1,535 research outputs found
Factorizing the Stochastic Galerkin System
Recent work has explored solver strategies for the linear system of equations
arising from a spectral Galerkin approximation of the solution of PDEs with
parameterized (or stochastic) inputs. We consider the related problem of a
matrix equation whose matrix and right hand side depend on a set of parameters
(e.g. a PDE with stochastic inputs semidiscretized in space) and examine the
linear system arising from a similar Galerkin approximation of the solution. We
derive a useful factorization of this system of equations, which yields bounds
on the eigenvalues, clues to preconditioning, and a flexible implementation
method for a wide array of problems. We complement this analysis with (i) a
numerical study of preconditioners on a standard elliptic PDE test problem and
(ii) a fluids application using existing CFD codes; the MATLAB codes used in
the numerical studies are available online.Comment: 13 pages, 4 figures, 2 table
Computational aspects of scalar dispersion modeling and simulation in complex flows
We present an overview of nowadays modeling capabilities and numerical challanges in the simulation of scalar dispersion phenomena in complex flows. Results from the simulation of a passive plume emitted from a line source downstream of a square obstacle are summarized to provide an example of a basic test case where the reliability of computational techniques can be carefully established
Computational aspects of scalar dispersion modeling and simulation in complex flows
We present an overview of nowadays modeling capabilities and numerical challanges in the simulation of scalar dispersion phenomena in complex flows. Results from the simulation of a passive plume emitted from a line source downstream of a square obstacle are summarized to provide an example of a basic test case where the reliability of computational techniques can be carefully established
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