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Die lösung der maxwellschen gleichungen durch vollständige flächenfeldsysteme
Author(s) -
Kersten H.,
Leis R.
Publication year - 1985
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670070103
Subject(s) - mathematics , maxwell's equations , boundary value problem , mathematical analysis , helmholtz equation , mathematical physics
The paper deals with approximation theorems for the solution of Maxwell's equations governing the mathematical description of the propagation of electromagnetic waves. The well‐known results ([10]) for the Helmholtz equation are generalized to Maxwell's equations: Systems of electric (resp. magnetic) dipoles are proved to span the space of all solutions of rot H + iω E = 0, rot E ‐ iω H = 0, with n × E prescribed on the boundary. The same result holds for the “Mie‐potentials”Which can be proved by a Lemma of Mie [6]. Two numerical examples for the three‐dimensional boundary value problems (field of a dipole, field of reflection) are presented.