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Graham Carey, Benjamin Kirk and Konstantin Lipnikov, "Nested grid iteration for incompressible viscous flow and transport", Inter. J. Comp. Fluid Dynamics, vol. 17, no. 4, pp. 253-262, 2003


We investigate the use of one-way cascadic multigrid strategies (CMG) in the solution of incompressible viscous flow using the finite element method. First we describe the basic CMG approach for representative elliptic boundary value problems and summarize the theoretical error estimates from approximation theory, desired smoother properties, and arithmetic complexity of the method. The extension of these error and complexity estimates to adaptive grids is also given. Then we present the mathematical formulation and the finite element approximation scheme for the class of fluid-thermal problems of interest. In supporting numerical experiments, we examine performance of the algorithm on both serial and distributed parallel systems. We carry out comparison studies with the standard BCG solution strategy on the fine level grid and study diagonal treatments for zero pressure blocks.

BibTeX Entry

author = {Graham Carey and Benjamin Kirk and Konstantin Lipnikov},
title = {Nested grid iteration for incompressible viscous flow and transport},
year = {2003},
journal = {Inter. J. Comp. Fluid Dynamics},
volume = {17},
number = {4},
pages = {253-262}