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FAST ALGORITHMS FOR THE SOLUTION OF STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

dc.contributor.advisorElman, Howard Cen_US
dc.contributor.authorMiller, Christopher Williamen_US
dc.date.accessioned2012-07-06T11:16:27Z
dc.date.available2012-07-06T11:16:27Z
dc.date.issued2011en_US
dc.identifier.urihttp://hdl.handle.net/1903/12532
dc.description.abstractWe explore the performance of several algorithms for the solution of stochastic partial differential equations including the stochastic Galerkin method and the stochastic sparse grid collocation method. We also introduce a new method called the adaptive kernel density estimation (KDE) collocation method, which addresses some of the deficiencies present in other stochastic PDE solution methods. This method combines an adaptive sparse grid collocation method with KDE to optimally allocate stochastic degrees of freedom. Several components of this method can be computationally expensive, such as automatic bandwidth selection for the kernel density estimate, evaluation of the kernel density estimate, and computation of the coefficients of the approximate solution. Fortunately all of these operations are easily parallelizable. We present an implementation of adaptive KDE collocation that makes use of NVIDIA's complete unified device architecture (CUDA) to perform the computations in parallel on graphics processing units (GPUs).en_US
dc.titleFAST ALGORITHMS FOR THE SOLUTION OF STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONSen_US
dc.typeDissertationen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.contributor.departmentApplied Mathematics and Scientific Computationen_US
dc.subject.pqcontrolledApplied mathematicsen_US
dc.subject.pqcontrolledComputer scienceen_US
dc.subject.pquncontrolledkernel density estimationen_US
dc.subject.pquncontrollednumerical analysisen_US
dc.subject.pquncontrolledstochastic collocationen_US
dc.subject.pquncontrolledUncertainty quantificationen_US


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