Abstract
For the computation of interior eigenpairs an educated initial guess on the eigenvalue is mandatory in general. The convergence behavior of eigensolvers can be improved by using a starting vector, which should be a reasonable approximation of the searched eigenvector. However, these two provisions do not lead necessarily to the searched eigenpair. We propose an extended selection strategy for the Ritz pairs occurring within the Jacobi-Davidson eigensolver algorithm and compare its performance with the Rayleigh quotient iteration. A complex unsymmetric standard eigenvalue problem resulting from a finite integration discretization of a dielectric disk in free-space serves for numerical experiments.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arbenz, P., Hochstenbach, M.E.: A Jacobi–Davidson method for solving complex symmetric eigenvalue problems. SIAM J. Sci. Comput. 25(5), 1655–1673 (2004)
Bandlow, B., Sievers, D., Schuhmann, R.: An improved Jacobi-Davidson method for the computation of selected eigenmodes in waveguide cross sections. IEEE Trans. Magn. 46(8), 3461 –3464 (2010)
Computer Simulation Technology AG (CST): CST Studio Suite. http://www.cst.com
Fokkema, D.R., Sleijpen, G.L.G., van der Vorst, H.A.: Jacobi-Davidson style QR and QZ algorithms for the reduction of matrixpencils. SIAM J. Sci. Comput. 20(1), 94–125 (1998)
Hochstenbach, M.E.: Jacobi-Davidson gateway. http://www.win.tue.nl/casa/research/topics/jd
Notay, Y.: Convergence analysis of inexact Rayleigh quotient iteration. SIAM J. Matrix Anal. Appl. 24, 627–644 (2002)
Ostrowski, A.M.: On the convergence of the Rayleigh quotient iteration for the computation of the characteristic roots and vectors V. Arch. Ration. Mech. Anal. 3, 472–481 (1959)
Schenk, O., Gärtner, K.: Solving unsymmetric sparse systems of linear equations with pardiso. Future Gener. Comput. Syst. 20(3), 475–487 (2004)
Sleijpen, G.L.G., Van der Vorst, H.A.: A Jacobi-Davidson iteration method for linear eigenvalue problems. SIAM J. Matrix Anal. Appl. 17(2), 401–425 (1996)
Smotrova, E., Nosich, A., Benson, T., Sewell, P.: Cold-cavity thresholds of microdisks with uniform and nonuniform gain: quasi-3-D modeling with accurate 2-D analysis. IEEE J. Sel. Top. Quant. Electron. 11(5), 1135 – 1142 (2005)
Weiland, T.: Eine Methode zur Lösung der Maxwellschen Gleichungen für sechskomponentige Felder auf diskreter Basis. AEÜ 31, 116–120 (1977)
Zhao, L., Cangellaris, A.: GT-PML: generalized theory of perfectly matched layers and its application to the reflectionless truncation of finite-difference time-domain grids. IEEE Trans. Microw. Theor. Tech. 44(12), 2555 –2563 (1996)
Acknowledgements
The authors wish to thank Dr. J. Rommes for bringing the potential application of the RQI to their attention.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Bandlow, B., Schuhmann, R. (2012). Mode Selecting Eigensolvers for 3D Computational Models. In: Michielsen, B., Poirier, JR. (eds) Scientific Computing in Electrical Engineering SCEE 2010. Mathematics in Industry(), vol 16. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22453-9_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-22453-9_14
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22452-2
Online ISBN: 978-3-642-22453-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)