Feasible fundamental solution of the multiphysics wave equation in inhomogeneous domains of complex shape

The spectral functions method for acoustic wave diffraction by a stress-free wedge: Theory and validation

“…This pole propagation process is applied recursively in order to determine all the poles of the spectral functions α j . This process stops when the generated poles are no longer in the domain Ω 0 defined in (29). All the generated poles then belong to Ω 0 ∪] − cos 2ϕ, +∞].…”

“…A successive approximations method is proposed in the particular case of a wedge-shaped separation between two media having the same acoustic wave velocity or in the case where the medium containing the incident wave is a wedge of angle lower than π. In the very general case of acoustic wave propagation in a homogeneous or inhomogeneous medium delimited by an arbitrary-shaped boundary, a mathematical model has been rigorously presented by Aizenberg and Ayzenberg [29], providing the analytical feasible fundamental solution for this problem. The notion of feasible fundamental solution is a generalization of Green's function for an unbounded medium.…”

2D elastic plane-wave diffraction by a stress-free wedge of arbitrary angle

“…The problem of acoustic diffraction in a system of wedge-shaped regions was studied by Klem-Musatov [15], but this system is too complex to be solved in general cases. For the very general problem of acoustic wave propagation in a homogeneous or inhomogeneous medium delimited by an arbitrary-shaped boundary, a mathematical model has been rigorously presented by Aizenberg and Ayzenberg [16]. Ayzenberg [17] shows how this model can be numerically applied to the case of wedge diffraction.…”