Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
O. Biró, K. Preis, On the use of the magnetic vector potential in the finite element analysis of three-dimensional eddy currents. IEEE Trans. Magn. 25(4), 3145–3159 (1989)
Y. Kawase, O. Miyatani, T. Yamaguchi, Numerical analysis of dynamic characteristics of electromagnets using 3-d finite element method with edge elements. IEEE Trans. Magn. 30(5), 3248–3251 (1994)
D. Arnold, R. Falk, R. Winther, Multigrid in H(div) and H(curl). NUMEM 85, 197–218 (2000)
R. Hiptmair, Multigrid method for Maxwell’s equations. SIAJN 36(1), 204–225 (1999)
M. Schinnerl, J. Schöberl, M. Kaltenbacher, Nested multigrid methods for the fast numerical computation of 3D magnetic fields. IEEE Trans. Magn. 36(4), 1557–1560 (2000)
W.L. Briggs, A Multigrid Tutorial, SIAM, 1987
U. Rüde, Mathematical and computational techniques for multilevel adaptive methods, (SIAM, 1993)
J.W. Ruge, K. Stüben, In Algebraic Multigrid (AMG), Multigrid Methods, Frontiers in Applied Mathematics, ed. by S. McCormick (SIAM, Philadelphia, 1986), pp. 73–130
Y. Saad, Iterative Methods for Sparse Linear Systems (PWS Publication, Company, 1996)
D. Braess, Finite Elemente (Springer, Berlin, 2003). (3. korregierte Auflage)
W. Hackbusch, Multigrid Methods and Application (Springer, Berlin, New York, 1985)
M. Jung, U. Langer, A. Meyer, W. Queck, M. Schneider, Multigrid Preconditioners and their Application. In: Proceedings of the 3rd GDR Multigrid Seminar held at Biesenthal, Karl-Weierstraß-Institut für Mathematik, pp. 11–52, May (1989)
J. Schöberl, An advancing front 2D/3D-mesh generator based on abstract rules, Comput. Vis. Sci. no. 1, 41–52, (1997)
T. Nakata, N. Takahashi, H. Morishige, J.L. Coulomb, C. Sabonnadiere, Analysis of 3D Static Force Problem. In: Proceedings of the TEAM Workshop on Computation of Applied Electromagnetics in Materials, pp. 73–79, (1993)
B. Heise, Mehrgitter-Newton-Verfahren zur Berechnung nichtlinearer magnetischer Felder, Ph.D. thesis, TU Chemnitz, 1994
K. Fujiwara, T. Nakata, H. Ohashi, Improvement for convergence characteristic of ICCG method for the A-\(\Phi \) method using edge elements. IEEE Trans. Magn. 32(3), 804–807 (1996)
D. Braess, Towards algebraic multigrid for elliptic problems of second order. COMPU 55, 379–393 (1995)
F. Kickinger, U. Langer, A note on the global extraction element-by-element method. ZAMM, no. 78, 965–966 (1998)
S. Reitzinger, Algebraic Multigrid Methods for Large Scale Finite Element Equations. Reihe C—Technik und Naturwissenschaften, no. 36, Universitätsverlag Rudolf Trauner, (2001)
P. Vanek, J. Mandel, M. Brezina, Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems. COMPU 56, 179–196 (1996)
A. Brandt, Algebraic multigrid theory: The symmetric case. APPMC 19, 23–56 (1986)
M. Kaltenbacher, H. Landes, S. Reitzinger, R. Peipp, 3D simulation of electrostatic-mechanical transducers using algebraic multigrid. IEEE Trans. Magn. 38(2), 985–988 (2002)
M. Kaltenbacher, S. Reitzinger, Algebraic Multigrid for Solving Electromechanical Problems. Multigrid Methods VI, Springer, Lecture Notes in Computational Science and Engineering, (1999)
M. Kaltenbacher, S. Reitzinger, Nonlinear 3D magnetic field computations using Lagrange FE-functions and algebraic multigrid. IEEE Trans. Magn. 38(2), 1489–1496 (2002)
M. Kaltenbacher, S. Reitzinger, J. Schöberl, Algebraic multigrid method for solving 3D nonlinear electrostatic and magnetostatic field problems. IEEE Trans. Magn. 36(4), 1561–1564 (2000)
S. Reitzinger, M. Kaltenbacher, Algebraic multigrid methods for magnetostatic field problems. IEEE Trans. Magn. 38(2), 477–480 (2002)
S. Reitzinger, J. Schöberl, Algebraic multigrid for edge elements. Numer. Linear Algebra Appl. 9, 223–238 (2002)
S. Reitzinger, U. Schreiber, U. van Rienen, Algebraic Multigrid for Complex Symmetric Matrices. Numerical Study, Technical Report 02–01, Johannes Kepler University Linz, SFB: Numerical and Symbolic Scientific Computing, (2002)
M. Rausch, M. Gebhardt, M. Kaltenbacher, H. Landes, Magnetomechanical field computation of a clinical magnetic resonance imaging (MRI) scanner. COMPEL—Int. J. Comput. Math. Electr. Electron. Eng. 22(3), 576–588 (2003)
G. Haase, M. Kuhn, U. Langer, S. Reitzinger, J. Schöberl, Parallel Maxwell solvers, scientific computing in electrical engineering. U. Van Rienen, M. Günther, and D. Hecht, (eds.), Lecture Notes in Computational Science and Engineering, vol. 18, Springer, (2000)
G. Haase, M. Kuhn, S. Reitzinger, Parallel AMG on distributed memory computers. SIAM J. Sci. Comput. 24(2), 410–427 (2002)
J. Schöberl, S. Zaglmayr, High order Nédélec elements with local complete sequence properties. COMPEL—Int. J. Comput. Math. Electr. Electron. Eng. 24(2), 374–384 (2005)
O. Schenk, K. Gärtner, On fast factorization pivoting methods for symmetric indefinite systems. Elec. Trans. Numer. Anal. 23, 158–179 (2006)
O. Schenk, K. Gärtner, Multigrid method for Maxwell’s equations. SIAM J. Numer. Anal. 36(1), 204–225 (1999)
A. Kameari, Improvement of ICCG convergence for thin elements in magnetic field analyses using the finite-element method. IEEE Trans. Magn. 44(6), 178–1181 (2008)
Ch. Chen, O. Bíró, Geometric multigrid with plane smoothing for thin elements in 3-D magnetic fields calculation. IEEE Trans. Magn. 48(2), 443–446 (2012)
A. Hauck, M. Ertl, J. Schöberl, M. Kaltenbacher, Accurate magnetostatic simulation of step-lap joints in transformer cores using anisotropic higher order FEM. COMPEL 32(5), 1581–1595 (2013)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2015 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Kaltenbacher, M. (2015). Algebraic Solvers. In: Numerical Simulation of Mechatronic Sensors and Actuators. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40170-1_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-40170-1_13
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40169-5
Online ISBN: 978-3-642-40170-1
eBook Packages: EngineeringEngineering (R0)