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.
The work of Prudencio and Cai was partially supported by the Department of Energy, DE-FC02-01ER25479, and by the National Science Foundation, CCR-0219190, ACI-0072089 and ACI-0305666. The work of Byrd was supported in part by the National Science Foundation, CCR-0219190, and by Army Research Office contract DAAD19-02-1-0407.
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Prudencio, E., Byrd, R., Cai, XC. (2005). Domain Decomposition Methods for PDE Constrained Optimization Problems . In: Daydé, M., Dongarra, J., Hernández, V., Palma, J.M.L.M. (eds) High Performance Computing for Computational Science - VECPAR 2004. VECPAR 2004. Lecture Notes in Computer Science, vol 3402. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11403937_43
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DOI: https://doi.org/10.1007/11403937_43
Publisher Name: Springer, Berlin, Heidelberg
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