Multigrid Methods On Unstructured Grids

One of the most important aspects in the numerical solution of partial differential equations is the efficient solution of the corresponding large systems of equations arising from their dis-cretization which are based on a gridding of the computational domain.Generally,there are two main different types of grids:structured meshes and unstructured grids.As multigrid methods and its related muti-methods always an efficitive and efficient solver,multigrid methods based on un-structured grids is one hotspot in computational mathematics.This work gives a multigrid method based on semi-structured grids,which is developed by an initial unstructured grids.Combining the thinkings of GMG and AMG,it privides a way to design multigrid methods based on 2D and 3D,P1 and P2 element.First,there are some theory about multigrid methods.Second,it introduces the details about how to design algorithms.Thirdly,by using numerical experiment and local mode analysis to confirm the efficience of this methods.Final is about the development and expand of the methods.