椭圆方程有限差分逼近的混合半迭代法

Hybrid Semi-iterative Methods for Solving Finite Difference Approximation to Elliptic Equation

利用局部消元法建立了求解椭圆型方程的有限差分格式,并根据Chebyshev多项式加速技术构造了一个混合半迭代法.该算法在第一层网格上仍使用经典的Jacobi迭代法,在内层网格上使用多项式加速技术.数值实验表明,新算法比Jacobi半迭代法收敛快.

A new finite difference approximation to elliptic equation is established by local elimination method in this paper,Then a hybrid semi-iterative method is designed according to Chebyshev polynomial acceleration techniques.The new algorithm used Jacobi iterative method on the first layer grid points and polynomial acceleration techniques on the inner layer grid points.Numerical experiments shows that the new algorithm has faster convergence rate then that of Jacobi semi-iterative method.