Invited Session Tue.3.MA 041

Tuesday, 15:15 - 16:45 h, Room: MA 041

Cluster 3: Complementarity & variational inequalities [...]

Differential variational inequalities


Chair: Mihai Anitescu



Tuesday, 15:15 - 15:40 h, Room: MA 041, Talk 1

Lei Wang
Large-scale differential variational inequalities for phase-field modeling

Coauthors: Shrirang Abhyankar, Mihai Anitescu, Jungho Lee, Lois Curfman Mcinnes, Todd Munson, Barry F. Smith


Recent progress on the development of scalable differential variational inequality multigrid-based solvers for the phase-field approach to mesoscale materials modeling is described. We have developed a reduced space method, augmented reduced space method, and semismooth method for variational inequalities in PETSc, leveraging experience by the optimization community in TAO. A geometric multigrid solver in PETSc is used to solve the resulting linear systems. We present strong and weak scaling results for 2D coupled Allen-Cahn/Cahn-Hilliard systems.



Tuesday, 15:45 - 16:10 h, Room: MA 041, Talk 2

Michael Hinterm├╝ller
A bundle-free implicit programming approach for MPECs in function space via smoothing

Coauthor: Thomas M. Surowiec


Using a standard first-order optimality condition for nonsmooth optimization problems, a general framework for a descent method is developed. This setting is applied
to a typical class of mathematical programs with equilibrium constraints in function
space from which a new algorithm is derived. Global convergence of the algorithm
is demonstrated in function space and the results are then illustrated by numerical



Tuesday, 16:15 - 16:40 h, Room: MA 041, Talk 3

Mohammad Hassan Farshbaf-Shaker
Optimal control of vector-valued elastic Allen-Cahn variational inequalities

Coauthor: Claudia Hecht


A vector-valued elastic Allen-Cahn-MPEC problem is considered and a penalization technique is applied to show the existence of an optimal control. We show that the stationary points of the penalized problems converge to some stationary points of the limit problem, which however are weaker than C-stationarity conditions.


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