I shall talk about how to design fast spectral-Galerkin algorithms forsome prototypical partial differential equations. We shall start withalgorithms in one dimension, then using a tensor product approach fortwo and three dimensions, and hyperbolic cross/spectral sparse gridfor higher dimensional problems.
Creator:
Shen, Jie (Purdue University)
Created:
2010-10-31
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Many scientific, engineering and financial applications requiresolving high-dimensional PDEs. However, traditional tensor productbased algorithms suffer from the so called 'curse of dimensionality'.We shall construct a new sparse spectral method forhigh-dimensional problems, and present, in particular,rigorous error estimates as well as efficien...
Creator:
Shen, Jie (Purdue University)
Created:
2010-11-03
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Identification of rare variants by resequencing is important both for detecting novel variations and for screening individuals for known disease alleles. New technologies enable low-cost resequencing of target regions, although it is still prohibitive to test more than a few individuals. We propose a novel pooling design that enables the recover...
Creator:
Shental, Noam (Open University of Israel)
Created:
2012-02-13
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We consider a model for the flow of granular matter which was proposed byHadeler and Kuttler (Granular Matter, 1999). The original model uses the height ofthe standing layer and the thickness of the moving layer as the unknowns.By introducing the slope the standing layer, one arrives at a 2 by 2 system ofbalance laws. This system is weakly linea...
Creator:
Shen, Wen (The Pennsylvania State University)
Created:
2009-07-28
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The current talk is concerned with the spectral theory, in particular, the principal eigenvalue theory, of nonlocal dispersal operators with time periodic dependence, and its applications. Nonlocal andrandom dispersal operators are widely used to model diffusion systems in applied sciences and share many properties.There are also some essential ...
Creator:
Shen, Wenxian (Auburn University)
Created:
2012-12-07
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The current talk is concerned with transition fronts of nonlocal dispersal evolution equations in heterogeneous media. As it is known, solutions of nonlocal dispersal evolution equations do not become smoother in space as time elapses. This lack of space regularity would cause a lot of difficulties in studying transition fronts in nonlocal dispe...
Creator:
Shen, Wenxian (Auburn University)
Created:
2016-06-25
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The current talk is concerned with traveling wave solutions of reaction diffusion equations in random media.I will first introduce the concept of random traveling wave solutions and present a general theorem about theexistence of such traveling wave solutions. I will then discuss the existence, uniqueness, and stability of random traveling wave ...
Creator:
Shen, Wenxian (Auburn University)
Created:
2012-10-22
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.