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The numerical simulation of wave propagation in semiclassical(high-frequency) problems is well known to pose a formidable challenge. In thiswork, a new phase-space approach for the numerical simulation of semiclassicalwave propagation, making use of the smoothed Wigner Transform (SWT), isproposed. There are numerous works which use the Wigner Transform (WT) in thestudy of a variety of wave propagation problems including high-frequency limitsfor linear, nonlinear and/or random waves. The WT however is well known topresent significant difficulties in the formulation of numerical schemes.Working with concrete examples for the semiclassical linear Schrodingerequation it is seen that the SWT approach is indeed significantly faster (in awell-defined sense) to work with than the WT and than full numerical solutionsof the original equation in the semiclassical regime. Comparisons with exactand numerical solutions are used to keep track of numerical errors.

Smoothed Wigner transforms in the numerical simulation of semiclassical (high-frequency) wave propagation