Free Access
Volume 49, Number 1, January-February 2015
Page(s) 141 - 170
Published online 14 January 2015
  1. A. Alonso Rodríguez and A. Valli, Eddy Current Approximation of Maxwell Equations, Springer, Milan (2010). [Google Scholar]
  2. R. Albanese and G. Rubinacci, Magnetostatic field computations in terms of two component vector potentials. Int. J. Numer. Methods Engrg. 29 (1990) 515–532. [CrossRef] [Google Scholar]
  3. H. Ammari, A. Buffa and J.-C. Nédélec, A justification of eddy currents model for the Maxwell equations. SIAM J. Appl. Math. 60 (2000) 1805–1823. [CrossRef] [MathSciNet] [Google Scholar]
  4. C. Amrouche, C. Bernardi, M. Dauge and V. Girault, Vector potentials in three-dimensional non-smooth domains. Math. Methods Appl. Sci. 21 (1998) 823–864. [CrossRef] [MathSciNet] [Google Scholar]
  5. C. Amrouche and N. El Houda Seloula, Lp-theory for vector potentials and Sobolev’s inequalities for vector vields. C.R. Acad. Sci. Paris Ser. I 349 (2011) 529–534. [CrossRef] [Google Scholar]
  6. F. Assous, P. Ciarlet, Jr. and E. Sonnendrücker, Resolution of the Maxwell equations in a domain with reentrant corners. Math. Model. Numer. Anal. 32 (1998) 359–389. [Google Scholar]
  7. A. Bermúdez, R. Rodríguez and P. Salgado, Numerical analysis of electric field formulations of the eddy current model. Numer. Math. 102 (2005) 181–201. [CrossRef] [MathSciNet] [Google Scholar]
  8. O. Bíró, Edge element formulations of eddy current problems. Comput. Methods Appl. Mech. Engrg. 169 (1999) 391–405. [Google Scholar]
  9. O. Bíró and A. Valli, The Coulomb gauged vector potential formulation for the eddy-current problem in general geometry: Well-posedness and numerical approximation. Comput. Methods Appl. Mech. Engrg. 196 (2007) 1890–1904. [CrossRef] [MathSciNet] [Google Scholar]
  10. A.-S. Bonnet-Ben Dhia, C. Hazard and S. Lohrengel, A singular field method for the solution of Maxwell’s equations in polyhedral domains. SIAM J. Appl. Math. 56 (1999) 2028–2044. [CrossRef] [MathSciNet] [Google Scholar]
  11. J.R. Bowler, Eddy-current interaction with an ideal crack. I. The forward problem. J. Appl. Phys. 75 (1994) 8128–8137. [CrossRef] [Google Scholar]
  12. J.R. Bowler, S.J. Norton and D.J. Harrison, Eddy-current interaction with an ideal crack. II. The inverse problem. J. Appl. Phys. 75 (1994) 8138–8144. [CrossRef] [Google Scholar]
  13. J.R. Bowler, Theory of eddy current crack response, Technical Report. Iowa State University, Center for Nondestructive Evaluation, Ames IA (2002). [Google Scholar]
  14. J.R. Bowler, Thin-skin eddy-current inversion for the determination of crack shapes. Inverse Probl. 18 (2002) 1891–1905. [CrossRef] [Google Scholar]
  15. J.R. Bowler, Y. Yoshida and N. Harfield, Vector-Potential Boundary-Integral Evaluation of Eddy-Current Interaction with a Crack. IEEE Trans. Magn. 33 (1997) 4287–4294. [CrossRef] [Google Scholar]
  16. A. Buffa and P. Ciarlet, Jr., On traces for functional spaces related to Maxwell equations, Part I: An integration by parts formula in Lipschitz polyhedra. Math. Methods Appl. Sci. 24 (2001) 9–30. [CrossRef] [MathSciNet] [Google Scholar]
  17. M. Costabel and M. Dauge, Singularities of electromagnetic fields in polyhedral domains. Arch. Ration. Mech. Anal. 151 (2000) 221–276. [CrossRef] [MathSciNet] [Google Scholar]
  18. M. Costabel and M. Dauge, Crack singularities for general elliptic systems. Math. Nachr. 235 (2002), pp. 29–49. [Google Scholar]
  19. M. Costabel and M. Dauge, Asymptotics without logarithmic terms for crack problems, Commun. Partial. Differ. Eq. 28 (2003) 869–926. [CrossRef] [MathSciNet] [Google Scholar]
  20. M. Costabel, M. Dauge and S. Nicaise, Singularities of eddy current problems. ESAIM: M2AN 37 (2003) 807–831. [CrossRef] [EDP Sciences] [Google Scholar]
  21. E. Creusé, S. Nicaise, Z. Tang, Y. Le Menach, N. Nemitz and F. Piriou, Residual-based a posteriori estimators for the Aϕ magnetodynamic harmonic formulation of the Maxwell system. Math. Models Methods Appl. Sci. 22 (2012) DOI: 10.1142/S021820251150028X. [Google Scholar]
  22. R.W. Freund, Conjugate gradient-type methods for linear systems with complex symmetric coefficient matrices. SIAM J. Sci. Statis. Comput. 13 (1992) 425–448. [Google Scholar]
  23. T.-P. Fries and M. Baydoun, Crack propagation with the extended finite element method and a hybrid explicit-implicit crack description. Int. J. Numer. Methods Engrg. 89 (2012) 1527–1558. [CrossRef] [Google Scholar]
  24. V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations, Springer, Berlin (1986). [Google Scholar]
  25. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman, London (1985). [Google Scholar]
  26. P. Grisvard, Singularities in boundary value problems. Masson, Paris (1992). [Google Scholar]
  27. N. Harfield and J.R. Bowler, Analysis of eddy-current interaction with a surface-breaking crack. J. Appl. Phys. 76 (1994) 4853–4856. [CrossRef] [Google Scholar]
  28. C. Hazard and M. Lenoir, On the solution of time-harmonic scattering problems for Maxwell’s equations. SIAM J. Math. Anal. 27 (1996) 1597–1630. [CrossRef] [MathSciNet] [Google Scholar]
  29. R. Hiptmair, Symmetric coupling for eddy current problems. SIAM J. Numer. Anal. 40 (2002) 41–65. [CrossRef] [MathSciNet] [Google Scholar]
  30. M. Křižek and P. Neittaanmäki, Finite element approximation for a div-rot system with mixed boundary conditions in non-smooth domains. Apl. Mat. 29 (1984) 272–285. [MathSciNet] [Google Scholar]
  31. F. Lefèvre, S. Lohrengel and S. Nicaise, An eXtended Finite Element Method for 2D edge elements. Int. J. Numer. Anal. Model. 8 (2011) 641–666. [Google Scholar]
  32. N. Moës, J. Dolbow and T. Belytschko, A finite element method for crack growth without remeshing. Int. J. Numer. Methods Engrg. 46 (1999) 131–150. [Google Scholar]
  33. P. Monk, Finite Element Methods for Maxwell’s Equations. Oxford University Press (2003). [Google Scholar]
  34. P.A. Pinsky, Partial Differential Equations and Boundary-Value Problems with Applications. McGraw-Hill, Singapore (1998). [Google Scholar]
  35. K. Preis, I. Bardi, O. Bíró, C. Magele, G. Vrisk and K.R. Richter, Different finite element formulations of 3D Magnetostatics fields. IEEE Trans. Magn. 28 (1992) 1056–1059. [CrossRef] [Google Scholar]
  36. Z. Ren, Influence of the R.H.S. on the Convergence Behaviour of the Curl-Curl Equation. IEEE Trans. Magn. 32 (1996) 655–658. [CrossRef] [Google Scholar]
  37. N. Sukumar, D.L. Chopp and B. Moran, Extended finite element method and fast marching method for three-dimensional fatigue crack propagation. Engrg. Fracture Mech. 70 (2003) 29–48. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you