热传导方程三层并行差分格式初始条件的计算

Initialization Method in Three-layer Parallel Difference Scheme for Heat Equation

给出二维热传导问题的三层差分格式初始条件的一种显式计算方法,对于由此形成的内边界预估校正三层并行差分算法,证明稳定性和收敛性定理.并行数值试验表明,方法稳定,且与通常采用隐式格式计算初始条件的方法相比,易于程序实现;与已有的扰动算法相比,能大幅度减小误差.

An explicit method is proposed to initiate three-layer difference scheme for two-dimensional heat problems.Stability and convergence theorem is shown with a three-layer domain decomposition parallel difference algorithm with inner boundary prediction-correction and explicit initialization.Parallel numerical experiments show that the method is numerical stable,and is more convenient in program realization compared with usual implicit initialization method.It reduces numerical errors greatly compared with existing perturbation methods.