ADI as a Preconditioning for Solving the Convection-Diffusion Equation
Copyright policy )ADI as a Preconditioning for Solving the Convection-Diffusion Equation
When a singularly perturbed convection-diffusion equation is discretised, the resulting matrix problem is commonly highly unsymmetric. Optimal acceleration parameters are found for problems of this type when the coefficients are constant. Both the cases of real and complex spectra are considered. The convergence is further improved by the incorporation of a Gauss-Seidel sweep. These ideas form the basis of a preconditioning for a Chebyshev semi-iteration method in the case when the coefficients are not constant. The methods are tested on several standard examples.
Optimal acceleration parameters, Iterative numerical methods for linear systems, numerical examples, convergence, singularly perturbed convection- diffusion equation, Numerical solution of discretized equations for boundary value problems involving PDEs, matrix splittings, preconditioning, Initial-boundary value problems for second-order parabolic equations, Chebyshev semi-iteration method, Gauss- Seidel, Singular perturbations in context of PDEs
Optimal acceleration parameters, Iterative numerical methods for linear systems, numerical examples, convergence, singularly perturbed convection- diffusion equation, Numerical solution of discretized equations for boundary value problems involving PDEs, matrix splittings, preconditioning, Initial-boundary value problems for second-order parabolic equations, Chebyshev semi-iteration method, Gauss- Seidel, Singular perturbations in context of PDEs
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