解二维扩散方程的一类有限差分并行算法

对于求解二维扩散方程,构造了一类简单、实用的有限差分并行算法。 采用斜向差分算子［1］,建立斜向隐式差分格式,再结合边界条件,对扩散方程进行求解。此算法虽然是隐格式,但可以利用边界条件显式计算，既保持了隐格式的稳定性和精度,也减少了计算复杂性。通过具体的数值算例表明,此类算法并行性好,精度高,并行格式简单,有很好的实用性。

A class of parallel finite difference methods for solving a two-dimensional diffusion equation

A class of simple and practical parallel finite difference methods for solving a two-dimensional diffusion equation were introduced. Based on the skew direction difference operator［1］, the implicit skew difference schemes were constructed, and the boundary condition was unified, to solve the diffusion equation. Although the schemes are implicit, this kind of algorithms can be computed explicitly with the boundary conditions. In this way, both the stability and accuracy of the implicit schemes were kept, and the complexity of calculation decreased. An example was presented to illustrate the usefulness of these parallel methods.