Fast Algorithms for Partial Differential Equations on Advanced Computers
Abstract
This report covers four areas of research. The first area is an analysis of preconditionings. We have examined the properties that a preconditioning must possess in order to yield an iterative method with convergence properties independent of the discretization parameters. The second area is an attempt to provide a framework for the construction of conjugate gradient methods. The third area of research is the analysis of the equations governing the transport of neutrally charged particles and the construction of iterative methods for the solution of discrete transport equations. The final area of research is supraconvergence which deals with accurately approximating the solution of partial differential equations on highly irregular meshes. The first topic is very theoretical in nature but will have important implications to the practical choice of preconditionings. The second area is also theoretical in nature, but leads immediately to the development of new iterative methods. The third area builds on the analysis of the continuous operators to yield insight into the behavior of discrete approximations. The final goal of this third project is the development of efficient numerical methods for the solution of discrete transport equations on massively parallel machines. The final area of research will lead to more efficient solution of differential equations on irregular meshes.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 02, 1989
- Accession Number
- ADA206469
Entities
People
- Thomas A. Manteuffel
Organizations
- University of Colorado Boulder