Toward overcoming computational barriers via phase-space hp-adaptivity, for atmospheric radiative transfer and general kinetic equations

Computational expense is a bottleneck for many kinetic equations, due to the high-dimensionality of position-velocity phase space. As an approach to alleviating this issue, I will present results that use hp-adaptive mesh refinement in both position space and velocity space. As a specific application, I will show promising results for atmospheric radiative transfer, toward overcoming the 1D barrier and allowing 3D radiative transfer with clouds. More generally, I will describe our efforts to create a general-purpose software package for any kinetic equation. The aim of the software (called Jexpresso, work in progress) is to utilize continuous Galerkin or discontinuous Galerkin spectral element methods with adaptivity for efficiency, combined with a user-friendly interface to allow a user to easily specify and solve any kinetic equation.