(candidate for the Numerical Analysis position)
Dr. Jayathi Raghavan
Department of Pure and Applied Mathematics
Washington State University
Iteration Techniques for Convection Dominated Flow Problems
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.
Monday, 28 February 2000
4:10 p.m. in Math 109
Coffee/treats at 3:30 p.m. Math 104 (lounge)
Spring 2000 Colloquium Schedule | Mathematical Sciences home | The University of Montana home