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Evaluating High Order Discontinuous Galerkin Discretization of the Boltzmann Collision Integral in $O(N^2)$ Operations Using the Discrete Fourier Transform. (arXiv:1801.05892v1 [math.NA])
来源于:arXiv
We present a numerical algorithm for evaluating the Boltzmann collision
operator with $O(N^2)$ operations based on high order discontinuous Galerkin
discretizations in the velocity variable. To formulate the approach, Galerkin
projection of the collision operator is written in the form of a bilinear
circular convolution. An application of the discrete Fourier transform allows
to rewrite the six fold convolution sum as a three fold weighted convolution
sum in the frequency space. The new algorithm is implemented and tested in the
spatially homogeneous case, and results in a considerable improvement in speed
as compared to the direct evaluation. Simultaneous and separate evaluations of
the gain and loss terms of the collision operator were considered. Less
numerical error was observed in the conserved quantities with simultaneous
evaluation. 查看全文>>