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2014-04-15 - Kathleen Hoffman
 
2014-10-14 - Howard Elman
 

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Upcoming (in Stanley Thomas 316 at 3pm)

September 23, 2014

Noa Marom, Physics & Engineering Physics, Tulane

 

September 30, 2014

Nicole Gasparini, Earth and Environmental Sciences, Tulane University

 

October 14, 2014

Howard Elman, Computer Science and Institute for Advanced Computer Studies, University of Maryland

https://www.cs.umd.edu/users/elman/

"Efficient Solution Algorithms for Stochastic Partial Differential Equations"

We consider new computational methods for solving partial differential equations (PDEs) when components of the problem such as diffusion coefficients or boundary conditions are not known with certainty but instead are represented as random fields.  In recent years, several computational techniques have been developed for such models that offer potential for improved efficiencies compared with traditional Monte-Carlo methods.  These include stochastic Galerkin methods, which use an augmented weak formulation of the PDE derived from averaging with respect to expected value, and stochastic collocation methods, which use a set of samples relatively small in cardinality that captures the character of the solution space. We give an overview of the relative advantages of these two methods and present efficient computational algorithms for solving the algebraic systems that arise from them.  In addition, we show that these algorithms can be combined with techniques of reduced-order modeling to significantly enhance efficiency with essentially no loss of accuracy.

Center for Computational Science, Stanley Thomas Hall 402, New Orleans, LA 70118 ccs@tulane.edu