[1] D. Begis, R. Glowinski:
Application de la méthode des éléments finis à la résolution d’un problème de domaine optimal. Méthodes de résolution des problèmes. Appl. Math. Optim. 2 (1975), 130–169. (French)
DOI 10.1007/BF01447854 |
MR 0443372
[2] A. Bossavit:
Computational Electromagnetism. Variational Formulations, Complementarity, Edge Elements. Academic Press, Orlando, 1998.
MR 1488417 |
Zbl 0945.78001
[3] D. Braess:
Finite Elements. Theory, Fast Solvers, and Applications in Solid Mechanics. Cambridge University Press, Cambridge, 2001.
MR 1827293 |
Zbl 0976.65099
[4] J. Chleboun, R. Mäkinen:
Primal hybrid formulation of an elliptic equation in smooth optimal shape problems. Adv. Math. Sci. Appl. 5 (1995), 139–162.
MR 1325963
[5] P. Doktor:
On the density of smooth functions in certain subspaces of Sobolev spaces. Comment. Math. Univ. Carolin. 14 (1973), 609–622.
MR 0336317
[6] G. E. Farin:
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Guide. Academic Press, Boston, 1997.
MR 1412572 |
Zbl 0919.68120
[7] V. Girault, P.-A. Raviart:
Finite Element Methods for Navier-Stokes equations. Theory and Algorithms. Springer-Verlag, Berlin, 1986.
MR 0851383
[8] W. Hackbusch, S. A. Sauter:
Composite finite elements for the approximation of PDEs on domains with complicated micro-structures. Numer. Math. 75 (1997), 447–472.
DOI 10.1007/s002110050248 |
MR 1431211
[9] W. Hackbusch, S. A. Sauter:
Composite finite elements for problems containing small geometric details. II: Implementation and numerical results. Comput. Vis. Sci. 1 (1997), 15–25.
DOI 10.1007/s007910050002
[10] J. Haslinger, T. Kozubek:
A fictitious domain approach for a class of Neumann boundary value problems with applications in shape optimization. East-West J. Numer. Math. 8 (2000), 1–23.
MR 1757143
[11] J. Haslinger, P. Neittaanmäki:
Finite Element Approximation for Optimal Shape, Material and Topology Design, 2nd ed. Wiley, Chichester, 1996.
MR 1419500
[12] R. Hiptmair:
Multilevel preconditioning for mixed problems in three dimensions. PhD. thesis, University of Augsburg, 1996.
MR 1399324 |
Zbl 0851.65089
[13] I. Kopřiva, D. Hrabovský, K. Postava, D. Ciprian, and J. Pištora: Anisotropy of the quadratic magneto-optical effects in a cubic crystal. Proceedings of SPIE, Vol. 4016, 2000, pp. 54–59.
[14] M. Křížek, P. Neittaanmäki:
Mathematical and Numerical Modelling in Electrical Engineering. Theory and Practice. Kluwer Academic Publishers, Dordrecht, 1996.
MR 1431889
[15] M. Kuhn, U. Langer, and J. Schöberl:
Scientific computing tools for 3d magnetic field problems. In: The Mathematics of Finite Elements and Applications. Proceedings of the 10th conference MAFELAP, 1999, J R. Whiteman (ed.), 2000, pp. 239–258.
MR 1801980
[16] D. Lukáš:
Shape optimization of homogeneous electromagnets. Scientific Computing in Electrical Engineering. Lect. Notes Comput. Sci. Eng. Vol. 18, U. van Rienen, M. Günther, and D. Hecht (eds.), 2001, pp. 145–152.
Zbl 1013.78012
[17] D. Lukáš: Optimal Shape Design in Magnetostatics. PhD. thesis. VŠB-Technical University, Ostrava, 2003.
[18] D. Lukáš, I. Kopřiva, D. Ciprian, and J. Pištora: Shape optimization of homogeneous electromagnets and their application to measurements of magnetooptic effects. Records of COMPUMAG (2001), 156–157.
[19] D. Lukáš, W. Mühlhuber, and M. Kuhn: An object-oriented library for the shape optimization problems governed by systems of linear elliptic partial differential equations. Transactions of the VŠB-Technical University Ostrava 1 (2001), 115–128.
[20] D. Lukáš, D. Ciprian, J. Pištora, K. Postava, and M. Foldyna: Multilevel solvers for 3-dimensional optimal shape design with an application to magneto-optics. Proceedings of the 9th International Symposium on Microwave and Optical Technology (ISMOT 2003, Ostrava), SPIE Vol. 5445, 2004, pp. 235–239.
[21] J. Lukeš, J. Malý:
Measure and Integral. MATFYZPRESS, Praha, 1995.
MR 2316454
[22] J. C. Nédélec:
Mixed finite elements in $\mathbb{R}^3$. Numer. Math. 35 (1980), 315–341.
DOI 10.1007/BF01396415
[23] O. Pironneau:
Optimal Shape Design for Elliptic Systems. Springer Series in Computational Physics. Springer-Verlag, New York, 1984.
MR 0725856
[24] J. Pištora, K. Postava, and R. Šebesta: Optical guided modes in sandwiches with ultrathin metallic films. Journal of Magnetism and Magnetic Materials 198–199 (1999), 683–685.
[25] K. Postava, D. Hrabovský, J. Pištora, A. R. Fert, Š. Višňovský, and T. Yamaguchi:
Anisotropy of quadratic magneto-optic effects in reflection. J. Appl. Phys. 91 (2002), 7293–7295.
DOI 10.1063/1.1449436
[26] P.-A. Raviart and J. M. Thomas:
A mixed finite element method for second order elliptic problems. Lecture Notes in Math. 606 (1977), 292–315.
DOI 10.1007/BFb0064470 |
MR 0483555
[27] S. Reitzinger, J. Schöberl:
An algebraic multigrid method for finite element discretizations with edge elements. Numer. Linear Algebra Appl. 9 (1997), 223–238.
MR 1893828
[28] J. Schöberl:
NETGEN: An advancing front 2D/3D-mesh generator based on abstract rules. Comput. Vis. Sci. 1 (1997), 41–52.
DOI 10.1007/s007910050004
[29] N. Takahashi: Optimization of die press model. Proceedings of the TEAM Workshop in the Sixth Round (Okayama, Japan), March 1996.
[30] U. van Rienen:
Numerical methods in computational electrodynamics. Linear Systems in Practical Applications, Lect. Notes Comp. Sci. Engrg. Vol. 12, Springer-Verlag, Berlin, 2001.
MR 1790270 |
Zbl 0977.78023
[31] A. K. Zvedin, V. A. Kotov: Modern Magnetooptics and Magnetooptical Materials. Institute of Physics Publishing, Bristol and Philadelphia, 1997.