PCEXOTIC#

Two level overlapping Schwarz preconditioner with exotic (non-standard) coarse grid spaces This uses the PCMG infrastructure restricted to two levels and the face and wirebasket based coarse grid spaces.

Notes#

Must be used with DMDA

By default this uses KSPGMRES on the fine grid smoother so this should be used with KSPFGMRES or the smoother changed to not use KSPGMRES

References#

• **** -*** These coarse grid spaces originate in the work of Bramble, Pasciak and Schatz, “The Construction of Preconditioners for Elliptic Problems by Substructing IV”, Mathematics of Computation, volume 53, 1989.

• **** -*** They were generalized slightly in “Domain Decomposition Method for Linear Elasticity”, Ph. D. thesis, Barry Smith, New York University, 1990.

• **** -*** They were then explored in great detail in Dryja, Smith, Widlund, “Schwarz Analysis of Iterative Substructuring Methods for Elliptic Problems in Three Dimensions, SIAM Journal on Numerical Analysis, volume 31. 1994. These were developed in the context of iterative substructuring preconditioners.

• **** -*** They were then ingeniously applied as coarse grid spaces for overlapping Schwarz methods by Dohrmann and Widlund. They refer to them as GDSW (generalized Dryja, Smith, Widlund preconditioners). See, for example, Clark R. Dohrmann, Axel Klawonn, and Olof B. Widlund. Extending theory for domain decomposition algorithms to irregular subdomains. In Ulrich Langer, Marco Discacciati, David Keyes, Olof Widlund, and Walter Zulehner, editors, Proceedings of the 17th International Conference on Domain Decomposition Methods in Science and Engineering, held in Strobl, Austria, 2006, number 60 in Springer Verlag, Lecture Notes in Computational Science and Engineering, 2007.

• **** -*** Clark R. Dohrmann, Axel Klawonn, and Olof B. Widlund. A family of energy minimizing coarse spaces for overlapping Schwarz preconditioners. In Ulrich Langer, Marco Discacciati, David Keyes, Olof Widlund, and Walter Zulehner, editors, Proceedings of the 17th International Conference on Domain Decomposition Methods in Science and Engineering, held in Strobl, Austria, 2006, number 60 in Springer Verlag, Lecture Notes in Computational Science and Engineering, 2007

• **** -*** Clark R. Dohrmann, Axel Klawonn, and Olof B. Widlund. Domain decomposition for less regular subdomains: Overlapping Schwarz in two dimensions. SIAM J. Numer. Anal., 46(4), 2008.

• **** -*** Clark R. Dohrmann and Olof B. Widlund. An overlapping Schwarz algorithm for almost incompressible elasticity. Technical Report TR2008 912, Department of Computer Science, Courant Institute of Mathematical Sciences, New York University, May 2008. URL:

The usual PCMG options are supported, such as -mg_levels_pc_type -mg_coarse_pc_type and -pc_mg_type

PCMG, PCSetDM(), PCExoticType, PCExoticSetType()