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