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Analysis of the perfectly matched layer problems for time dependent Maxwell equations. (English) Zbl 1153.78335

Summary: We study the perfectly matched layer method for electromagnetic scattering problems. Particularly we analyze the initial-boundary value problems of the transverse magnetic mode (TM) to Maxwell’s equation. An exterior domain in two spacial dimension is truncated by a square with a layer filled by a certain artificial medium. Using energy method we obtain some stability estimates for this initial-boundary value problem on the truncated domain. Then we define the weak formulation of this problem and prove existence and uniqueness. The results are extended to polar coordinates and three dimensional problems.

MSC:

78M25 Numerical methods in optics (MSC2010)
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
65Z05 Applications to the sciences
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