论文标题
非线性反应扩散系统的二阶指数时间差异方案
A second-order exponential time differencing scheme for non-linear reaction-diffusion systems with dimensional splitting
论文作者
论文摘要
通过将ETD方案与近似于矩阵指数的近似值函数（RDP）以及尺寸拆分集成因子技术相结合，开发了二阶$ L $稳定的指数时间差异（ETD）方法。使用该方案求解了两个和三个维度的各种非线性反应扩散方程，以迪利奇，诺伊曼或周期性的边界条件求解，并表现出胜过各种其他二阶隐式明确的方案。通过进一步使用基本的并行化技术，获得了额外的性能提升。
A second-order $L$-stable exponential time-differencing (ETD) method is developed by combining an ETD scheme with approximating the matrix exponentials by rational functions having real distinct poles (RDP), together with a dimensional splitting integrating factor technique. A variety of non-linear reaction-diffusion equations in two and three dimensions with either Dirichlet, Neumann, or periodic boundary conditions are solved with this scheme and shown to outperform a variety of other second-order implicit-explicit schemes. An additional performance boost is gained through further use of basic parallelization techniques.
