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Estep, D.

Publications and source records attributed to Estep, D..

6 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Exploration of efficient reduced-order modeling and a posteriori error estimation

Efficient algorithms are considered for the computation of a reduced-order model based on the proper orthogonal decomposition methodology for the solution of parameterized elliptic partial differential equations. The method relies on partitioning the parameter space into subdomains based on the properties of the solution space and then forming a reduced basis for each of the subdomains. This yields more efficient offline and online stages for the proper orthogonal decomposition method. We extend these ideas for inexpensive adjoint based a posteriori error estimation of both the expensive finite element method solutions and the reduced-order model solutions, for a single and multiple quantities of interest. Finally, various numerical results indicate the efficacy of the approach.

42 ENGINEERING↗
DOE OSTI2015

Parameter estimation and prediction for groundwater contamination based on measure theory

The problem of groundwater contamination in an aquifer is one with many uncertainties. Properly quantifying these uncertainties is es- sential in order to make reliable probabilistic based predictions and decisions regarding remediation strategies. In this work, a measure-theoretic frame- work is employed to quantify uncertainties in a simpli ed groundwater con- tamination transport model. Given uncertain data from observation wells, the stochastic inverse problem is solved numerically to obtain a probability measure on the space of unknown model parameters characterizing ground- water ow and contaminant transport in an aquifer, as well as unknown model boundary or source terms such as the contaminant source release into the environment. This probability measure is used to make predictions of future contaminant concentrations and to analyze possible remediation techniques. The ability to identify regions of small but nonzero probability using this method is illustrated.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

Definition and solution of a stochastic inverse problem for the Manning’s n parameter field in hydrodynamic models

The uncertainty in spatially heterogeneous Manning’s n fields is quantified using a novel formulation and numerical solution of stochastic inverse problems for physics-based models. The uncertainty is quantified in terms of a probability measure and the physics-based model considered here is the state-of-the-art ADCIRC model although the presented methodology applies to other hydrodynamic models. An accessible overview of the formulation and solution of the stochastic inverse problem in a mathematically rigorous framework based on measure theory is presented in this paper. Technical details that arise in practice by applying the framework to determine the Manning’s n parameter field in a shallow water equation model used for coastal hydrodynamics are presented and an efficient computational algorithm and open source software package are developed. A new notion of “condition” for the stochastic inverse problem is defined and analyzed as it relates to the computation of probabilities. Finally, this notion of condition is investigated to determine effective output quantities of interest of maximum water elevations to use for the inverse problem for the Manning’s n parameter and the effect on model predictions is analyzed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

First steps toward a multiphysics exemplars and benchmarks suite

A workshop report (Keyes et al., 2012) summarizes challenges and opporunities in multiphysics simulations from algorithmic and architectural perspectives, where "algorithmic" includes both mathematical analysis and computational complexity and "architectural" includes both software and hardware environments. The report discusses the significant and still remaining key needs for conducting the mathematical analysis and developing the corresponding flexible software necessary to ensure that coupling schemes are accurate, stable, robust, consistent, and are implemented correctly, as prerequisites for developing predictive multiphysics simulations. Such work is essential for exploiting emerging extreme-scale computing resources for scientific discovery.

Keyes, D. E.↗