Free Access
Issue
ESAIM: M2AN
Volume 55, Number 4, July-August 2021
Page(s) 1439 - 1460
DOI https://doi.org/10.1051/m2an/2021026
Published online 13 July 2021
  1. R. Abraham and J.E. Marsden, Foundations of Mechanics, 2nd edition. Addison-Wesley (1987). [Google Scholar]
  2. J. Baez and J.P. Muniain, Gauge Fields, Knots and Gravity. Series on Knots and Everything. World Scientific (1994). [Google Scholar]
  3. D. Bleecker, Gauge Theories and Variational Principles. Addison-Wesley (1981). [Google Scholar]
  4. A. Bossavit, How weak is the ‘weak solution’ in finite element methods? IEEE Trans. Magn. 34 (1998) 2429–2432. [Google Scholar]
  5. A. Bossavit, On the geometry of electromagnetism, 1. Affine space. J. Jpn. Soc. Appl. Electromag. Mech. 6 (1998) 17–28. [Google Scholar]
  6. A. Bossavit, On the geometry of electromagnetism, 2. Geometrical objects. J. Jpn. Soc. Appl. Electromag. Mech. 6 (1998) 114–123. [Google Scholar]
  7. A. Bossavit, On the geometry of electromagnetism, 3. Integration, stokes, faraday’s law. J. Jpn. Soc. Appl. Electromag. Mech. 6 (1998) 223–240. [Google Scholar]
  8. A. Bossavit, On the geometry of electromagnetism, 4. Maxwell’s house. J. Jpn. Soc. Appl. Electromag. Mech. 6 (1998) 318–326. [Google Scholar]
  9. A. Bossavit, Computational electromagnetism and geometry: building a finite-dimensional “Maxwell’s house”. J. Jpn. Soc. Appl. Electromag. Mech. 7 (1999) 150–159. [Google Scholar]
  10. A. Bossavit, Computational electromagnetism and geometry: convergence. J. Jpn. Soc. Appl. Electromag. Mech. 7 (1999) 401–408. [Google Scholar]
  11. A. Bossavit, Computational electromagnetism and geometry: network constitutive laws. J. Jpn. Soc. Appl. Electromag. Mech. 7 (1999) 294–301. [Google Scholar]
  12. A. Bossavit, Computational electromagnetism and geometry: from degrees of freedom to fields. J. Jpn. Soc. Appl. Electromag. Mech. 8 (2000) 102–109. [Google Scholar]
  13. A. Bossavit, Computational electromagnetism and geometry: some questions and answers. J. Jpn. Soc. Appl. Electromag. Mech. 8 (2000) 372–377. [Google Scholar]
  14. A. Bossavit, Computational electromagnetism and geometry: the “Galerkin hodge’’. J. Jpn. Soc. Appl. Electromag. Mech. 8 (2000) 203–209. [Google Scholar]
  15. A. Bossavit, ‘Generalized finite differences’ in computational electromagnetics. edited by F.L. Teixeira. In: Progress in Electromagnetics Research, PIER, EMW, Cambridge, MA (2001) 45–64. [Google Scholar]
  16. A. Bossavit, On the notion of anisotropy of constitutive laws: some implications of the ‘Hodge implies metric’ result. Compel 20 (2001) 233–239. [Google Scholar]
  17. A. Bossavit and L. Kettunen, Yee-like schemes on a tetrahedral mesh, with diagonal lumping. Int. J. Numer. Model. Electron. Networks Devices Fields 12 (1999) 129–142. [Google Scholar]
  18. A. Bossavit and L. Kettunen, Correction to ‘Yee-like schemes on staggered cellular grids: a synthesis between FIT and FEM approaches’. IEEE Trans. Magn. 36 (2000) 4050. [Google Scholar]
  19. A. Bossavit and L. Kettunen, Yee-like schemes on staggered cellular grids: a synthesis between FIT and FEM approaches. IEEE Trans. Magn. 36 (2000) 861–867. [CrossRef] [Google Scholar]
  20. L. Codecasa and M. Politi, Explicit, consistent, and conditionally stable extension of fd-td to tetrahedral grids by fit. IEEE Trans. Magn. 44 (2008) 1258–1261. [Google Scholar]
  21. H. Flanders, Differential Forms with Application to the Physical Sciences. Dover (1989). [Google Scholar]
  22. T. Frankel, The Geometry of Physics, an Introduction, 3rd edition. Cambridge Univ. Press, Cambridge, USA (2012). [Google Scholar]
  23. A. Frölicher and A. Nijenhuis, Theory of vector–valued differential forms: part I. Derivations in the graded ring of differential forms. Indagationes Mathematicae (Proceedings) 59 (1956) 338–350. [Google Scholar]
  24. A.N. Hirani, Discrete exterior calculus. PhD thesis, Caltech, Pasadena, California, 5 (2003). [Google Scholar]
  25. W.V.D. Hodge, The Theory and Applications of Harmonic Integrals. Cambridge Univ. Press, Cambridge, USA (1941). [Google Scholar]
  26. E. Kanso, M. Arroyo, Y. Tong, A. Yavari, J.E. Marsden and M. Desbrun, On the geometric character of stress in continuum mechanics. Z. Angew. Math. Phys. 58 (2007) 1–14. [Google Scholar]
  27. J. Keäränen, E. Koljonen, T. Tarhasaari and L. Kettunen, Effect of cell type on convergence of wave propagation schemes. IEEE Trans. Magn. 40 (2004) 1452–1455. [Google Scholar]
  28. L. Kettunen, S. Mönkölä, J. Parkkonen and T. Rossi, General conservation law for a class of physics field theories. arXiv:1908.10634. [Google Scholar]
  29. T. Kovanen, T. Tarhasaari and L. Kettunen, Formulation of small-strain magneto-elastic problems. https://arxiv.org/abs/1602.04966. [Google Scholar]
  30. J. Lohi, Discrete exterior calculus and higher order Whitney forms. Master’s thesis, University of Jyväskylä (2019). [Google Scholar]
  31. J. Räbinä, L. Kettunen, S. Mönkölä and T. Rossi, Generalized wave propagation problems and discrete exterior calculus. ESAIM : M2AN 52 (2018) 1195–1218. [EDP Sciences] [Google Scholar]
  32. F. Rapetti and A. Bossavit, Whitney forms of higher degree. SIAM J. Numer. Anal. 47 (2009) 2369–2386. [Google Scholar]
  33. R. Segev and G. Rodnay, Cauchy’s theorem on manifolds. J. Elasticity 56 (1999) 129–144. [Google Scholar]
  34. T. Tarhasaari, L. Kettunen and A. Bossavit, Some realizations of a discrete Hodge operator: a reinterpretation of finite element techniques. IEEE Trans. Magn. 35 (1999) 1494–1497. [CrossRef] [Google Scholar]
  35. F. Teixeira and W.C. Chew, Lattice electromagnetic theory from a topological viewpoint. J. Math. Phys. 40 (1999) 169–187. [Google Scholar]
  36. E. Tonti, A direct discrete formulation of field laws: the Cell method. CMES Comput. Model. Eng. Sci. 2 (2001) 237–258. [Google Scholar]
  37. E. Tonti, The Mathematical Structure of Classical and Relativistic Physics. Birkhäuser (2013). [Google Scholar]
  38. T. Weiland, Time domain electromagnetic field computation with finite difference methods. Int. J. Numer. Model. Electron. Networks Devices Fields 9 (1996) 295–319. [Google Scholar]
  39. H. Whitney, Geometric Integration Theory. Princeton Univ. Press, USA (1957). [CrossRef] [Google Scholar]
  40. A. Yavari, On geometric discretization of elasticity. J. Math. Phys. 49 (2008). [Google Scholar]
  41. K. Yee, Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Trans. Antennas Propag. 14 (1966) 302–307. [Google Scholar]
  42. K. Yosida, Functional Analysis. Springer-Verlag, Berlin Heidelberg (1995). [Google Scholar]

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