Abstract
In this paper, we consider spatially homogeneous linear kinetic models arising from semiconductor device simulations and investigate how various deterministic numerical methods approximate their scattering operators. In particular, methods including first and second order discontinuous Galerkin methods, a first order collocation method, a Fourier-collocation spectral method, and a Nyström method are examined when they are applied to one-dimensional models with singular or continuous scattering kernels. Mathematical properties are discussed for the corresponding discrete scattering operators. We also present numerical experiments to demonstrate the performance of these methods. Understanding how the scattering operators are approximated can provide insights into designing efficient algorithms for simulating kinetic models and for the implicit discretizations of the problems in the presence of multiple scales.
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Acknowledgments
The third author was partially supported by NSF Grant DMS-1318186, and the fifth author was partially supported by NSF Grants DMS-0847241 and DMS-1318409.
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Chen, Y., Chen, Z., Cheng, Y., Gillman, A., Li, F. (2016). Study of Discrete Scattering Operators for Some Linear Kinetic Models. In: Brenner, S. (eds) Topics in Numerical Partial Differential Equations and Scientific Computing. The IMA Volumes in Mathematics and its Applications, vol 160. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-6399-7_5
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DOI: https://doi.org/10.1007/978-1-4939-6399-7_5
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