Flexible Complementarity Solvers for Large-Scale Applications

2003/07/22 by Steven J. Benson, Todd S. Munson, Benson, Steven J. +1 · 4 citations
Mathematics · #65K01 #90C08 #FOS: Mathematics #Optimization and Control (math.OC) #math.OC #msc:65K01 #msc:90C08

paper · pdf · doi:10.48550/arxiv.math/0307305

17 pages; 2 figures

arxiv created 2003/07/22 · arxiv updated 2009/12/01

Abstract

Discretizations of infinite-dimensional variational inequalities lead to linear and nonlinear complementarity problems with many degrees of freedom. To solve these problems in a parallel computing environment, we propose two active-set methods that solve only one linear system of equations per iteration. The linear solver, preconditioner, and matrix structures can be chosen by the user for a particular application to achieve high parallel performance. The parallel scalability of these methods is demonstrated for some discretizations of infinite-dimensional variational inequalities.

Cited by

• Iterative convergence in phase-field brittle fracture computations: exact line search is all you need
• Mesh-dependent iteration count growth in primal-dual active set strategies
• On phase-field regularization in dynamic fracture with brittle and cohesive formulations
• Variational phase-field modeling of cohesive fracture with flexibly tunable strength surface

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