Title: A coercive Helmholtz model: Formulation, wavenumber-explicit analysis, and preconditioned high-order FEM

We consider a frequency-domain wave propagation model governed by the Helmholtz partial differential equation and an impedance boundary condition. The celebrated standard variational formulation of the model is non-coercive. It has been an open problem to establish a coercive variational formulation of the heterogeneous model. The main focus of this talk is on solving this continuous model formulation and analysis problem, and hence establishing an efficient preconditioned numerical algorithm for simulating our novel coercive variational formulation. For the heterogeneous media, with size varying from tens to hundreds of wavelengths, we demonstrate that our new preconditioned-FEM model requires a very low number of GMRES iterations, and the number of iterations is independent of the wavenumber of the model.