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We present an optimization-level domain decomposition (DD ) preconditioner for the solution of advection dominated elliptic linearâ€“quadr atic optimal control problems. The DD preconditioner is basedâ€¦ (More)

- Pavel B. Bochev, Denis Ridzal, Kara Peterson
- J. Comput. Physics
- 2014

This paper examines the application of optimization and control ideas to the formulation of feature-preserving numerical methods, with particular emphasis on the conservative and bound-preservingâ€¦ (More)

A Trust-Region Algorithm with Adaptive Stochastic Collocation for PDE Optimization under Uncertainty

- Drew P. Kouri, Matthias Heinkenschloss, Denis Ridzal, Bart G. van Bloemen Waanders
- SIAM J. Scientific Computing
- 2013

The numerical solution of optimization problems governed by partial differential equations (PDEs) with random coefficients is computationally challenging because of the large number of deterministicâ€¦ (More)

- Matthias Heinkenschloss, Denis Ridzal
- SIAM Journal on Optimization
- 2014

We develop and analyze a trust-region sequential quadratic programming (SQP) method for the solution of smooth equality constrained optimization problems, which allows the inexact and hence iterativeâ€¦ (More)

- Joseph Young, Denis Ridzal
- SIAM J. Scientific Computing
- 2012

In this article, we use a dimension reduction technique called random projection to reduce the computational cost of estimating unknown parameters in models based on partial differential equationsâ€¦ (More)

- Pavel B. Bochev, Denis Ridzal
- SIAM J. Numerical Analysis
- 2008

A recent study [4] reveals that convergence of finite element methods usingH(div ,Î©)compatible finite element spaces deteriorates on non-affine quadrilateral grids. This phenomena is particularlyâ€¦ (More)

- Drew P. Kouri, Matthias Heinkenschloss, Denis Ridzal, Bart G. van Bloemen Waanders
- SIAM J. Scientific Computing
- 2014

This paper improves the trust-region algorithm with adaptive sparse grids introduced in [SIAM J. Sci. Comput., 35 (2013), pp. A1847â€“A1879] for the solution of optimization problems governed byâ€¦ (More)

- Pavel Bleher, Denis Ridzal
- 2001

We study statistical properties of zeros of random polynomials and random analytic functions associated with the pseudoeuclidean group of symmetries SU(1, 1), by utilizing both analytical andâ€¦ (More)

- Pavel B. Bochev, Denis Ridzal
- Computers & Mathematics with Applications
- 2016

We present an abstract mathematical framework for an optimization-based additive decomposition of a large class of variational problems into a collection of concurrent subproblems. The frameworkâ€¦ (More)

- Eric C. Cyr, Larry Musson, John N. Shadid, Thomas Smith, Denis Ridzal
- 2011

We develop a new formulation of the Control Volume Finite Element Method (CVFEM) with a multidimensional Scharfetter-Gummel (SG) upwinding for the drift-diffusion equations. The formulation usesâ€¦ (More)