Abstract
We report on a comparison of the implicitly restarted Lanczos algorithm as implemented in ARPACK and the Jacobi-Davidson algorithm for solving large sparse generalized symmetric matrix eigenvalue problems. These problems occur in the computation of a few of the lowest frequencies of standing electro-magnetic waves in cavity resonators. The computational domain is discretized by a finite element method based on edge elements to avoid spurious modes.
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References
Adam, St., Arbenz, P., Geusi, R.: Eigenvalue solvers for electromagnetic fields in cavities. Tech. Report 275, ETH Zürich, Computer Science Department, October 1997, (Available at URL http://www.inf.ethz.ch/publications/tr.html)
Arbenz, P., Geus, R.: Parallel solvers for large eigenvalue problems originating from Maxwell’s equations. Euro-Par ’98, Springer-Verlag, 1998, (Lecture Notes in Computer Science)
Barret, R., Berry, M., Chan, T. F., Demmel. J., Donato, J., Dongarra, J., Eijkhout, V., Pozo, R., Romine, Ch., van der Vorst, H.: Templates for the solution of linear systems: Building blocks for iterative methods. Society for Industrial and Applied Mathematics, Philadelphia, PA, 1994, (Available from Netlib at URL http://www.netlib.org/templates/index.html)
Bespalov, A.N.: Finite element method for the eigenmode problem of a RF cavity resonator. Soviet Journal of Numerical Analysis and Mathematical Modelling 3 (1988), 163–178
Calvetti, D., Reichel, L., Sorensen, D.C.: An implicitely restarted Lanczos method for large symmetric eigenvalue problems. Electronic Transmissions on Numerical Analysis 2 (1994), 1–21
Fokkema, D.R., Sleijpen, G.L.G., van der Vorst, H.A.: Jacobi-Davidson style QR and QZ algorithms for the partial reduction of matrix pencils. Preprint 941, revised version, Utrecht University, Department of Mathematics, Utrecht, The Netherlands, January 1997
Grimes, R., Lewis, J.G., Simon, H.: A shifted block Lanczos algorithm for solving sparse symmetric generalized eigenproblems. SIAM J. Matrix Anal. Appl. 15 (1994), 228–272
Kikuchi, F.: Mixed and penalty formulations for finite element analysis of an eigenvalue problem in electromagnet ism. Computer Methods in Applied Mechanics and Engineering 64 (1987), 509–521
Lehoucq, R. B.: Private communication, May 1998
Lehoucq, R. B., Sorensen, D. C., Yang, C.: ARPACK users’ guide: Solution of large scale eigenvalue problems by implicitely restarted Arnoldi methods. Department of Mathematical Sciences, Rice University, Houston TX, October 1997, (The software and this guide are available at URL ftp://ftp.caam.rice.edu/pub/software/ARPACK/)
Nédélec, J.C.:Mixed finite elements in IR3. Numerische Mathematik 35 (1980), 315–341
Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM J. Numer. Anal. 12 (1975), 617–629
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Arbenz, P., Geus, R. (1999). Eigenvalue Solvers for Electromagnetic Fields in Cavities. In: Bungartz, HJ., Durst, F., Zenger, C. (eds) High Performance Scientific and Engineering Computing. Lecture Notes in Computational Science and Engineering, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60155-2_30
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DOI: https://doi.org/10.1007/978-3-642-60155-2_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65730-9
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