An algebraic multigrid method for finite element discretizations with edge elements

Numerical Linear Algebra with Applications

Volumn 9, Issue 3, 2002, Pages 223-238

  Reitzinger, S ^a   Schoberl J ^a  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

Author keywords

Algebraic multigrid; Finite element method; Maxwell's equations; N d lec's edge elements

Indexed keywords

EID: 0142055288     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/nla.271     Document Type: Article

References (23)

1. 3, Numerische Mathematik 1986; 50:57-81.
2. Hiptmair R. Multigrid method for Maxwell's equations. SIAM Journal on Numerical Analysis 1999; 36(1): 204-225.
3. Arnold D, Falk R, Winther R. Multigrid in H(div) and H(curl). Numerische Mathematik 2000; 85:197-218.
4. Beck R, Deuflhard P, Hiptmair R, Hoppe, R Wohlmuth B. Adaptive multilevel methods for edge element discretizations of Maxwell's equations. Surveys on Mathematics for Industry 1999; 8:271-312.
5. Kuhn M, Langer U, Schöberl J. Scientific computing tools for 3D magnetic field problems, In Whiteman JR (ed.). The Mathematics of Finite Elements and Applications X. Elsevier: Amsterdam, 2000; 239-258.
6. Schinnerl M, Schöberl J, Kaltenbacher M. Nested multigrid methods for the fast numerical computation of 3D magnetic fields, IEEE Transactions on Magnetics, 2000; 36(4):1557-1560.
7. Hackbusch W. Multigrid Methods and Application. Springer: Berlin, Heidelberg, New York, 1985.
8. Braess D. Towards algebraic multigrid for elliptic problems of second order. Computing 1995; 55:379-393.
9. Brandt A. Algebraic multigrid theory: the symmetric case. Applied Mathematics and Computation 1986; 19: 23-56.
10. Brandt A, McCormick S, Ruge JW. Algebraic multigrid (AMG) for automatic multigrid solution with application to geodetic computations. Report, Inst. Comp. Studies Colorado State Univ., 1982.
11. Brandt A, McCormick S, Ruge JW. Algebraic multigrid (AMG) for sparse matrix equations. In Evans DJ (ed.). Sparsity and its Application, Cambridge: Cambridge University Press, 1985; 257-284.
12. Kickinger F. Algebraic multigrid for discrete elliptic second-order problems, Multigrid Methods V. Proceedings of the 5th European Multigrid conference, Hackbusch W (ed.). Springer Lecture Notes in Computational Science and Engineering, vol. 3. Springer: Berlin, 1998; 157-172.
13. Ruge JW, Stüben K. Efficient solution of finite difference and finite element equations. In Multigrid Methods for integral and differential equations, Paddon D, Holstein H (eds), vol. 3. Clarendon Press: Oxford, 1985; 169-212.
14. Ruge JW, Stüben K. Algebraic multigrid (AMG), multigrid methods. In Frontiers in Applied Mathematics, McCormick S (ed.) vol. 5. SIAM: Philadelphia, 1986:73-130.
15. Vanek P, Mandel J, Brezina M. Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems. Computing 1996; 56:179-196.
16. Beck R. Algebraic multigrid by component splitting for edge elements on simplicial triangulations. Preprint SC 99-40, Konrad-Zuse-Zentrum für Informationstechnik Berlin, December 1999.
17. Ida N, Bastos PA. Electromagnetics and Calculation of Fields, Springer: Berlin, 1997.
18. Demkowicz L, Vardapetyan L, Modeling of Electromagnetic Absoption/Scattering Problems Using hp-Adaptive Finite Elements. Computer Methods in Applied Mechanics and Engineering 1998; 1:103-124.
19. Brezzi F, Fortin F. Mixed and Hybrid Finite Element Methods. Springer: Berlin, 1991.
20. Costabel M, Dauge M. Singularities of electromagnetic fields in polyhedral domains. Archive for Rational Mechanics and Analysis 2000; 151:221-276.
21. Ciarlet PG. The Finite Element Method for Elliptic Problems. North-Holland Publishing Company, Amsterdam: New York, Oxford, 1987.
22. Jung M, LangerU. Applications of multilevel methods to practical problems. Surveys on Mathematics for Industry 1991; 1:217-257.
23. Jung M, Langer U, Meyer A, Queck W, Schneider M. Multigrid preconditioners and their application. Proceedings of the 3rd GDR Multigrid Seminar held at Biesenthal, Karl-Weierstraß-Institut für Mathematik, May 1989:11-52.