A Schur Complement Method for Compressible Navier-Stokes Equations

Dao, Thu–Huyen; Ndjinga, Michaël; Magoulès, Frédéric

doi:10.1007/978-3-642-35275-1_64

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Lecture Notes in Computational Science and Engineering

2013

DOI: 10.1007/978-3-642-35275-1_64

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A Schur Complement Method for Compressible Navier-Stokes Equations

Thu–Huyen Dao

Michaël Ndjinga

Frédéric Magoulès

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2016

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“…While DD methods have been applied successfully to a large variety of nonlinear problems (see e.g. [27,3] for porous media flow problems, [45,1] for problems from physiology, [26] for nonlinear parabolic systems, and [14] for the compressible Navier-Stokes equations), comparably much less has been written about the analysis of DD methods for nonlinear PDEs; see [10,38,37,36,16,6,46] for the steady case, and [17,23] for evolution problems.…”

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confidence: 99%

Discrete analysis of domain decomposition approaches for mesh generation via the equidistribution principle

Haynes

Kwok

2016

Math. Comp.

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Moving mesh methods based on the equidistribution principle are powerful techniques for the space-time adaptive solution of evolution problems. Solving the resulting coupled system of equations, namely the original PDE and the mesh PDE, however, is challenging in parallel. Recently several Schwarz domain decomposition algorithms were proposed for this task and analyzed at the continuous level. However, after discretization, the resulting problems may not even be well posed, so the discrete algorithms requires a different analysis, which is the subject of this paper. We prove that when the number of grid points is large enough, the classical parallel and alternating Schwarz methods converge to the unique monodomain solution. Thus, such methods can be used in place of Newton's method, which can suffer from convergence difficulties for challenging problems. The analysis for the nonlinear domain decomposition algorithms is based on M-function theory and is valid for an arbitrary number of subdomains. An asymptotic convergence rate is provided and numerical experiments illustrate the results.

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confidence: 99%

Discrete analysis of domain decomposition approaches for mesh generation via the equidistribution principle

Haynes

Kwok

2016

Math. Comp.

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A Schur Complement Method for Compressible Navier-Stokes Equations

Cited by 1 publication

References 3 publications

Discrete analysis of domain decomposition approaches for mesh generation via the equidistribution principle

Discrete analysis of domain decomposition approaches for mesh generation via the equidistribution principle

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