An Asymptotic Preserving Discontinuous Galerkin Method for a Linear Boltzmann Semiconductor Model
A key property of the linear Boltzmann semiconductor model is that as the collision frequency tends to infinity, the phase space density $$f$$ = $$f$$ ($x, v, t$) converges to an isotropic function $M (v)$$ρ$$(x, t)$, called the drift-diffusion limit, where $$M$$ is a Maxwellian and the physical density $$ρ$$ satisfies a second-order parabolic PDE known as the drift-diffusion equation. Numerical approximations that mirror this property are said to be asymptotic preserving. In this paper we build a discontinuous Galerkin method to the semiconductor model, and we show this scheme is both uniformly stable in $$ε$$, where 1/$$ε$$ is the scale of the collision frequency, and asymptotic preserving. Here in particular, we discuss what properties the discrete Maxwellian must satisfy in order for the schemes to converge in $$ε$$ to an accurate $$h$$-approximation of the drift-diffusion limit. Discrete versions of the drift-diffusion equation and error estimates in several norms with respect to $$ε$$ and the spacial resolution are also included.
- Research Organization:
- Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- Grant/Contract Number:
- AC05-00OR22725
- OSTI ID:
- 2351095
- Journal Information:
- SIAM Journal on Numerical Analysis, Journal Name: SIAM Journal on Numerical Analysis Journal Issue: 3 Vol. 62; ISSN 0036-1429
- Publisher:
- Society for Industrial and Applied Mathematics (SIAM)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
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