Accession Number

ADA564031

Title

Solving Boltzmann and FokkerPlanck Equations Using Sparse Representation.

Publication Date

May 2011

Media Count

9p

Personal Author

J. Shen

Abstract

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 FokkerPlanck 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 FokkerPlanck equations. Besides the work presented in this report, a number of other related publications by the PIs were also partially supported by this grant.

Keywords

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


Source Agency

Non Paid ADAS

NTIS Subject Category

72B  Algebra, Analysis, Geometry, & Mathematical Logic 72E  Operations Research

Corporate Author

Purdue Univ., West Lafayette, IN. Dept. of Mathematics.

Document Type

Technical report

Title Note

Final rept. Apr 2008May 2011.

NTIS Issue Number

1302

Contract Number

FA95500810416
