求解界面方程的Chebyshev加速算法

非重叠区域分解算法在于建立和求解相关的界面方程．建立界面方程在理论上虽。然容易推导，例如某些问题可用Gauss块消去法，但在实际计算时并不可行，所以界面方程在一些算法中是陷式的．而求解界面方程一般要进行预处理，本提出一种区域分解算法，可得出界面方程的显式表达．算法是完全并行的，所得出的界面方程的系数矩阵的条件数已与网参数无关，事实上就是(Sh^（1）)^-1Sh，进而可直接用收敛速度较快的Chebyshev加速算法求解该界面方程，在充分应用并行计算方法的条件下，本算法与[4]中的算法相比计算效率提高．

Chebyshev Semi-iteraive Method For Interface Equation

When we apply the non-overlapping domain decomposition method to solve PDE,we mainly deduce the interface equations and solve them~ .Theoretically,it is easy to deduce the interface equations,for example we can use the Gaussian factorization process~ ,which is not applicable in practice.The fact is that the interface equations are not explicit in some algorithms~ .Aand we also have to find the interface preconditioners.In this paper,a domain decompositioin algorithm is given,by which we have the explicit interface equation is independent of mesh size h,in face the matrix is (S~ (1)_h)~ -1S_h.Then we just apply the Chebyshev seme-iterative method to solve the interface equation.If the parallel algorithm is carried out in practice,our method has higher efficiency then the method in .