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Stability and convergence analysis of time-domain perfectly matched layers for the wave equation in waveguides. (English) Zbl 1493.65142

The stability and convergence analysis of the time-domain perfectly matched layers (PMLs) for the wave equation in 3D waveguides is considered. The paper is outlined as follows. Section 1 is an Introduction. In Section 2, the problem is presented, notations are introduced and the PML method is recalled. Section 3 is dedicated to the well-posedness and stability analysis of the PMLs. In Section 4, convergence estimates for the PMLs in the time domain are proved. Section 5 contains numerical studies of optimality of the estimates of Section 4. In Section 6, some conclusions are given, the results of the article are outlined and possible extensions of the techniques used herein are discussed. In the four Appendixes A, B, C, and D the proof of some statements is given.

MSC:

65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35L05 Wave equation
44A10 Laplace transform
78A50 Antennas, waveguides in optics and electromagnetic theory
78A40 Waves and radiation in optics and electromagnetic theory
35Q60 PDEs in connection with optics and electromagnetic theory
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