A Spectral Method for Linear Half-Space Kinetic Equations

10:00 AM - 11:00 AM
Weiran Sun, Assistant Professor, Department of Mathematics, Simon Fraser University
CSMD Seminar Series
Building 5100, Room 128 (JICS Auditorium)

Email: Cory Hauck

Abstract sent on behalf of the speaker:

Half-space equations naturally arise in boundary layer analysis of kinetic equations. In this talk we will present a unified proof for the well-posedness of a class of linear half-space equations with general incoming data. We will also show a spectral method to numerically resolve these type of equations in a systematic way. Our main strategy in both analysis and numerics includes three steps: adding damping terms to the original half-space equation, using an inf-sup argument and even-odd decomposition to establish the well-posedness of the damped equation, and then recovering solutions to the original half-space equation. The accuracy of the damped equation is shown to be quasi-optimal and the numerical error of approximations to the original equation is controlled by that of the damped equation. Numerical examples are shown for the isotropic neutron transport equation and the linearized BGK equation. This is joint work with Qin Li and Jianfeng Lu.

If you would like to meet Weiran Sun, please contact Cory Hauck at hauckc@ornl.gov or Liz Hebert at hebertem@ornl.gov.


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