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000151267 037__ $$aFZJ-2014-01258
000151267 1001_ $$0P:(DE-HGF)0$$aRuprecht, Daniel$$b0$$eCorresponding author
000151267 245__ $$aParareal for diffusion problems with space- and time-dependent coefficients
000151267 260__ $$c2014
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000151267 520__ $$aFor the time-parallel Parareal method, there exists both numerical and analytical proof that it converges very well for diffusive problems like the heat equation. Many applications, however, do not lead to simple homogeneous diffusive scenarios but feature strongly inhomogeneous and possibly anisotropic coefficients. The paper presents results from a numerical study of how space- and time-dependent coefficients in a diffusion setup affect Parareal's convergence behaviour. It is shown that, for the presented examples, non-constant diffusion coefficients have only marginal influence on how fast Parareal converges. Furthermore, an example is shown that illustrates how for linear problems the maximum singular value of the Parareal iteration matrix can be used to estimate convergence rates.
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000151267 536__ $$0G:(GEPRIS)450829162$$aDFG project 450829162 - Raum-Zeit-parallele Simulation multimodale Energiesystemen (450829162)$$c450829162$$x1
000151267 588__ $$aDataset connected to arXivarXiv
000151267 7001_ $$0P:(DE-Juel1)132268$$aSpeck, Robert$$b1$$ufzj
000151267 7001_ $$0P:(DE-HGF)0$$aKrause, Rolf$$b2
000151267 8564_ $$uhttp://arxiv.org/abs/1401.7829
000151267 909CO $$ooai:juser.fz-juelich.de:151267$$pVDB
000151267 9101_ $$0I:(DE-588b)5008462-8$$6P:(DE-Juel1)132268$$aForschungszentrum Jülich GmbH$$b1$$kFZJ
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000151267 9141_ $$y2014
000151267 9201_ $$0I:(DE-Juel1)JSC-20090406$$kJSC$$lJülich Supercomputing Center$$x0
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