Multigrid Methods For Elliptic Partial Differential Equations With Discontinuous Coefficients

Elliptic partial differential equations with discontinuous coe?cients are rele-vant to many applications. We designed two e?cient multigrid methods for theseproblems in this paper. One used idea of solving local residual equation using thestandard stencil and the skewed stencil of the centered di?erence approximationto the Laplacian operator. It solves jumping of coe?cients successfully. We callthis method is FULL-LOCAL multigrid method in this paper. Another employthe Nelder-Mead simplex algorithm and skills in space geometry. It is also eff-cient. We call it as N-M approximation multigrid method. And there are manynumerical examples in this paper, which are compared new methods with severaltraditional methods. We found that new mathods are optimal.