D. N. Arnold, R. S. Falk, and R. Winther, Finite Element Exterior Calculus, Homological Techniques, and Applications, Acta Numer. 15, Cambridge University Press, Cambridge, UK, 2006.
D. N. Arnold, R. S. Falk, and R. Winther, Finite element exterior calculus: from Hodge theory to numerical stability, Bull. Amer. Math. Soc. (N.S.), 47 (2010), pp. 281-354.
A. Bossavit, Magnetostatic problems in multiply connected regions: Some properties of the curl operator, in Physical Science, Measurement and Instrumentation, Management and Education-Reviews IEE Proc. A, 135 (1988), pp. 179 -187. (Pubitemid 18592210)
A. Bossavit, Computational Electromagnetism, Academic Press, New York, 1998.
A. Bossavit, How weak is the weak solution in finite element methods?, IEEE Trans. Magnetics, 34 (1998), pp. 2429-2432. (Pubitemid 128747341)
CHomP, http://chomp.rutgers.edu/software (2012).
K. Clarkson, A Program for Convex Hulls, http://www.netlib.org/voronoi/ hull.html (1995).
T. K. Dey, A. N. Hirani, and B. Krishnamoorthy, Optimal homologous cycles, total unimodularity, and linear programming, in Proceedings of the 42nd ACM Symposium on Theory of Computing, 2010, pp. 221-230.
T. K. Dey, K. Li, and J. Sun, Computing geometry-aware handle and tunnel loops in 3d models, ACM Trans. Graph, 27 (2008), p. 45.
P. Dlotko and R. Specogna, Efficient cohomology computation for electromagnetic modeling, CMES Comput. Model. Eng. Sci., 60 (2010), pp. 247-278.
P. Dlotko, R. Specogna, and F. Trevisan, Automatic generation of cuts on large-sized meshes for the T -Ω geometric eddy-current formulation, Comput. Methods Appl. Mech. Engrg., 198 (2009), pp. 3765-3781.
P. Dular, C. Geuzaine, F. Henrotte, and W. Legros, A general environment for the treatment of discrete problems and its application to the finite element method, IEEE Trans. Magnetics, 34 (1998), pp. 3395-3398.
P. Dular, P. Kuo-Peng, C. Geuzaine, N. Sadowski, and J. P. A. Bastos, Dual magnetodynamic formulations and their source fields associated with massive and stranded inductors, IEEE Trans. Magnetics, 36 (2000), pp. 1293-1299. (Pubitemid 32020007)
P. Dular, W. Legros, and A. Nicolet, Coupling of local and global quantities in various finite element formulations and its application to electrostatics, magnetostatics and magnetodynamics, IEEE Trans. Magnetics, 34 (1998), pp. 3078-3081.
H. Edelsbrunner and E. P. Mucke, Three-dimensional alpha shapes, in Proceedings of the 1992 Workshop on Volume Visualization, ACM, 1992, pp. 75-82.
J. Erickson and K. Whittlesey, Greedy optimal homotopy and homology generators, in Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms, 2005, pp. 1038-1046. (Pubitemid 40858027)
C. Geuzaine and J.-F. Remacle, Gmsh: A three-dimensional finite element mesh generator with built-in pre- and post-processing facilities, Internat. J. Numer. Methods Engrg., 79 (2009), pp. 1309-1331.
P. W. Gross and P. R. Kotiuga, Electromagnetic Theory and Computation, Cambridge University Press, Cambridge, UK, 2004.
X. Gu and S.-T. Yau, Global conformal surface parameterization, in Proceedings of the 2003 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, 2003, pp. 127- 137.
A. Hatcher, Algebraic Topology, Cambridge University Press, Cambridge, UK, 2002.
F. Henrotte and K. Hameyer, An algorithm to construct the discrete cohomology basis functions required for magnetic scalar potential formulations without cuts, IEEE Trans. Magnetics, 39 (2003), pp. 1167-1170.
J.-G. Dumas, F. Heckenbach, B. D. Saunders and V. Welker, GAP Homology, http://www.eecis.udel.edu/dumas/Homology (2011).
T. Kaczynski, M. Mrozek, and M. Slusarek, Homology computation by reduction of chain complexes, Comput. Math. Appl., 35 (1998), pp. 59 - 70. (Pubitemid 128381286)
L. Kettunen, K. Forsman, and A. Bossavit, Formulation of the eddy current problem in multiply connected regions in terms of h, Internat. J. Numer. Methods Engrg., 41 (1998), pp. 935-954. (Pubitemid 128607833)
M. Mrozek and B. Batko, Coreduction homology algorithm, Discrete Comput. Geom., 41 (2009), pp. 96-118.
J. R. Munkres, Elements of Algebraic Topology, Perseus Books, New York, 1984.
M. Pellikka, Magnetodynamics with Cohomology Conditions, http://onelab.info/wiki/Magnetodynamics-with-cohomology-conditions.
M. Pellikka, S. Suuriniemi, and L. Kettunen, Homology in electromagnetic boundary value problems, Boundary Value Problems, 2010 (2010), 381953.
M. Pellikka, S. Suuriniemi, and L. Kettunen, Powerful heuristics and basis selection bring computational homology to engineers, IEEE Trans. Magnetics, 47 (2011), pp. 1226-1229.
J.-F. Remacle, C. Geuzaine, G. Compere, and E. Marchandise, High-quality surface remeshing using harmonic maps, Internat. J. Numer. Methods Engrg., 83 (2010), pp. 403-425.
Z. Ren, T - Ω-formulation for eddy-current problems in multiply connected regions, IEEE Trans. Magnetics, 38 (2002), pp. 557-560. (Pubitemid 34531221)
R. Specogna, Complementary geometric formulations for electrostatics, Internat. J. Numer. Methods Engrg., 86 (2011), pp. 1041-1068.
S. Suuriniemi, Homological Computations in Electromagnetic Modeling, Ph.D. thesis, Department of Electrical Engineering, Tampere University of Technology, Tampere, Finland, 2004.
S. Suuriniemi, J. Kangas, and L. Kettunen, Driving a coupled field-circuit problem, COMPEL, 26 (2007), pp. 899-909. (Pubitemid 47141721)
C. K. Yap, Fundamental Problems of Algorithmic Algebra, Oxford University Press, New York, 2000.
A. Yavari, On geometric discretization of elasticity, J. Math. Phys., 49 (2008).
A. Zomorodian and G. Carlsson, Localized homology, Comput. Geom., 41 (2008), pp. 126-148.