Generalized Electromagnetic Scattering in a Complex Geometry

✍ Scribed by Jukka Liukkonen

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 130 KB
• Volume: 254
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.2000.7205

✦ Synopsis

We consider generalized time-harmonic Maxwell's equations on a real manifold of arbitrary dimension. Since the field tensors have complex coefficients the manifold is endowed with complex tangent and cotangent bundles and a complex valued pseudo-Riemannian metric. The lack of geodesics in general forces us to a restricted and careful use of standard differential geometric methods. We apply our machinery to scattering by a bounded body. As the main result we prove that the existence and uniqueness of a solution to an exterior boundary value problem is independent of the metric. This study originates from the perfectly matched layer or PML technique in computational electromagnetics.