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- W96749757 abstract "We consider an elliptic optimal control problem in two dimensions, in which the control variable corresponds to the Neumann data on a boundary segment, and where the performance functional is regularized to ensure that the problem is well posed. A finite element discretization of this control problem yields a saddle point linear system, which can be reduced to a symmetric positive definite Hessian system for determining the control variables. We formulate a robust preconditioner for this reduced Hessian system, as a matrix product involving the discrete Neumann to Dirichlet map and a mass matrix, and show that it yields a condition number bound which is uniform with respect to the mesh size and regularization parameters. On a uniform grid, this preconditioner can be implemented using a fast sine transform. Numerical tests verify the theoretical bounds." @default.
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- W96749757 date "2008-01-01" @default.
- W96749757 modified "2023-09-27" @default.
- W96749757 title "A Robust Preconditioner for the Hessian System in Elliptic Optimal Control Problems" @default.
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- W96749757 doi "https://doi.org/10.1007/978-3-540-75199-1_66" @default.
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