Precondition strategies for all-at-once distributed parameter estimation problems

Eldad Haber



We discuss the solution of problems which arise from 3D distributed parameter estimation problems. Using an all-at-once approach, upon discretization and differentiation, we obtain a a very large KKT type system. In order to solve the system we discuss a family of solvers and preconditioners based on an inexact reduced Hessian approach combined with flexible Krylov solvers. We demonstrate the robustness and effectiveness of our approach on a 3D inverse problem which evolve from Maxwell's equations in 3D