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Young, Joseph G. ; Ridzal, Denis R.
In the following paper, we discuss how to design an ensemble of experiments through the use of compressed sensing. Specifically, we show how to conduct a small number of physical experiments and then use compressed sensing to reconstruct a larger set of data. In order to accomplish this, we organize our results into four sections. We begin by extending the theory of compressed sensing to a finite product of Hilbert spaces. Then, we show how these results apply to experiment design. Next, we develop an efficient reconstruction algorithm that allows us to reconstruct experimental data projected onto a finite element basis. Finally, we verify our approach with two computational experiments.
Ridzal, Denis R. ; Young, Joseph G.
Walsh, Timothy W. ; Aguilo Valentin, Miguel A. ; Ridzal, Denis R. ; Young, Joseph G.
Walsh, Timothy W. ; Ridzal, Denis R. ; Young, Joseph G.
Walsh, Timothy W. ; Ridzal, Denis R. ; Young, Joseph G.
Young, Joseph G. ; Ridzal, Denis R.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Ridzal, Denis R. ; Young, Joseph G. ; Bochev, Pavel B. ; Peterson, Kara J.
This paper is the final of three related articles that develop and demonstrate a new optimization-based framework for computational modeling. The framework uses optimization and control ideas to assemble and decompose multiphysics operators and to preserve their fundamental physical properties in the discretization process. One application of the framework is in the formulation of robust algorithms for optimization-based transport (OBT). Based on the theoretical foundations established in Part 1 and the optimization algorithm for the solution of the remap subproblem, derived in Part 2, this paper focuses on the application of OBT to a set of benchmark transport problems. Numerical comparisons with two other transport schemes based on incremental remapping, featuring flux-corrected remap and the linear reconstruction with van Leer limiting, respectively, demonstrate that OBT is a competitive transport algorithm. © 2012 Springer-Verlag.
Walsh, Timothy W. ; Ridzal, Denis R. ; Young, Joseph G.
Aguilo Valentin, Miguel A. ; Ridzal, Denis R. ; Young, Joseph G.
Young, Joseph G. ; Ridzal, Denis R. ; Aguilo Valentin, Miguel A.
Aguilo Valentin, Miguel A. ; Ridzal, Denis R. ; Young, Joseph G.
Young, Joseph G. ; Ridzal, Denis R. ; Bochev, Pavel B.
Young, Joseph G. ; Ridzal, Denis R.
Young, Joseph G. ; Ridzal, Denis R.
Collis, Samuel S. ; Ober, Curtis C. ; Overfelt, James R. ; Young, Joseph G.
Ridzal, Denis R. ; Young, Joseph G. ; Bochev, Pavel B.
Ridzal, Denis R. ; Young, Joseph G.
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