A Schwarz alternating procedure for singular perturbation problems. (English) Zbl 0865.65087

The author considers for one- and two-dimensional singularly perturbed problems an algorithm based on a domain decomposition method. To find a domain decomposition which is well-suited for the singularly perturbed problem one needs some knowledge of the position of the boundary and transition layers but there is also a practical way proposed to implement an adaptive domain decomposition method. For two-dimensional problems it is shown that a combination of the ADI-iteration and the Schwarz alternating procedure offers a good option to be effectively used. As an example the procedure is illustrated in detail for a combustion problem.


65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
65N06 Finite difference methods for boundary value problems involving PDEs
80A25 Combustion
35B25 Singular perturbations in context of PDEs
35J25 Boundary value problems for second-order elliptic equations
35J40 Boundary value problems for higher-order elliptic equations
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