Discretization of boundary integral equations by differential forms on dual grids

IEEE Transactions on Magnetics

Volumn 40, Issue 2 II, 2004, Pages 826-829

  Kurz, Stefan ^a   Rain, Oliver ^b   Rischmüller, Volker ^b   Rjasanow, Sergej ^c  

^a HELMUT SCHMIDT UNIVERSITY   (Germany)

^b ROBERT BOSCH GMBH   (Germany)

^c SAARLAND UNIVERSITY   (Germany)

Author keywords

Boundary element methods; Differential forms; Integral equations

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY ELEMENT METHOD; FINITE ELEMENT METHOD; INTEGRAL EQUATIONS; LAPLACE TRANSFORMS; MATHEMATICAL OPERATORS; PERMITTIVITY; VECTORS;

BOUNDARY-ELEMENT METHODS; DIFFERENTIAL FORMS; DUAL GRIDS; RHAM MAPS;

ELECTROMAGNETISM;

EID: 2342456562     PISSN: 00189464     EISSN: None     Source Type: Journal    
DOI: 10.1109/TMAG.2004.824902     Document Type: Article

References (12)

1. R. Hiptmair, "Finite elements in computational electromagnetism, " Acta Numerica, pp. 237-339, 2002.
2. A. Bossavit, "Generalized finite differences in computational electromagnetics," in Geometric Methods for Computational Electromagnetics, F. Teixeira, Ed. Cambridge, Massachusetts: EMW, 2001, vol. 32, Progress in Electromagnetics Research, pp. 45-64.
3. _, "On the representation of differential forms by potentials in dimension 3," in Scientific Computing in Electrical Engineering, U. van Rienen, M. Günther, and D. Hecht, Eds. Berlin: Springer-Verlag, 2001, vol. 18, Lecture Notes in Computational Science and Engineering, pp. 97-104.
4. C. Geuzaine, T. Tarhasaari, L. Kettunen, and P. Dular, "Discretization schemes for hybrid methods," IEEE Trans. Magn., vol. 37, pp. 3112-3115, Sept. 2001.
5. T. Tarhasaari, L. Kettunen, and C. Geuzaine, "Discretization of sources of integral operators," IEEE Trans. Magn., vol. 36, pp. 659-662, July 2000.
6. A. Bossavit, "The 'scalar' Poincaré Steklov operator and the 'vector' one: Algebraic structures which underlie their duality," in Domain Decomposition Methods for Partial Differential Equations. Philadelphia, PA: SIAM, 1991, ch. 2, pp. 19-26.
7. W. McLean, Strongly Elliptic Systems and Boundary Integral Equations. Cambridge, U.K.: Cambridge Univ. Press, 2000.
8. A. Buffa and P. Ciarlet, Jr., "On traces for functional spaces related to Maxwell's equations. Part I: An integration by parts formula in Lipschitz polyhedra; Part II: Hodge decompositions on the boundary of Lipschitz polyhedra and applications," Math. Methods Appl. Sci., vol. 24, pp. 9-48, 2001.
9. G. de Rham, Differentiable Manifolds. Berlin, Germany: Springer-Verlag, 1984.
10. K. Warnick and D. Arnold, "Electromagnetic Green functions using differential forms," J. Electromagn. Waves Applicat., vol. 10, no. 3, pp. 427-438, 1996.
11. R. Hiptmair, "Symmetric coupling for eddy current problems," SIAM J. Numer. Anal., vol. 40, pp. 41-65, 2002.
12. h, ℤ) for triangulated surfaces: Construction and classification," Universität Tübingen, Tech. Rep. 160, Mar. 2001.