Algebraic multigrid preconditioning of the Hessian in optimization constrained by a partial differential equation |
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Authors: | Andrew T Barker Andrei Drgnescu |
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Institution: | Andrew T. Barker,Andrei Dr?g?nescu |
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Abstract: | 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. |
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Keywords: | algebraic multigrid elliptic equations finite element methods PDE‐constrained optimization |
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