an:04126645
Zbl 0687.65106
Chan, Tony F.; Goovaerts, Danny
Schur complement domain decomposition algorithms for spectral methods
EN
Appl. Numer. Math. 6, No. 1-2, 53-64 (1989).
00221884
1989
j
65N35 65F10 35J05 65Y05 65F35
preconditioning; Poisson equation; parallel algorithms; preconditioned conjugate gradient; Schur complement domain decomposition algorithms; spectral methods; condition number
Schur complement domain decomposition algorithms for spectral methods are considered. Both the Funaro-Maday-Patera weak \(C^ 1\) matching on the interfaces [cf. \textit{A. T. Patera}, J. Comput. Phys. 54, 468-488 (1984; Zbl 0535.76035)] and \textit{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.
W.Heinrichs
Zbl 0535.76035; Zbl 0476.65078