求解带间断系数非线性椭圆问题的两重网格法

利用有限差分法离散带间断系数的非线性椭圆问题,针对离散后所得到的非线性方程组,从减少计算量的角度出发,只使用一个辅助的粗层网格空间,并在最细层网格上求解线性校正方程组,构造了两重网格(NETG)法.数值结果表明,新算法在计算量和计算时间方面优于以往的算法.

A Two-Level Method for Solving Nonlinear Elliptic Problems with a Jumping Coefficient

An efficient two-level method is studied to solve the nonlinear systems which arise from a nonlinear elliptic problem with a jumping coefficient by a finite difference method. Only one auxiliary coarse grid space is needed with a suitable mesh size discretization, and linear correction equations are applied instead of the nonlinear systems on the finest grid space. Numerical results are given to verify the computational cost and efficiency of the proposed approach and the results are compared with the existing numerical methods for solving nonlinear elliptic problems with a jumping coefficient.