Uncertainty quantification for high frequency waves

Sammanfattning: We consider high frequency waves satisfying the scalar wave equationwith highly oscillatory initial data. The speed of propagation of the mediumas well as the phase and amplitude of the initial data is assumed to beuncertain, described by a finite number of independent random variables withknown probability distributions. We introduce quantities of interest (QoIs)aslocal averages of the squared modulus of the wave solution, or itsderivatives.The regularity of these QoIs in terms of the input random parameters and thewavelength is important for uncertainty quantification methods based oninterpolation in the stochastic space. In particular, the size of thederivativesshould be bounded and independent of the wavelength. In the contributedpapers, we show that the QoIs indeed have this property, despite the highlyoscillatory character of the waves.