Solving Boltzmann and Fokker-Planck Equations Using Sparse Representation
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 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 31, 2011
- Accession Number
- ADA564031
Entities
People
- Jie Shen
- Weinan E
Organizations
- Purdue University