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An asymptotic induced numerical method for the convection-diffusion- reaction equation. (English) Zbl 0676.65102

Mathematics for large scale computing, Lect. Notes Pure Appl. Math. 120, 81-114 (1989).
[For the entire collection see Zbl 0673.00019.]
A new approach to solving time dependent reaction convection diffusion equation with small parameter on the diffusion term is discussed and demonstrated. The method is based on a domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions were certain reduced equations may be solved in place of the full equation. Domain decomposition provides parallelism at the highest level, and within each domain there is ample opportunity to exploit parallelism. Run-time results demonstrate the viability of the method.
Reviewer: Hou Zongyi

MSC:

65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
65Y05 Parallel numerical computation
65H10 Numerical computation of solutions to systems of equations
35K57 Reaction-diffusion equations

Citations:

Zbl 0673.00019