Domain decomposition for 3D nonlinear magnetostatic problems: Newton-Krylov-Schur vs. Schur-Newton-Krylov methods

Parallel Lagrange-Newton-Krylov-Schur Methods for PDE-Constrained Optimization. Part I: The Krylov-Schur Solver

Large scale optimization of systems governed by partial differential equations (PDEs) is a frontier problem in scientific computation. The state-of-the-art for such problems is reduced quasi-Newton sequential quadratic programming (SQP) methods. These methods take full advantage of existing PDE solver technology and parallelize well. However, their algorithmic scalability is questionable; for c...

Hybrid Newton - Krylov / Domain Decomposition

Krylov-Schur Methods in SLEPc

About SLEPc Technical Reports: These reports are part of the documentation of slepc, the Scalable Library for Eigenvalue Problem Computations. They are intended to complement the Users Guide by providing technical details that normal users typically do not need to know but may be of interest for more advanced users.

Parallel Lagrange-newton-krylov-schur Methods for Pde-constrained Optimization Part I: the Kkt Preconditioner

1. Introduction. Optimization problems that are constrained by partial differential equations (PDEs) arise naturally in many areas of science and engineering. In the sciences, such problems often appear as inverse problems in which some of the parameters in a simulation are unavailable, and must be estimated by comparison with physical data. These parameters are typically boundary conditions, i...

Newton-Krylov Type Algorithm for Solving Nonlinear Least Squares Problems

The minimization of a quadratic function within an ellipsoidal trust region is an important subproblem for many nonlinear programming algorithms. When the number of variables is large, one of the most widely used strategies is to project the original problem into a small dimensional subspace. In this paper, we introduce an algorithm for solving nonlinear least squares problems. This algorithm i...