Gauss-Seidel Iteration for Stiff ODES from Chemical Kinetics
Gauss-Seidel Iteration for Stiff ODES from Chemical Kinetics
复制标题
化学动力学中的刚性 ODES 的高斯-赛德尔迭代
DOI：
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发表时间：
1994
影响因子：
3.1
通讯作者：
J. Verwer
中科院分区：
文献类型：
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作者：
J. Verwer
利用化学动力学方程的特殊形式，提出了一种简单的高斯-赛德尔技术。采用经典艾特肯外推法加速收敛。该技术的目的是在使用操作员分裂的远程运输空气污染代码中使用的硬求解器中实现。拆分必然会导致大量的集成重启。由于高斯-塞德尔迭代是无矩阵的，它比改进的牛顿方法开销小得多。因此，使用这种技术可以保持较低的启动成本。本文给出了应用于大气化学中刚性常微分方程（ODE）的二阶后向微分公式（BDF）求解器的一个原型的初步数值结果。包括与通用BDF代码DASSL的有利比较。无基质技术也可能对其他化学反应流体流动问题感兴趣。
A simple Gauss–Seidel technique is proposed that exploits the special form of the chemical kinetics equations. Classical Aitken extrapolation is applied to accelerate convergence. The technique is meant for implementation in stiff solvers that are used in long range transport air pollution codes using operator splitting. Splitting necessarily gives rise to a great deal of integration restarts. Because the Gauss–Seidel iteration works matrix free, it has much less overhead than the modified Newton method. Start-up costs therefore can be kept low with this technique. Preliminary promising numerical results are presented for a prototype of a second order backward differentiation formula (BDF) solver applied to a stiff ordinary differential equation (ODE) from atmospheric chemistry. A favourable comparison with the general purpose BDF code DASSL is included. The matrix free technique may also be of interest for other chemically reacting fluid flow problems.