TY - GEN

T1 - Why classical schwarz methods applied to certain hyperbolic systems converge even without overlap

AU - Dolean, Victorita

AU - Gander, Martin J.

PY - 2008/12/1

Y1 - 2008/12/1

N2 - 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.

AB - 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.

KW - domain decomposition methods

KW - partial differential equations

KW - Cauchy-Riemann equations

KW - discretization

KW - elliptic problems

KW - hyperbolic partial differential equation

KW - hyperbolic system

KW - Schwarz method

UR - http://www.scopus.com/inward/record.url?scp=78651592977&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-75199-1_59

DO - 10.1007/978-3-540-75199-1_59

M3 - Conference contribution book

AN - SCOPUS:78651592977

SN - 9783540751984

VL - 60

T3 - Lecture Notes in Computational Science and Engineering

SP - 467

EP - 475

BT - Domain Decomposition Methods in Science and Engineering XVII

PB - Springer

T2 - 17th International Conference on Domain Decomposition Methods

Y2 - 3 July 2006 through 7 July 2006

ER -