Uncertainty quantification for high frequency waves

Abstract: We consider high frequency waves satisfying the scalar wave equation withhighly oscillatory initial data. The speed of propagation of the medium aswell as the phase and amplitude of the initial data is assumed to be uncertain,described by a finite number of independent random variables with knownprobability distributions. We introduce quantities of interest (QoIs) as localaverages of the squared modulus of the wave solution, or its derivatives. Theregularity of these QoIs in terms of the input random parameters and the wavelength is important for uncertainty quantification methods based on interpo-lation in the stochastic space. In particular, the size of the derivatives shouldbe bounded and independent of the wavelength. In the contributed papers, weshow that the QoIs indeed have this property, despite the highly oscillatorycharacter of the waves.