Recent Approaches in Linear and Nonlinear Solvers and Optimization for Large and Complex Computational Mechanics Problems

Recent Approaches in Linear and Nonlinear Solvers and Optimization for Large and Complex Computational Mechanics Problems

Sturler, Eric de

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.

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.

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DOI:

Como citar:

Sturler, Eric de; "Recent Approaches in Linear and Nonlinear Solvers and Optimization for Large and Complex Computational Mechanics Problems", p-3-3. In: Proceedings of the 13th International Symposium on Multiscale, Multifunctional and Functionally Graded Materials [=Blucher Material Science Proceedings, v.1, n.1]. São Paulo: Blucher, 2014.
ISSN 23589337, DOI