# 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 <type> -mg_coarse_pc_type <type> and  -pc_mg_type <type>


## See Also
 `PCMG`, `PCSetDM()`, `PCExoticType`, `PCExoticSetType()`

## Level
advanced

## Location
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ksp/pc/impls/wb/wb.c.html#PCEXOTIC">src/ksp/pc/impls/wb/wb.c</A>


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[Edit on GitLab](https://gitlab.com/petsc/petsc/-/edit/release/src/ksp/pc/impls/wb/wb.c)


[Index of all PC routines](index.md)  
[Table of Contents for all manual pages](/docs/manualpages/index.md)  
[Index of all manual pages](/docs/manualpages/singleindex.md)  
