A Fast Solver for a Nonsmooth Optimization problem in a phase separation model

A Fast Solver for a Nonsmooth Optimization problem in a phase separation model Short CVThe speaker has spent roughly 8.5 years in Europe working on research projects in various institutes. Currently, he is doing postdoc in the department of mathematics and computer science at FU, Berlin. Before that, he had two postdoctoral positions at Fraunhofer ITWM and KU Leuven. He has his PhD from INRIA, Saclay and a master degree in mathematics and computing from IIT, Guwahati. His research interests include various aspects of PDE solvers such as developing new iterative solvers, their convergence analysis, and their parallel implementation.Abstract Phase separation phenomena are now typically modelled by Cahn-Hilliard equations. To model the observed deep quench event, a nonsmooth obstacle potential have been proposed. Recently, a Newton-Schur method was proposed that may be viewed as Uzawa iteration with a flavour of active set strategy. Solution of obstacle problem identifies the active sets, then the problem reduces to a linear problem on nonactive set. This corresponds to solving a saddle point problem but on truncated domains.In this talk, the speaker will discuss efficient preconditioning for solving linear saddle point problems on truncated domains. In particular, some optimal existing saddle point solvers will be adapted on truncated domains. Spectrum analysis and numerical experiments will show the robustness of these solvers for various evolutions. References: [1] P. Kumar, Fast Preconditioned Solver for Truncated Saddle Point Problem in Nonsmooth Cahn-Hilliard Model, Studies in Computational Intelligence, Book Chapter, to appear, 2016 [2] P. Kumar, Preconditioners based on approximation of nonstandard norms for phase separation applications, ICNAAM 2015, Greece, AIP proceedings, to appear, 2016