TY - JOUR
T1 - A robust two-level domain decomposition preconditioner for systems of PDEs
AU - Spillane, Nicole
AU - Dolean, Victorita
AU - Hauret, Patrice
AU - Nataf, Frédéric
AU - Pechstein, Clemens
AU - Scheichl, Robert
PY - 2011/12/31
Y1 - 2011/12/31
N2 - Coarse spaces are instrumental in obtaining scalability for domain decomposition methods. However, it is known that most popular choices of coarse spaces perform rather weakly in presence of heterogeneities in the coefficients in the partial differential equations, especially for systems. Here, we introduce in a variational setting a new coarse space that is robust even when there are such heterogeneities. We achieve this by solving local generalized eigenvalue problems which isolate the terms responsible for slow convergence. We give a general theoretical result and then some numerical examples on a heterogeneous elasticity problem.
AB - Coarse spaces are instrumental in obtaining scalability for domain decomposition methods. However, it is known that most popular choices of coarse spaces perform rather weakly in presence of heterogeneities in the coefficients in the partial differential equations, especially for systems. Here, we introduce in a variational setting a new coarse space that is robust even when there are such heterogeneities. We achieve this by solving local generalized eigenvalue problems which isolate the terms responsible for slow convergence. We give a general theoretical result and then some numerical examples on a heterogeneous elasticity problem.
KW - domain decomposition methods
KW - coarse spaces
KW - partial differential equations
UR - http://www.scopus.com/inward/record.url?scp=83155192111&partnerID=8YFLogxK
U2 - 10.1016/j.crma.2011.10.021
DO - 10.1016/j.crma.2011.10.021
M3 - Article
AN - SCOPUS:83155192111
SN - 1631-073X
VL - 349
SP - 1255
EP - 1259
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
IS - 23-24
ER -