Exploiting Tensor Structure in Kinetic Equations: High Performance Aspects
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In this talk we discuss important extensions of the abstract tensor framework for kinetic equations with the ultimate goal of tackling problems with complicated geometry, discretized with methods of arbitrary order in space and velocity. Since direct solvers destroy the tensor structure, we show how to effectively employ iterative methods with efficient preconditioners for the solution of linear systems arising in Quasi Newton methods applied to the nonlinear residual of the kinetic equation. We discuss how we accelerate the convergence of Quasi Newton methods by including separable approximations of arbitrary order of boundary terms or nonlinear collisions into the linear tensor equations. We close with numerical examples for the Boltzmann equation with hard sphere collision operator that support our theoretical findings.
