University of Maryland Department of Computer Science and Institute for Advanced
Computer Studies
Efficient Solution Algorithms for Stochastic Partial Differential Equations
December 3, 2014
3:00pm PGH 646
Abstract
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.
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Last modified: April 11 2016 - 18:14:43