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 -