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Schur complement domain decomposition algorithms for spectral methods. (English) Zbl 0687.65106
Schur complement domain decomposition algorithms for spectral methods are considered. Both the Funaro-Maday-Patera weak \(C^ 1\) matching on the interfaces [cf. A. T. Patera, J. Comput. Phys. 54, 468-488 (1984; Zbl 0535.76035)] and S. A. Orszag’s exact \(C^ 1\) matching [ibid. 37, 70-92 (1980; Zbl 0476.65078)] are considered. Numerical results show that the condition number of the Schur complement system is of order \(O(n^ 2)\). It is shown how this can be improved to nearly O(1) by a boundary probe preconditioned.
Reviewer: W.Heinrichs

MSC:
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65Y05 Parallel numerical computation
65F35 Numerical computation of matrix norms, conditioning, scaling
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