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# NEPCISS

NEPCISS = “ciss” - A contour integral eigensolver based on the Sakurai-Sugiura scheme.

## Notes

This solver is based on the numerical contour integration idea proposed initially for linear problems by Sakurai and Sugiura [2003]. In nonlinear eigenproblems, a Rayleigh-Ritz projection is done, resulting in a small dense nonlinear eigenproblem [Asakura et al., 2009, Yokota and Sakurai, 2013].

Contour integral methods are able to compute all eigenvalues lying inside a region of the complex plane. Use `NEPGetRG()` to specify the region. However, the computational cost is usually high because multiple linear systems must be solved. Use `NEPCISSGetKSPs()` to configure the `KSP` objects for this.

Details of the implementation in SLEPc can be found in [Maeda et al., 2016].

## References

[Asa09]

J. Asakura, T. Sakurai, H. Tadano, T. Ikegami, and K. Kimura. A numerical method for nonlinear eigenvalue problems using contour integrals. JSIAM Lett., 1:52–55, 2009. doi:10.14495/jsiaml.1.52.

[Mae16]

Y. Maeda, T. Sakurai, and J. E. Roman. Contour integral spectrum slicing method in SLEPc. Technical Report STR-11, Universitat Politècnica de València, 2016. URL: https://slepc.upv.es/documentation.

[Sak03]

T. Sakurai and H. Sugiura. A projection method for generalized eigenvalue problems using numerical integration. J. Comput. Appl. Math., 159(1):119–128, 2003. doi:10.1016/S0377-0427(03)00565-X.

[Yok13]

S. Yokota and T. Sakurai. A projection method for nonlinear eigenvalue problems using contour integrals. JSIAM Lett., 5:41–44, 2013. doi:10.14495/jsiaml.5.41.

## See Also

NEP: Nonlinear Eigenvalue Problems, `NEP`, `NEPType`, `NEPSetType()`, `NEPGetRG()`

## Level

beginner

## Location

src/nep/impls/ciss/nciss.c

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