Abstract
In this paper, we develop a new representation for outgoing solutions to the time harmonic Maxwell equations in unbounded domains in R{double struck}3. This representation leads to a Fredholm integral equation of the second kind for solving the problem of scattering from a perfect conductor, which does not suffer from spurious resonances or low-frequency breakdown, although it requires the inversion of the scalar surface Laplacian on the domain boundary. In the course of our analysis, we give a new proof of the existence of nontrivial families of time-harmonic solutions with vanishing normal components that arise when the boundary of the domain is not simply connected. We refer to these as k-Neumann fields, since they generalize, to nonzero wave numbers, the classical harmonic Neumann fields. The existence of k-Neumann fields was established earlier by Kress.
Original language | English (US) |
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Pages (from-to) | 413-463 |
Number of pages | 51 |
Journal | Communications on Pure and Applied Mathematics |
Volume | 63 |
Issue number | 4 |
DOIs | |
State | Published - Apr 2010 |
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics