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Numerically solving the Boltzmann kinetic equations with the small Knudsen number is challenging due to the stiff nonlinear collision terms. A class of asymptotic preserving schemes was introduced in [6] to handle this kind of problems. The idea is to penalize the stiff collision term by a BGK type operator. This method, however, encounters its own(More)
Numerically solving the Boltzmann kinetic equations with the small Knudsen number is challenging due to the stiff nonlinear collision term. A class of asymptotic preserving schemes was introduced in [5] to handle this kind of problems. The idea is to penalize the stiff collision term by a BGK type operator. This method, however, encounters its own(More)
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)
We construct an efficient numerical scheme for the quantum Fokker-Planck-Landau (FPL) equation that works uniformly from kinetic to fluid regimes. Such a scheme inevitably needs an implicit discretization of the nonlinear collision operator, which is difficult to invert. Inspired by work [9] we seek a linear operator to penalize the quantum FPL collision(More)
We introduce a novel iterative estimation scheme for separation of blended seismic data from simultaneous sources. The scheme is based on an augmented estimation problem, which can be solved by iteratively constraining the deblended data using shaping regularization in the seislet domain. We formulate the forward modeling operator in the common receiver(More)
We present a new asymptotic-preserving scheme for the semiconductor Boltzmann equation with two-scale collisions — a leading-order elastic collision together with a lower-order interparticle collision. When the mean free path is small, numerically solving this equation is prohibitively expensive due to the stiff collision terms. Furthermore, since the(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)