TY - JOUR
T1 - A unified approach to parallel space decomposition methods
AU - Frommer, Andreas
AU - Renaut, Rosemary
N1 - Funding Information:
We are thankful to Daniel B. Szyld for his helpful comments on an earlier version of this paper. The research of the second author was supported under grant NSF DMS9402943.
PY - 1999/10/15
Y1 - 1999/10/15
N2 - We consider (relaxed) additive and multiplicative iterative space decomposition methods for the minimization of sufficiently smooth functionals without constraints. We develop a general framework which unites existing approaches from both parallel optimization and finite elements. Specifically this work unifies earlier research on the parallel variable distribution method in minimization, space decomposition methods for convex functionals, algebraic Schwarz methods for linear systems and splitting methods for linear least squares. We develop a general convergence theory within this framework, which provides several new results as well as including known convergence results.
AB - We consider (relaxed) additive and multiplicative iterative space decomposition methods for the minimization of sufficiently smooth functionals without constraints. We develop a general framework which unites existing approaches from both parallel optimization and finite elements. Specifically this work unifies earlier research on the parallel variable distribution method in minimization, space decomposition methods for convex functionals, algebraic Schwarz methods for linear systems and splitting methods for linear least squares. We develop a general convergence theory within this framework, which provides several new results as well as including known convergence results.
KW - 65H10
KW - Block Jacobi
KW - Block SOR
KW - Finite elements
KW - Minimization Coordinate descent
KW - Multisplittings Parallel computation
KW - Parallel variable distribution
KW - Space decomposition methods
UR - http://www.scopus.com/inward/record.url?scp=0033318097&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0033318097&partnerID=8YFLogxK
U2 - 10.1016/S0377-0427(99)00235-6
DO - 10.1016/S0377-0427(99)00235-6
M3 - Article
AN - SCOPUS:0033318097
SN - 0377-0427
VL - 110
SP - 205
EP - 223
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
IS - 1
ER -