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An iterative procedure with interface relaxation for domain decomposition methods. (English) Zbl 0678.65082
A domain decomposition method for second order elliptic problems proposed by the third author [Calcolo 24, No.3/4, 201-240 (1987; Zbl 0649.65064)] is improved. The method reduces the problem to a sequence of mixed boundary value problems on each subdomain. At each iteration a relaxation is accomplished at the subdomain interfaces. A value of the relaxation parameter is automatically given, which may yield exact convergence in a finite number of steps.
The method is applied to the spectral collocation approximation of a differential problem using either Chebyshev or Legendre collocation points.
Reviewer: F.Chatelin

MSC:
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
35J25 Boundary value problems for second-order elliptic equations
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