Multigrid method: Difference between revisions

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==Bramble–Pasciak–Xu preconditioner==

Originally described in Xu’sXu's Ph.D. thesis <ref>Xu, Jinchao. Theory of multilevel methods. Vol. 8924558. Ithaca, NY: Cornell University, 1989.</ref>

and later published in Bramble-Pasciak-Xu,<ref>Bramble, James H., Joseph E. Pasciak, and Jinchao Xu. "Parallel multilevel preconditioners." Mathematics of Computation 55, no. 191 (1990): 1–22.</ref> the BPX-preconditioner is one of the two major multigrid

approaches (the other is the classic multigrid algorithm such as V-cycle) for solving large-scale algebraic systems that arise from the discretization of models in science and engineering described by partial differential equations. In view of the subspace correction framework,<ref>Xu, Jinchao. "Iterative methods by space decomposition and subspace correction." SIAM review 34, no. 4 (1992): 581-613.