Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

A Justification of Eddy Currents Model for the Maxwell Equations

H. Ammari, A. Buffa and J.-C. Nédélec
SIAM Journal on Applied Mathematics
Vol. 60, No. 5 (May, 2000), pp. 1805-1823
Stable URL: http://www.jstor.org/stable/3061711
Page Count: 19
  • Subscribe ($19.50)
  • Cite this Item
A Justification of Eddy Currents Model for the Maxwell Equations
Preview not available

Abstract

This paper is concerned with the approximation of the Maxwell equations by the eddy currents model, which appears as a correction of the quasi-static model. The eddy currents model is obtained by neglecting the displacement currents in the Maxwell equations and exhibits an elliptic character in the time-harmonic formulation. Our main concern in this paper is to show that the eddy currents model approximates the full Maxwell system up to the second order with respect to the frequency if and only if an additional condition on the current source is fulfilled. Otherwise, it is a first-order approximation to the Maxwell equations. We also study the well-posedness of the eddy currents model and investigate the time-dependent case. All our results strongly depend on the topology properties of the domains under consideration. This dependence which is specific to Maxwell's equations does not appear for the two- or the three-dimensional Helmholtz operator.

Page Thumbnails

  • Thumbnail: Page 
1805
    1805
  • Thumbnail: Page 
1806
    1806
  • Thumbnail: Page 
1807
    1807
  • Thumbnail: Page 
1808
    1808
  • Thumbnail: Page 
1809
    1809
  • Thumbnail: Page 
1810
    1810
  • Thumbnail: Page 
1811
    1811
  • Thumbnail: Page 
1812
    1812
  • Thumbnail: Page 
1813
    1813
  • Thumbnail: Page 
1814
    1814
  • Thumbnail: Page 
1815
    1815
  • Thumbnail: Page 
1816
    1816
  • Thumbnail: Page 
1817
    1817
  • Thumbnail: Page 
1818
    1818
  • Thumbnail: Page 
1819
    1819
  • Thumbnail: Page 
1820
    1820
  • Thumbnail: Page 
1821
    1821
  • Thumbnail: Page 
1822
    1822
  • Thumbnail: Page 
1823
    1823