order, conditionally stable, partitioned
spectral deferred correction (SDC) method for solving multiphysics problems
using a sequence of pre-existing single-physics solvers. This method extends
the work in [1, 2], which used implicit-explicit Runge-Kutta methods (IMEX) to
build high-order, partitioned multiphysics solvers. We consider a generic
multiphysics problem modeled as a system of coupled ordinary differential
equations (ODEs), coupled through coupling terms that can depend on the state
of each subsystem; therefore the method applies to both a semi-discretized
system of partial differential equations (PDEs) or problems naturally modeled
as coupled systems of ODEs. The sufficient conditions to build arbitrarily
high-order partitioned SDC schemes are derived. Based on these conditions,
various of partitioned SDC schemes are designed. The stability of the
first-order partitioned SDC scheme is analyzed in detail on a coupled, linear
model problem. We show that the scheme is conditionally stable, and under
conditions on the coupling strength, the scheme can be unconditionally stable.
We demonstrate the performance of the proposed partitioned solvers on several
classes of multiphysics problems including a simple linear system of ODEs,
advection-diffusion-reaction systems, and fluid-structure interaction problems
with both incompressible and compressible flows, where we verify the design
order of the SDC schemes and study various stability properties. We also
directly compare the accuracy, stability, and cost of the proposed partitioned
SDC solver with the partitioned IMEX method in [1, 2] on this suite of test
problems. The results suggest that the high-order partitioned SDC solvers are
more robust than the partitioned IMEX solvers for the numerical examples
considered in this work, while the IMEX methods require fewer implicit solves.

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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph