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Explore the intricacies of full envelope discontinuous Petrov-Galerkin (DPG) approximation for electromagnetic waveguides in this comprehensive seminar presented by Leszek F. Demkowicz from the University of Texas at Austin. Delve into the stability and convergence analysis of the full envelope approximation used in optical amplifier simulations, with a focus on Transverse Mode Instabilities (TMI). Examine the challenges of simulating long fibers and the innovative solutions involving exponential ansatz and superefficient MPI/openMP hp FE code. Investigate the stability analysis of both acoustic and Maxwell waveguides, uncovering the unexpected difficulties in vector-valued equations and non-self-adjoint operators. Gain insights into the application of perturbation theory and the final results regarding boundedness below constants in relation to waveguide length. This seminar, part of the FEM@LLNL series sponsored by the MFEM project, offers valuable knowledge for researchers and practitioners in finite element methods and electromagnetic simulations.
