Domain decomposition methods for PDE constrained optimization problems

Authors:
Ernesto Prudencio;Richard Byrd;Xiao-Chuan Cai
Affiliations:
Department of Computer Science, University of Colorado, Boulder, CO;Department of Computer Science, University of Colorado, Boulder, CO;Department of Computer Science, University of Colorado, Boulder, CO
Venue:
VECPAR'04 Proceedings of the 6th international conference on High Performance Computing for Computational Science
Year:
2004

Citing 14
Cited 0

Domain decomposition algorithms with small overlap

SIAM Journal on Scientific Computing
Choosing the forcing terms in an inexact Newton method

SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Finite-Dimensional Approximation of a Class of Constrained Nonlinear Optimal Control Problems

SIAM Journal on Control and Optimization
Domain decomposition: parallel multilevel methods for elliptic partial differential equations

Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Parallel Newton--Krylov--Schwarz Algorithms for the Transonic Full Potential Equation

SIAM Journal on Scientific Computing
A Penalized Neumann Control Approach for Solving an Optimal Dirichlet Control Problem for the Navier--Stokes Equations

SIAM Journal on Control and Optimization
Numerical Approximation of Optimal Flow Control Problems by a Penalty Method: Error Estimates and Numerical Results

SIAM Journal on Scientific Computing
A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems

SIAM Journal on Scientific Computing
Nonlinearly Preconditioned Inexact Newton Algorithms

SIAM Journal on Scientific Computing
Iterative Methods for Sparse Linear Systems

Iterative Methods for Sparse Linear Systems
Restricted Additive Schwarz Preconditioners with Harmonic Overlap for Symmetric Positive Definite Linear Systems

SIAM Journal on Numerical Analysis
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)

Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Parallel Lagrange--Newton--Krylov--Schur Methods for PDE-Constrained Optimization. Part I: The Krylov--Schur Solver

SIAM Journal on Scientific Computing
Parallel Lagrange--Newton--Krylov--Schur Methods for PDE-Constrained Optimization. Part II: The Lagrange--Newton Solver and Its Application to Optimal Control of Steady Viscous Flows

SIAM Journal on Scientific Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

Optimization problems constrained by nonlinear partial differential equations have been the focus of intense research in scientific computing lately. Current methods for the parallel numerical solution of such problems involve sequential quadratic programming (SQP), with either reduced or full space approaches. In this paper we propose and investigate a class of parallel full space SQP Lagrange-Newton-Krylov-Schwarz (LNKSz) algorithms. In LNKSz, a Lagrangian functional is formed and differentiated to obtain a Karush-Kuhn-Tucker (KKT) system of nonlinear equations. Inexact Newton method with line search is then applied. At each Newton iteration the linearized KKT system is solved with a Schwarz preconditioned Krylov subspace method. We apply LNKSz to the parallel numerical solution of some boundary control problems of two-dimensional incompressible Navier-Stokes equations. Numerical results are reported for different combinations of Reynolds number, mesh size and number of parallel processors.