HAL CCSD
Stability of Perfectly Matched Layers for Maxwell's Equations in Rectangular Solids
Halpern, Laurence
Rauch, Jeffrey
Laboratoire Analyse, Géométrie et Applications (LAGA) ; Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord
University of Michigan [Ann Arbor] ; University of Michigan System
hal-04049577
https://hal.science/hal-04049577
https://hal.science/hal-04049577/document
https://hal.science/hal-04049577/file/MaxwellRotSolo.pdf
https://hal.science/hal-04049577
2023
en
Perfectly matched layers
Maxwell's equations
absorbing boundary conditions
trihedral corner
stability
MSC: 35L50, 35L53, 35J25, 35Q61, 35B30, 78M20.
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
info:eu-repo/semantics/preprint
Preprints, Working Papers, ...
Perfectly matched layers are an essential tool designed in the nineties for the computation of electromagnetic waves. The method replaces the Maxwell equations by a larger system, and introduce variable absorption coefficients that are nonvanishing near the boundary of the computational box. Classic absorbing conditions are imposed at the boundary. Well posedness of the resulting initial boundary value problem is proved here for the first time. The analysis proceeds by Laplace transform in time on smoothed domains. There we design boundary conditions for a non selfadjoint Helmholtz system. Estimates uniform in the smoothing are proved using carefully constructed test functions. One estimate is of energy type with less positivity than usual. A second follows Jerison-Kenig-Mitrea from elliptic problems in Lipschitz domains.
2023-03-28
info:eu-repo/semantics/OpenAccess