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# 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.

## Options Database Keys

- -pc_exotic_type <face,wirebasket> - use a coarse grid point for each face, or edge and vertex

- -pc_exotic_direct_solver - use a direct solver to construct interpolation instead of an iterative solver

## Notes

Must be used with `DMDA` in three dimensions

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`

These coarse grid spaces originate in the work of Bramble, Pasciak and Schatz [BPS89]. They were generalized slightly in “Domain Decomposition Method for Linear Elasticity”, Ph. D. thesis, Barry Smith, [Smi90]. They were then explored in great detail in Dryja, Smith, Widlund [DSW94]. 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, [DKW08c], [DKW08a], [DKW08b], [DW09].

In this code the wirebasket includes a constant for each face, as well as the true “wirebasket”. Other wirebasket algorithms exist that only have constants for edges and vertices.

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

## References

[BPS89]

James H Bramble, Joseph E Pasciak, and Alfred H Schatz. The construction of preconditioners for elliptic problems by substructuring. IV. Mathematics of Computation, 53(187):1–24, 1989.

[DKW08a]

Clark R Dohrmann, Axel Klawonn, and Olof B Widlund. A family of energy minimizing coarse spaces for overlapping Schwarz preconditioners. In Domain decomposition methods in science and engineering XVII, pages 247–254. Springer, 2008.

[DKW08b]

Clark R Dohrmann, Axel Klawonn, and Olof B Widlund. Domain decomposition for less regular subdomains: overlapping Schwarz in two dimensions. SIAM journal on numerical analysis, 46(4):2153–2168, 2008.

[DKW08c]

Clark R Dohrmann, Axel Klawonn, and Olof B Widlund. Extending theory for domain decomposition algorithms to irregular subdomains. Springer, 2008.

[DW09]

Clark R Dohrmann and Olof B Widlund. An overlapping Schwarz algorithm for almost incompressible elasticity. SIAM journal on numerical analysis, 47(4):2897–2923, 2009.

[DSW94]

Maksymilian Dryja, Barry F Smith, and Olof B Widlund. Schwarz analysis of iterative substructuring algorithms for elliptic problems in three dimensions. SIAM journal on numerical analysis, 31(6):1662–1694, 1994.

[Smi90]

Barry F Smith. Domain decomposition algorithms for the partial differential equations of linear elasticity. New York University, 1990.

## See Also

KSP: Linear System Solvers, `PCMG`, `PCSetDM()`, `PCExoticType`, `PCExoticSetType()`

## Level

advanced

## Location

src/ksp/pc/impls/wb/wb.c

Index of all PC routines
Table of Contents for all manual pages
Index of all manual pages