Iteration Techniques for Convection Dominated Flow Problems

Document Type

Presentation Abstract

Presentation Date

2-28-2000

Abstract

There are many problems in engineering and scientific disciplines that can be described by convection-diffusion equations. In a convection-diffusion equation, if the convection term is very dominant, the linear system of equations that result from either finite-differencing or finite elementing will not have a diagonally dominant coefficient matrix. So, if one tries a convectional iteration method (Jacobi or Gauss-Seidel) to solve the linear system of equations, the iteration matrix may not satisfy the spectral radius condition for convergence and hence no converging solution may be obtained. The problem can be overcome, under certain conditions, if one uses a two-step iteration procedure involving the spectral enveloping ellipse for the iteration matrix. The talk will present such a two step method that combines an Arnoldi-Chebyshev approach for convection-diffusion computations, that generate faster and better solutions. A domain decomposition method for solving convection diffusion problems will be discussed. Finally, a finite difference singular perturbation technique for solving problems with boundary layers, will be presented.

Additional Details

Monday, 28 February 2000
4:10 p.m. in Math 109
Coffee/treats at 3:30 p.m. Math 104 (lounge)

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