Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems

Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems. Stokes control

The governing dynamics of fluid flow is stated as a system of partial differential equations referred to as the Navier-Stokes system. In industrial and scientific applications, fluid flow control becomes an optimization problem where the governing partial differential equations of the fluid flow are stated as constraints. When discretized, the optimal control of the Navier-Stokes equations lead...

Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems. Poisson and convection-diffusion control

Saddle point matrices of a special structure arise in optimal control problems. In this paper we consider distributed optimal control for various types of scalar stationary partial differential problems and compare the efficiency of several numerical solution methods. We test the particular case when the arising linear system can be compressed after eliminating the control function. In that cas...

Preconditioned Krylov Subspace Methods for Eigenvalue Problems

Preconditioned Krylov Subspace Methods in Nonlinear Optimization

One of the possible ways of solving general problems of constrained nonlinear optimization is to convert them into a sequence of unconstrained problems. Then the need arises to solve an unconstrained optimization problem reliably and efficiently. For this aim, Newton methods are usually applied, often in combination with sparse Cholesky decomposition. In practice, however, this approach may not...

Preconditioned Krylov Subspace Methods for Transport Equations

Transport equations have many important applications. Because the equations are based on highly non-normal operators, they present diiculties in numerical computations. The iterative methods have been shown to be one of eecient numerical methods to solve transport equations. However, because of the nature of transport problems, convergence of iterative methods tends to slow for many important p...