On robust domain decomposition solvers and the automation of adjoint and tangent linear models of differential-algebraic equations

Abstract:

Balancing Domain Decomposition by Constraints (BDDC) preconditioners represent the first alternative to Algebraic Multigrid methods for the solution of large and sparse linear systems arising from the Finite Element Method (FEM). The first part of the talk will introduce the solver and discuss its strengths and weaknesses. Recent numerical results on H(div) and H(curl) spaces, demonstrating the robustness of the method with respect to higher-order spaces, higher-order meshes, adaptive mesh refinement and coefficients heterogeneity, will be provided.

The possibility of automating the derivation of adjoint and tangent linear models of differential-algebraic equations is attractive since these equations represent the key ingredient in many aspects of computational science, including data assimilation, parameter identification, sensitivity analysis, shape optimization, and optimal control, to cite a few. In the second part of the talk, we present a novel framework to automate these computations within the PETSc library. Preliminary results for PDE-constrained optimization with a low-frequency approximation of the Maxwell equations and for generalized stability theory applied to second grade phase-field models will be presented.

Biography:

Stefano Zampini earned his Ph.D. in Applied Mathematics from Università degli Studi di Milano in 2011. While a Ph.D. candidate and for three years afterward, he worked for the Italian supercomputing center CINECA as a computational scientist. In 2014, he joined the Extreme Computing Research Center at King Abdullah University of Science and Technology (Saudi Arabia) as research scientist.

His research interests are in Domain Decomposition methods and, more generally, on the efficient numerical solution of partial differential equations. He has experience in computational cardiology, subsurface inversion, linear elasticity, and multiphase flow. He is a developer of the Portable and Extensible Toolkit for Scientific computations (PETSc) developed and maintained at the Argonne National Laboratory.