Algebraic Multigrid and the Fast Adaptive Composite Grid Method in Large Scale Computation

摘要

This report describes research undertaken at the Research Institute of Colorado on two computational mathematics topics: algebraic multigrid (AMG), and the fast adaptive composite grid method (FAC). Conventional or geometric multigrid algorithms depend on knowledge of the underlying geometry for a given problem (e.g., a partial differential equation). This knowledge is used to predetermine coarser grids and the attendant operators and intergrid transfers. Although very efficient solvers can be developed in this way, the dissemination and use of geometric multigrid have been impeded by the need to tailor the algorithm to each application. A fairly general black box solver based on multigrid principles would be useful in overcoming these difficulties. The second project area was the study of FAC in the context of multiprocessor computer systems. FAC is developed for elliptic equations.