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# Accession Number:

## ADA295790

# Title:

## Massively Parallel Iterative Methods: Multiscale Preconditioners and Implicit Methods.

# Descriptive Note:

## Final rept. 17 Jun 91-30 Sep 94,

# Corporate Author:

## CALIFORNIA UNIV LOS ANGELES DEPT OF MATHEMATICS

# Report Date:

## 1995-03-22

# Pagination or Media Count:

##
8.0

# Abstract:

## Nonlinear and linear systems of equations often arise in scientific computation, for example in implicit methods in Computational Fluid Dynamics CFD. It is important to find cost-effective and accurate methods to solve such systems. Iterative methods are among those widely used, especially for 3D problems. In this project, we consider iterative methods which are especially suited to massively parallel architectures. To accelerate convergence of these iterative methods, preconditioners are often used. Good preconditioners reduce the number of iterations and involves few arithmetic operations per iteration. Effective parallel preconditioners must account for the global coupling inherent in elliptic problems. On the other hand, efficient parallel implementation often favors local computations. Multiscale iterative methods represent a good compromise between these two conflicting goals. We focused our attention on two classes of multiscale preconditioners multilevel basis preconditioners and domain decomposition preconditioners.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#