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Tuesday, December 10

Fast algorithms for quantum Boltzmann collision operators

Jingwei Hu, The Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin
Householder Fellowship Interview Presentation
10:00 PM — 11:00 PM, Building 5100, Room 128 (JICS Auditorium)
Contact: Cory Hauck (hauckc@ornl.gov), 865.574.0730

Abstract

The quantum Boltzmann equation describes the non-equilibrium dynamics of a quantum system consisting of bosons or fermions. The most prominent feature of the equation is a high-dimensional integral operator modeling particle collisions, whose nonlinear and nonlocal structure poses a great challenge for numerical simulation. I will introduce two fast algorithms for the quantum Boltzmann collision operator. The first one is a quadrature based solver specifically designed for the collision operator in reduced energy space. Compared to cubic complexity of direct evaluation, our algorithm runs in only linear complexity (optimal up to a logarithmic factor). The second one accelerates the computation of the full phase space collision operator. It is a spectral algorithm based on a special low-rank decomposition of the collision kernel. Numerical examples including an application to semiconductor device modeling are presented to illustrate the efficiency and accuracy of proposed algorithms.

If you would like to meet with Jingwei Hu, please contact Billy Fields (fieldsbd@ornl.gov) or Cory Hauck at any time.