Numerical Waves

Numerous numerical methods have recently been developed to study self-adjoint spectral problems and wave propagation. In particular, these methods seek to avoid phenomena of pollution that can be spectral (the discretisation makes appear fictitious eigenvalues) or numerical (the interpolation properties are degraded in the case of the high frequencies). However, these methods are much less effective in studying non-self-adjoint spectral problems (describing the propagation of waves in an absorbing or open medium), where pseudo-spectral effects may occur, not to mention the inherent difficulties to heterogeneous media. Understanding these effects often requires sophisticated tools of partial differential equations (e.g. semi-classical analysis). The purpose of this conference is to bring together experts in numerical approaches to wave propagation problems, and specialists in the spectral theory of non self-adjoint operators. The meeting of these two communities should make it possible to develop more robust schemes to study the wave propagation in an open medium.