Accelerated Convergence of Structures Banded Systems Using Constrained Corrections
Abstract
Descretization of fluid flow equations results in a structured banded system of equations. Interative methods used to solve such a system transfer information rapidly between neighboring points but exhibit slow global communication when the system is large. This phenomenon results in a slow convergence with the asymptotic stages showing a spatially smooth behavior for the errors, iterative corrections, and residuals. This smooth behavior is exploited by approximating the error and corrections with an interpolation over a selected subset of the grid. A variational form is used to compress the original system of equations into a smaller system. This compression is repeated through several levels of grid sizes to obtain a dramatic improvement in convergence rate. A relaxation parameter is dynamically calculated at each step with a negligible increase in computational effort. Although the method was developed for solving full potential flow using a variational principle, it is applicable to other problems with the structured banded property.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1981
- Accession Number
- ADA108805
Entities
People
- Karl Kneile