Abstract
We present and analyze a new iterative solver for implicit discretizations of a simplified Boltzmann-Poisson system. The algorithm builds on recent work that incorporated a sweeping algorithm for the Vlasov-Poisson equations as part of nested inner-outer iterative solvers for the Boltzmann-Poisson equations. The new method eliminates the need for nesting and requires only one transport sweep per iteration. It arises as a new fixed-point formulation of the discretized system which we prove to be contractive for a given electric potential. We also derive an accelerator to improve the convergence rate for systems in the drift-diffusion regime. We numerically compare the efficiency of the new solver, with and without acceleration, against a recently developed nested iterative solver.
| Original language | English |
|---|---|
| Pages (from-to) | B733-B758 |
| Journal | SIAM Journal on Scientific Computing |
| Volume | 43 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2021 |
Funding
\ast Submitted to the journal's Computational Methods in Science and Engineering section September 10, 2020; accepted for publication (in revised form) March 9, 2021; published electronically June 10, 2021. The U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for U.S. Government purposes. Copyright is owned by SIAM to the extent not limited by these rights. https://doi.org/10.1137/20M1365922 Funding: This work was sponsored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the U.S. Department of Energy (DOE).
Keywords
- Boltzmann-Poisson equations
- Domain decomposition
- Drift-diffusion limit
- Implicit time integration
- Semiconductor
- Synthetic acceleration