Optimizing the Inexact Newton Krylov Method Using Combinatorial Approaches

Inexact-hessian-vector Products for Efficient Reduced-space Pde-constrained Optimization

We investigate reduced-space Newton-Krylov (NK) algorithms for engineering parameter optimization problems constrained by partial-differential equations. We review reduced-space and full-space optimization algorithms, and we show that the efficiency of the reduced-space strategy can be improved significantly with inexact-Hessianvector products computed using approximate second-order adjoints. R...

Inexact Newton Dogleg Methods

The dogleg method is a classical trust-region technique for globalizing Newton’s method. While it is widely used in optimization, including large-scale optimization via truncatedNewton approaches, its implementation in general inexact Newton methods for systems of nonlinear equations can be problematic. In this paper, we first outline a very general dogleg method suitable for the general inexac...

A Parallel Inexact Newton Method Using A Krylov Multisplitting Algorithm

A parallel Newton-Krylov flow solver for the Euler equations on multi-block grids

We present a parallel Newton-Krylov algorithm for solving the three-dimensional Euler equations on multi-block structured meshes. The Euler equations are discretized on each block independently using second-order accurate summation-by-parts operators and scalar numerical dissipation. Boundary conditions are imposed and block interfaces are coupled using simultaneous approximation terms (SATs). ...

Accelerated Inexact Newton Schemes for Large Systems of Nonlinear Equations

Classical iteration methods for linear systems, such as Jacobi iteration, can be accelerated considerably by Krylov subspace methods like GMRES. In this paper, we describe how inexact Newton methods for nonlinear problems can be accelerated in a similar way and how this leads to a general framework that includes many well-known techniques for solving linear and nonlinear systems, as well as new...