Abstract:

Optimal design, nonlinear inverse and data assimilation problems, nonlinear time-dependent problems, and uncertainty quanti cation in computational mechanics lead to di cult and time consuming simulations involving ill-conditioned problems. We will survey recent approaches to drastically reduce the cost of such computations. This survey includes approaches at the nonlinear solver/optimization level as well as approaches at the linear solver/preconditioning level and the interaction of these, including model reduction, stochastic computations, and strategies, such as Krylov recycling, for the fast solution of sequences or groups of related linear systems. Results will be demonstrated on several applications.