Conclusions

Abstract

the multigrid linear-system solvers in this book can be divided into three families, each of which is suitable for a particular kind of application. Elliptic PDEs that are discretized on uniform, rectangular grids, such as applications in image processing, should probably be solved by the multigrid methods in Part II, which can be implemented by efficient data structures such as arrays of numbers. On the other hand, PDEs that are discretized on locally refined meshes should probably be solved by the multigrid method in Part III, which uses the special topological properties of the locally refined mesh to obtain an appropriate hierarchy of transfer and coarse-grid matrices. Finally, PDEs that are discretized on completely unstructured grids may use the multilevel methods in Part IV, which are suitable for general unstructured grids.