Comparison of hierarchical basis functions for efficient multilevel solvers

IET Science, Measurement and Technology

Volumn 1, Issue 1, 2007, Pages 48-52

  Ingelstrom P ^a   Hill, V ^a   Dyczij Edlinger, R ^a  

^a SAARLAND UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE ELEMENT METHOD; HIERARCHICAL SYSTEMS; INTERPOLATION; LINEAR SYSTEMS; MAXWELL EQUATIONS; PROBLEM SOLVING;

COMPUTING TIMES; HIERARCHICAL BASIS FUNCTIONS; MULTILEVEL SOLVERS; TETRAHEDRAL MESHES;

FUNCTION EVALUATION;

EID: 34047097855     PISSN: 17518822     EISSN: None     Source Type: Journal    
DOI: 10.1049/iet-smt:20060025     Document Type: Conference Paper

References (12)

1. Smith, B., Bjørstad, P., and Gropp, W.: ' Domain decomposition - parallel multilevel methods for elliptic partial differential equations ', (Cambridge University Press, 1996)
2. Lee, J.F., and Sun, D.K.: ' p-type multiplicative Schwarz (pMUS) method with vector finite elements for modeling three-dimensional waveguide discontinuities ', IEEE Trans. Microw. Theory Tech., 2004, 52, (2), p. 864-870 0018-9480
3. 3 ', Numerische Mathematik, 1980, 35, p. 315-341 10.1007/BF01396415
4. Ingelström, P.: ' A new set of H(curl)-conforming hierarchical basis functions for tetrahedral meshes ', IEEE Trans. Microw. Theory Tech., 2006, 54, (1), p. 106-114 10.1109/TMTT.2005.860295 0018-9480
5. Webb, J.P.: ' Hierarchical vector basis functions of arbitrary order for triangular and tetrahedral finite elements ', IEEE Trans. Antennas Propag., 1999, 47, (8), p. 1244-1253 10.1109/8.791939 0018-926X
6. Ren, Z., and Ida, N.: ' High-order differential form-based elements for the computation of electromagnetic field ', IEEE Trans. Magn., 2000, 36, (4), p. 1472-1478 0018-9464
7. Sun, D.K., Lee, J.F., and Cendes, Z.: ' Construction of nearly orthogonal Nedelec bases for rapid convergence with multilevel preconditioned solvers ', SIAM J. Sci. Comput., 2001, 23, (4), p. 1053-1076 10.1137/S1064827500367531 1064-8275
8. Schöberl, J., and Zaglmayr, S.: ' High-order Nedelec elements with local complete sequence properties ', COMPEL, 2005, 24, (2), p. 374-384
9. Trottenberg, U., Oosterlee, C.W., and Schüller, A.: ' Multigrid ', (Academic Press, 2001)
10. Hu, N., Guo, X.-Z., and Katz, I.N.: ' Multi-p preconditioners ', SIAM J. Sci. Comput., 1997, 18, (6), p. 1676-1697 10.1137/S1064827595279368 1064-8275
11. Reiter, J.M., and Arndt, F.: ' Rigorous analysis of arbitrarily shaped H- and E-plane discontinuities in rectangular waveguides by a full-wave boundary contour mode-matching method ', IEEE Trans. Microw. Theory Tech., 1995, 43, (4), p. 796-801 10.1109/22.375226 0018-9480
12. Webb, J.P.: ' Combined direct-iterative matrix solvers for hierarchical vector finite elements ', IEEE Trans. Magn., 2002, 38, (2), p. 345-348 10.1109/20.996093 0018-9464