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5. The Canadian Statistical Sciences Institute 2003–2022.

Author

Thompson, Mary, Reid, Nancy, and Estep, Don

Subjects
STATISTICS, FOUNDING, DATA science
Abstract

Copyright of Canadian Journal of Statistics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Published
2022
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8. Preface

Author

Dieci, Luca, Estep, Don, and Van De Velde, Eric

Published
1997

9. Solving Stochastic Inverse Problems using Sigma-Algebras on Contour Maps

Author

Butler, Troy, Estep, Don, Tavener, Simon, Wildey, Timothy, Dawson, Clint, and Graham, Lindley

Subjects
FOS: Mathematics, Numerical Analysis (math.NA), Mathematics - Numerical Analysis, 28-02, 28C99, 97N40, 34A45, 60F99
Abstract

We compute approximate solutions to inverse problems for determining parameters in differential equation models with stochastic data on output quantities. The formulation of the problem and modeling framework define a solution as a probability measure on the parameter domain for a given $\sigma-$algebra. In the case where the number of output quantities is less than the number of parameters, the inverse of the map from parameters to data defines a type of generalized contour map. The approximate contour maps define a geometric structure on events in the $\sigma-$algebra for the parameter domain. We develop and analyze an inherently non-intrusive method of sampling the parameter domain and events in the given $\sigma-$algebra to approximate the probability measure. We use results from stochastic geometry for point processes to prove convergence of a random sample based approximation method. We define a numerical $\sigma-$algebra on which we compute probabilities and derive computable estimates for the error in the probability measure. We present numerical results to illustrate the various sources of error for a model of fluid flow past a cylinder., Comment: 26 pages, 24 figures

Published
2014

10. Multiphysics simulations: Challenges and opportunities.

Author

Keyes, David E, McInnes, Lois C, Woodward, Carol, Gropp, William, Myra, Eric, Pernice, Michael, Bell, John, Brown, Jed, Clo, Alain, Connors, Jeffrey, Constantinescu, Emil, Estep, Don, Evans, Kate, Farhat, Charbel, Hakim, Ammar, Hammond, Glenn, Hansen, Glen, Hill, Judith, Isaac, Tobin, and Jiao, Xiangmin

Subjects
SIMULATION methods & models, ALGORITHMS, PERSPECTIVE (Art), COMPUTATIONAL complexity, COMPUTER systems, ELECTRONIC data processing
Abstract

We consider multiphysics applications from algorithmic and architectural perspectives, where “algorithmic” includes both mathematical analysis and computational complexity, and “architectural” includes both software and hardware environments. Many diverse multiphysics applications can be reduced, en route to their computational simulation, to a common algebraic coupling paradigm. Mathematical analysis of multiphysics coupling in this form is not always practical for realistic applications, but model problems representative of applications discussed herein can provide insight. A variety of software frameworks for multiphysics applications have been constructed and refined within disciplinary communities and executed on leading-edge computer systems. We examine several of these, expose some commonalities among them, and attempt to extrapolate best practices to future systems. From our study, we summarize challenges and forecast opportunities. [ABSTRACT FROM AUTHOR]

Published
2013
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