swMATH ID: 42057
Software Authors: Franceschini, Andrea; Ferronato, Massimiliano; Frigo, Matteo; Janna, Carlo
Description: A reverse augmented constraint preconditioner for Lagrange multiplier methods in contact mechanics. Frictional contact is one of the most challenging problems in computational mechanics. Typically, it is a tough non-linear problem often requiring several Newton iterations to converge and causing troubles also in the solution to the related linear systems. When contact is modeled with the aid of Lagrange multipliers, the impenetrability condition is enforced exactly, but the associated Jacobian matrix is indefinite and needs a special treatment for a fast numerical solution. In this work, a constraint preconditioner is proposed where the primal Schur complement is computed after augmenting the zero block. The name extit{Reverse} is used in contrast to the traditional approach where only the structural block undergoes an augmentation. Besides being able to address problems characterized by singular structural blocks, often arising in contact mechanics, it is shown that the proposed approach is significantly cheaper than traditional constraint preconditioning for this class of problems and it is suitable for an efficient HPC implementation through the Chronos parallel package. Our conclusions are supported by several numerical experiments on mid- and large-size problems from various applications. The source files implementing the proposed algorithm are freely available on GitHub.
Homepage: https://www.sciencedirect.com/science/article/abs/pii/S0045782522000421
Keywords: contact mechanics; Lagrange multiplier; augmentation; multigrid preconditioner
Related Software: Chronos; FSAIPACK; DEMPack; ParMETIS
Referenced in: 1 Publication

Referenced in 1 Field

1 Numerical analysis (65-XX)

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