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- Jingwei Hu, Lexing Ying
- 2012

This paper introduces a fast spectral algorithm for the quantum Boltzmann collision operator. In the usual spectral framework, one of the terms in the operator cannot be evaluated efficiently. The new approach is based on the fundamental property of the exponential function which allows one to construct a new decomposition of the collision kernel to speed… (More)

Generalized Radon transforms such as the hyperbolic Radon transform cannot be implemented as efficiently in the frequency domain as convolutions, thus limiting their use in seismic data processing. We introduce a fast butterfly algorithm for the hyperbolic Radon transform. The basic idea is to reformulate the transform as an oscillatory integral operator… (More)

This paper introduces a fast algorithm for the energy space boson Boltzmann collision operator. Compared to the direct O(N 3) calculation and the previous O(N 2 log N) method [Markowich and Pareschi, 2005], the new algorithm runs in complexity O(N log 2 N), which is optimal up to a logarithmic factor (N is the number of grid points in energy space). The… (More)

- Jingwei Hu, Sergey Fomel
- 2012

SUMMARY We introduce a fast butterfly algorithm for the hyperbolic Radon transform commonly used in seismic data processing. For two-dimensional data, the algorithm runs in complexity O(N 2 log N), where N is representative of the number of points in either dimension of data space or model space. Using a series of examples, we show that the proposed… (More)

We develop a stochastic Galerkin method for the Boltzmann equation with uncertainty. The method is based on the generalized polynomial chaos (gPC) approximation in the stochastic Galerkin framework, and can handle random inputs from collision kernel, initial data or boundary data. We show that a simple singular value decomposition of gPC related… (More)

In this paper we develop high order asymptotic preserving methods for the spatially inhomogeneous quantum Boltzmann equation. We follow the work in Li and Pareschi [18] where asymptotic preserving exponential Runge-Kutta methods for the classical inhomo-geneous Boltzmann equation were constructed. A major difficulty here is related to the non Gaussian… (More)

A B S T R A C T The conventional velocity scan can be computationally expensive for large-scale seismic data sets, particularly when the presence of anisotropy requires multiparameter scanning. We introduce a fast algorithm for 3D azimuthally anisotropic velocity scan by generalizing the previously proposed 2D butterfly algorithm for hyperbolic Radon… (More)

We develop a class of stochastic numerical schemes for Hamilton-Jacobi equations with random inputs in initial data and/or the Hamiltonians. Since the gradient of the Hamilton-Jacobi equations gives a symmetric hyperbolic system, we utilize the generalized polynomial chaos (gPC) expansion with stochastic Galerkin procedure in random space and the Jin-Xin… (More)

We design an asymptotic-preserving scheme for the semiconductor Boltzmann equation which leads to an energy-transport system for electron mass and internal energy as mean free path goes to zero. As opposed to the classical drift-diffusion limit where the stiff collisions are all in one scale, new difficulties arise in the two-scale stiff collision terms… (More)