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K-State Today

January 26, 2017

Mathematics Colloquium Lecture Jan. 26

By Reta McDermott

Corey Bryant, Cerner Corporation, will present "Goal-Oriented Predictive Simulation: Reliable Finite Element Solutions Under Uncertainty" as part of the Mathematics Department Colloquium Lecture series at 2:30 p.m. Thursday, Jan. 26, in 122 Cardwell Hall.

The abstract for the lecture is: Computational models are increasingly being used to inform engineering design and public policy decisions. Which raises the question: How reliable are the predictions provided by these models? Reliable prediction begins with the proper mathematical representation. In practical applications however, analytical solutions for the full mathematical model are not available and one resorts to numerical solutions — introducing discretization error. The description of the problem is usually imperfect as well, involving uncertainty in the geometry, boundary conditions, or material behavior. Fortunately, the complete solution may not be required. Often a quantity of interest (QoI), or a specific feature of the solution, is the primary concern of the analyst; for example, the average velocity of turbulent channel flow, final concentrations in a chemical reaction, or the flow rate through porous media.

In this talk, Bryant will demonstrate the use of goal-oriented finite element methods for predicting QoIs under uncertainty. Techniques for estimating the error in QoIs are based on the solution of an adjoint problem related to the particular quantity of interest. Bryant will introduce the established theory for linear deterministic problems and discuss extensions to nonlinear systems. Incorporating uncertainty makes realistic simulation difficult; Bryant will present an adaptive technique for constructing response surfaces of the QoI. Instead of sampling the solution of a differential equation, this approximate model can be used to perform statistical inference and Bayesian model selection.

Finally, Bryant will present a framework for how these techniques can be used to target "stochastic QoIs," or the probability of an event. While the theory is general, and widely applicable, Bryant will present results for applications in fluids.

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