Higher-Order Numerical Schemes and Operator Splitting for Solving 3D Paraxial Wave Equations in Heterogeneous Media
Résumé
We investigate numerical schemes for solving 3D paraxial wave equations that are compatible with the use of splitting methods without losing accuracy. The novelty of these paraxial equations (introduced in \cite{col.jol:2}) compared with classical alternate directions methods is to use more than the two usual cross-line and in-line directions for the splitting. It gives rise to a series of 2D extrapolations in each direction of splitting. Propagation along depth is done with a higher-order method based on a conservative Runge Kutta method. The discretization along the lateral variable is done using higher-order finite difference variational schemes. We present a detailed plane wave analysis in a homogeneous medium that leads to a classification of several particular schemes with respect to the numerical dispersion they generate. The dispersion an= alysis extended to 3D helps chosing the «best» coefficients of the extrapolati= on operators on the dispersion point of view. We conclude with numerical experiments in 2D as well as in 3D homogeneous and heterogeneous media.