Chris Siefert

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We propose and examine block-diagonal preconditioners and variants of indefinite preconditioners for block two-by-two generalized saddle-point problems. That is, we consider the nonsymmetric, nonsingular case where the (2,2) block is small in norm, and we are particularly concerned with the case where the (1,2) block is different from the transposed (2,1)(More)
Several Schur complement-based preconditioners have been proposed for solving (generalized) saddle-point problems. We consider matrices where the Schur complement has rapid decay over some graph known a priori. This occurs for many matrices arising from the discretization of systems of partial differential equations, and this graph is then related to the(More)
Approved for public release; further dissemination unlimited. NOTICE: This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government, nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, make any warranty, express or(More)
Several Schur complement-based preconditioners have been proposed for solving (generalized) saddle-point problems. We consider probing-based methods for approximating those Schur complements in the preconditioners of the type proposed by [Murphy, Golub and Wathen '00], [de Sturler and Liesen '03] and [Siefert and de Sturler '04]. This approach can be(More)
Conventional least squares finite element methods (LSFEM) for incompressible flows conserve mass approximately. In some cases, this can lead to an unacceptable loss of mass and unphysical solutions. In this report we formulate a new, locally conservative LSFEM for the Stokes equations which computes a discrete velocity field that is point-wise divergence(More)
Several Schur complement-based preconditioners have been proposed for solving (generalized) saddle-point problems. We consider probing-based methods for approximating those Schur complements in the preconditioners of the type proposed by [Murphy, Golub and Wathen '00], [de Sturler and Liesen '03] and [Siefert and de Sturler '04]. This approach can be(More)
We examine block-diagonal preconditioners and efficient variants of indefinite preconditioners for block two-by-two generalized saddle-point problems. We consider the general, nonsymmetric, nonsingular case. In particular, the (1,2) block need not equal the transposed (2,1) block. Our preconditioners arise from computationally efficient splittings of the(More)
Approved for public release; further dissemination unlimited. NOTICE: This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government, nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, make any warranty, express or(More)
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