Adaptive local multigrid methods for solving time-harmonic eddy-current problems

IEEE Transactions on Magnetics

Volumn 42, Issue 2, 2006, Pages 309-318

  Sterz, Oliver ^a,b   Hauser, Andreas ^b   Wittum, Gabriel ^b  

^a CST GmbH   (Germany)

^b UNIVERSITY OF HEIDELBERG   (Germany)

Author keywords

Adaptive mesh refinement; Eddy currents; Edge elements; Finite element methods; Frequency domain; Local multigrid methods; Red green refinement

Indexed keywords

ALGORITHMS; FINITE ELEMENT METHOD; FREQUENCY DOMAIN ANALYSIS; ITERATIVE METHODS; MATHEMATICAL MODELS; PROBLEM SOLVING;

ADAPTIVE MESH-REFINEMENT; EDGE ELEMENTS; FREQUENCY DOMAIN; LOCAL MULTIGRID METHODS; RED-GREEN REFINEMENT;

EDDY CURRENTS;

EID: 31344457278     PISSN: 00189464     EISSN: None     Source Type: Journal    
DOI: 10.1109/TMAG.2005.859064     Document Type: Article

References (23)

1. O. Sterz, "Modellierung und Numerik zeitharmonischer Wirbel-stromprobleme in 3D," Ph.D. dissertation (in German), Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, Universität Heidel-berg, 2003.
2. A. Bossavit, "Two dual formulations of the 3-D eddy-currents problem," COMPEL, vol. 4, no. 2, pp. 103-116, 1985.
3. _, Computational Electromagnetism. Variational Formulation, Complementarity, Edge Elements, ser. Academic Press Electromagnetism. San Diego, CA: Academic, 1998, vol. 2.
4. R. Hiptmair, "Multigrid method for Maxwell's equations," SIAM J. Numer. Anal., vol. 36, no. 1, pp. 204-225, 1999.
5. 2 AN, vol. 34, no. 1, pp. 159-182, 2000.
6. R. Verfürth, A Review of a Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques. Stuttgart, Germany: Teubner-Verlag, 1996.
7. R. Bank, A. Sherman, and A. Weiser et al., "Refinement algorithm and data structures for regular local mesh refinement," in Scientific Computing, R. Stepleman et al., Eds. Amsterdam, The Netherlands: IMACS, North-Holland, 1983, vol. 44, pp. 3-17.
8. J. Bey, Finite-Volumen und Mehrgitterverfahren Für Elliptische Randwertprobleme (in German), ser. Advances in numerical mathematics. Stuttgart, Leipzig, Germany: Teubner, 1998.
9. P. Bastian, Parallele Adaptive Mehrgitterverfahren, ser. Teubner Skripten zur Numerik: Teubner-Verlag, 1996.
10. S. Lang, "Parallele Numerische Simulation Instationärer Probleme mit adaptiven Methoden auf unstrukturierten Gittern," Ph.D. dissertation (in German), Universität Stuttgart, Stuttgart, Germany, 2001. Mitteilungen des Instituts für Wasserbau, Heft 110.
11. R. Bank, PLTMG: A Software Package for Solving Elliptic Partial Differential Equations, User's Guide 6.0. Philadelphia, PA: SIAM, 1990.
12. P. Bastian, K. Birken, K. Johannsen, S. Lang, N. Neuss, H. Rentz-Reichert, and C. Wieners, "UG - A flexible software toolbox for solving partial differential equations," Comput. Vis. Sci., vol. 1, pp. 27-40, 1997.
13. W. Hackbusch, Multi-Grid Methods and Applications. Berlin, Germany: Springer-Verlag, 1985.
14. A. Brandt, "Multi-level adaptive solutions to boundary-value problems," Math. Comp., vol. 31, no. 138, pp. 333-390, 1977.
15. M. Rivara, "Design and data structure of a fully adaptive finite element software," ACM Trans. Math. Software, vol. 10, pp. 242-246, 1984.
16. D. Arnold, R. Falk, and R. Winther, "Multigrid in H(div) and H (curl)," Numer. Math., vol. 85, no. 2, pp. 175-195, 2000.
17. H. van der Vorst, "BI-CGSTAB: A fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems," SIAM J. Sci. Stat. Comput., vol. 13, no. 2, pp. 631-644, 1992.
18. R. Freund, "Transpose-free quasiminimal residual methods for non-Hermitian linear systems," IMA Vol. Math. Appl., vol. 60, no. 69, pp. 69-93, 1994.
19. K. Fujiwara and T. Nakata, "Results for benchmark problem 7," COMPEL, vol. 9, no. 3, pp. 137-154, 1990.
20. O. Sterz, "Multigrid for time harmonic eddy currents without gauge," in Scientific Computing in Electrical Engineering, Proceedings of the 4th International Workshop Scientific Computing in Electrical Engineering, Eindhoven, The Netherlands, Jun. 23-28, 2002, ser. LNCSE. Berlin, Germany: Springer-Verlag, 2004.
21. P. Bastian and G. Wittum, "On robust and adaptive multi-grid methods," in Multigrid Methods IV, Proceedings of the Fourth European Multi-grid Conference, Amsterdam, The Netherlands, Jul. 6-9, 1993, ser. ISNM. Basel, Switzerland: Birkhäuser, 1994, vol. 116, pp. 1-17.
22. C. Wieners, "The implementation of adaptive multigrid methods for finite elements," Universität Stuttgart, Germany, 1997. SFB 404 Preprint 97/12.
23. _, "Local multigrid methods on hierarchical meshes," in Proc. 17th GAMM-Seminar, Leipzig, Germany, 2001, pp. 1-8.