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Accession Number
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ADA564031
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Title
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Solving Boltzmann and Fokker-Planck Equations Using Sparse Representation.
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Publication Date
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May 2011
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Media Count
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9p
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Personal Author
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J. Shen
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Abstract
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A major issue in modeling and computation is how to handle high dimensional problems. We can divide these high dimensional problems into two classes: moderately high dimensional problems or very high dimensional problems. In the former class, we have problems such as the Boltzmann equation and Fokker-Planck equation, whose dimensionality is moderately high but are amendable to sparse grid based methods. In the latter class, we have problems such as exploration of the configuration space of a large molecule. These problems often involve hundreds of thousands of dimensions, and methods based on fixed grids are far from being adequate. We developed various techniques in handling these problems using the hyperbolic cross/sparse representation for the former class, and adaptive sampling for the latter. These developments are aimed at providing a solid foundation for efficient and reliable numerical simulations of Boltzmann and Fokker-Planck equations. Besides the work presented in this report, a number of other related publications by the PIs were also partially supported by this grant.
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Keywords
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Adaptive minimum action methods
Approximation(Mathematics)
Atomistic modeling
Boltzmann equation
Computation science
Fokker planck equations
Hyperbolic cross approximations
Korobov spaces
Mathematical models
Sequential multiscale modeling
Sparse matrix
Sparse representation
Subcritical instabilities
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Source Agency
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Non Paid ADAS
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NTIS Subject Category
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72B - Algebra, Analysis, Geometry, & Mathematical Logic
72E - Operations Research
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Corporate Author
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Purdue Univ., West Lafayette, IN. Dept. of Mathematics.
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Document Type
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Technical report
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Title Note
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Final rept. Apr 2008-May 2011.
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NTIS Issue Number
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1302
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Contract Number
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FA9550-08-1-0416
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