Why Classical Schwarz Methods Applied to Certain Hyperbolic Systems Can Converge even Without OverlapReport as inadecuate




Why Classical Schwarz Methods Applied to Certain Hyperbolic Systems Can Converge even Without Overlap - Download this document for free, or read online. Document in PDF available to download.

1 JAD - Laboratoire Jean Alexandre Dieudonné 2 Section des Mathematiques

Abstract : Overlap is essential for the classical Schwarz method to be convergent when solving elliptic problems. Over the last decade, it was however observed that when solving systems of hyperbolic partial differential equations, the classical Schwarz method can be convergent even without overlap. We show that the classical Schwarz method without overlap applied to the Cauchy-Riemann equations which represent the discretization in time of such a system, is equivalent to an optimized Schwarz method for a related elliptic problem, and thus must be convergent, since optimized Schwarz methods are well known to be convergent without overlap.





Author: Victorita Dolean - Martin Gander -

Source: https://hal.archives-ouvertes.fr/



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