Partitioning methods for reaction-diffusion problems
Partitioning methods for reaction-diffusion problems
复制标题
反应扩散问题的划分方法
DOI：
10.1016/j.apnum.2005.09.001
复制
发表时间：
2006
影响因子：
2.8
通讯作者：
G. Warnecke
中科院分区：
文献类型：
--
作者：
W. Heineken;G. Warnecke
本文考虑在随时间变化的空间网格上用线性有限元数值求解反应扩散方程组。对于积分的时间变量的W-方法与几个变量的隐式/显式分区使用。对于网格自适应，提出了一种灵活的细化和粗化控制算法。分块W-方法保持了隐式格式的稳定性，但减小了待解线性方程组的规模。我们结合联合收割机局部分区与分区之间的扩散和反应条款，导致大量的各种各样的方法。在数值试验中比较了几种划分方法的效率。计算表明，如果使用分区格式，而不是一个全隐式的W-方法的效率增加。我们包括三个线性求解器的数值比较。讨论了迭代过程的最优截断。
We consider the numerical solution of reaction–diffusion systems using linear finite elements on a space grid changing in time. For the integration with respect to the time variable a W-method with several variants of implicit/explicit partitioning is used. For grid adaption an algorithm featuring a flexible refinement and coarsening control is proposed. The partitioned W-methods keep the stability of implicit schemes but reduce the size of the linear systems to be solved. We combine local partitioning with partitioning between the diffusion and reaction terms, leading to a large variety of methods. The efficiency of several partitioning methods is compared in numerical tests. The calculations show an increase of efficiency if partitioned schemes are used instead of a fully implicit W-method. We include a numerical comparison of three linear solvers. Optimal truncation of the iteration process is discussed.