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This note is intended as a brief introduction to the theory and practice of perfectly matched layer (PML) absorbing boundaries for wave equations, originally developed for MIT courses 18.369 and 18.336. It focuses on the complex stretched-coordinate viewpoint, and also discusses the limitations of PML.
In this article, several discontinuous Petrov-Galerkin (DPG) methods with perfectly matched layers (PMLs) are derived along with their quasi-optimal graph test norms. Ultimately, two different complex coordinate stretching strategies are considered i
For scattering problems of time-harmonic waves, the boundary integral equation (BIE) methods are highly competitive, since they are formulated on lower-dimension boundaries or interfaces, and can automatically satisfy outgoing radiation conditions. F
We investigate in a $2$D setting the scattering of time-harmonic electromagnetic waves by a plasmonic device, represented as a non dissipative bounded and penetrable obstacle with a negative permittivity. Using the $textrm{T}$-coercivity approach, we
Density matrix perturbation theory (DMPT) is known as a promising alternative to the Rayleigh-Schrodinger perturbation theory, in which the sum-over-state (SOS) is replaced by algorithms with perturbed density matrices as the input variables. In this
The optical resonance problem is similar to but different from time-steady Schr{o}dinger equation. One big challenge is that the eigenfunctions in resonance problem is exponentially growing. We give physical explanation to this boundary condition and