EPSCISS

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

Notes

This solver is based on the numerical contour integration idea proposed initially by Sakurai and Sugiura [2003] and improved later by adding a Rayleigh-Ritz projection step [Sakurai and Tadano, 2007].

Contour integral methods are able to compute all eigenvalues lying inside a region of the complex plane. Use EPSGetRG() to specify the region. However, the computational cost is usually high because multiple linear systems must be solved. For this, we can use the KSP object inside ST, or several independent KSPs, see EPSCISSSetUseST().

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

References

[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.

[Sak07]

T. Sakurai and H. Tadano. CIRR: a Rayleigh-Ritz type method with contour integral for generalized eigenvalue problems. Hokkaido Math. J., 36(4):745–757, 2007. doi:10.14492/hokmj/1272848031.

See Also

EPS: Eigenvalue Problem Solver, EPS, EPSType, EPSSetType(), EPSGetRG()

Level

beginner

Location

src/eps/impls/ciss/ciss.c

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