Victorita Dolean: Robust solvers for time harmonic wave propagation problems

Time harmonic wave propagation problems are notoriously difficult to solve especially in high frequency regime. Several reasons are at the origin of this: first of all the oscillatory nature of the solution, meaning that the number of degrees of freedom after discretisation increases drastically with the wave number (especially for lower order approximations) giving rise to complex valued large problems to solve.

Secondly, the indefiniteness of the operator: its spectral properties only making it difficult to control and predict the behaviour of a Krylov type solver. Not to mention the inherent challenges when the wave propagation takes place in a heterogeneous medium. We try to answer partially to some of the questions (with strong numerical evidence) by proposing a few methods which proved to be robust with respect to the wave number. These methods are further applied to heterogeneous physically realistic problems arising in electrical engineering and geophysics.

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