Computational methods for Cahn-Hilliard variational inequalities

We consider the non-standard fourth order parabolic Cahn-Hilliard variational inequality with constant as well as non-constant diffusional mobility. We propose a primal-dual active set method as solution technique for the discrete variational inequality given by a (semi-)implicit Euler discretization in time and linear finite elements in space. We show local convergence of the method by reinterpretation as a semi-smooth Newton method. The discrete saddle point system arising in each iteration step is handled by either a Gauss-Seidel type method, the application of a multi-frontal direct solver or a preconditioned conjugate gradient method applied to the Schur complement. Finally we show the efficiency of the method and the preconditioning with several numerical simulations

Computer Aided Verification

The open access two-volume set LNCS 11561 and 11562 constitutes the refereed proceedings of the 31st International Conference on Computer Aided Verification, CAV 2019, held in New York City, USA, in July 2019. The 52 full papers presented together with 13 tool papers and 2 case studies, were carefully reviewed and selected from 258 submissions. The papers were organized in the following topical sections: Part I: automata and timed systems; security and hyperproperties; synthesis; model checking; cyber-physical systems and machine learning; probabilistic systems, runtime techniques; dynamical, hybrid, and reactive systems; Part II: logics, decision procedures; and solvers; numerical programs; verification; distributed systems and networks; verification and invariants; and concurrency