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A FULL APPROXIMATION SCHEME MULTILEVEL METHOD FOR NONLINEAR VARIATIONAL INEQUALITIES.

A FULL APPROXIMATION SCHEME MULTILEVEL METHOD FOR NONLINEAR VARIATIONAL INEQUALITIES.

Authors :
BUELER, ED
FARRELL, PATRICK E.
Source :
SIAM Journal on Scientific Computing. 2024, Vol. 46 Issue 4, pA2421-A2444. 24p.
Publication Year :
2024

Abstract

We present the full approximation scheme constraint decomposition (FASCD) multilevel method for solving variational inequalities (VIs). FASCD is a joint extension of both the full approximation scheme multigrid technique for nonlinear partial differential equations, due to A. Brandt, and the constraint decomposition (CD) method introduced by X.-C. Tai for VIs arising in optimization. We extend the CD idea by exploiting the telescoping nature of certain subset decompositions arising from multilevel mesh hierarchies. When a reduced-space (active set) Newton method is applied as a smoother, with work proportional to the number of unknowns on a given mesh level, FASCD V-cycles exhibit nearly mesh-independent convergence rates. The full multigrid cycle version is an optimal solver. The example problems include differential operators which are symmetric linear, nonsymmetric linear, and nonlinear, in unilateral and bilateral VI problems. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
10648275
Volume :
46
Issue :
4
Database :
Academic Search Index
Journal :
SIAM Journal on Scientific Computing
Publication Type :
Academic Journal
Accession number :
179540909
Full Text :
https://doi.org/10.1137/23M1594200