Algebraic multigrid preconditioning of the Hessian in optimization constrained by a partial differential equation

Barker, Andrew T.; Drăgănescu, Andrei

doi:10.1002/nla.2333

Algebraic multigrid preconditioning of the Hessian in optimization constrained by a partial differential equation

Journal Article · Tue Sep 15 00:00:00 EDT 2020 · Numerical Linear Algebra with Applications

DOI:https://doi.org/10.1002/nla.2333· OSTI ID:1786516

^[1]; Drăgănescu, Andrei ^[2]

Center for Applied Scientific Computing Lawrence Livermore National Laboratory Livermore California USA
University of Maryland, Baltimore County Baltimore Maryland USA

Summary

We construct an algebraic multigrid (AMG) based preconditioner for the reduced Hessian of a linear‐quadratic optimization problem constrained by an elliptic partial differential equation. While the preconditioner generalizes a geometric multigrid preconditioner introduced in earlier works, its construction relies entirely on a standard AMG infrastructure built for solving the forward elliptic equation, thus allowing for it to be implemented using a variety of AMG methods and standard packages. Our analysis establishes a clear connection between the quality of the preconditioner and the AMG method used. The proposed strategy has a broad and robust applicability to problems with unstructured grids, complex geometry, and varying coefficients. The method is implemented using the Hypre package and several numerical examples are presented.

View Accepted Manuscript (Publisher)

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0005455; AC52-07NA27344

OSTI ID:: 1786516

Journal Information:: Numerical Linear Algebra with Applications, Journal Name: Numerical Linear Algebra with Applications Journal Issue: 1 Vol. 28; ISSN 1070-5325

Publisher:: Wiley Blackwell (John Wiley & Sons)Copyright Statement

Country of Publication:: United Kingdom

Language:: English

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