12:00-12:30 lunch；12:30-13:30 Talk

Abstract: We propose a Hermite-Galerkin spectral method to numerically solve the spatially homogeneous 

Fokker-Planck-Landau equation with singular quadratic collision model. To compute the collision model,

we adopt a novel approximation formulated by a combination of a simple linear term and a quadratic term

very expensive to evaluate. Using the Hermite expansion, the quadratic term is evaluated exactly by

calculating the spectral coefficients. To deal with singularities, we make use of Burnett polynomials so that

even very singular collision model can be handled smoothly. Numerical examples demonstrate that our

method can capture low-order moments with satisfactory accuracy and performance. Future work include

the application to the inhomogenous case and proof of stability and convergence of the Hermite moment methods.

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