Symmetric Gauss-Seidel Method with a Preconditioned Fixed-Point Iteration for the Steady-State Boltzmann equation
<|reference_start|>Symmetric Gauss-Seidel Method with a Preconditioned Fixed-Point Iteration for the Steady-State Boltzmann equation: We introduce a numerical solver for the steady-state Boltzmann equation based on the symmetric Gauss-Seidel (SGS) method. To solve the nonlinear system on each grid cell derived from the SGS method, a fixed-point iteration preconditioned with its asymptotic limit is developed. The preconditioner only requires solving an algebraic system which is easy to implement and can speed up the convergence significantly especially in the case of small Knudsen numbers. Additionally, we couple our numerical scheme with the multigrid method to accelerate convergence. A variety of numerical experiments are carried out to illustrate the effectiveness of these methods.<|reference_end|>
@article{cai2024symmetric,
    title={Symmetric Gauss-Seidel Method with a Preconditioned Fixed-Point
  Iteration for the Steady-State Boltzmann equation},
    author={Zhenning Cai, Xiaoyu Dong, Jingwei Hu},
    journal={arXiv preprint arXiv:2409.01910},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.01910},
    primaryClass={math.NA cs.NA}
}