A geometrical optics-based numerical method for high frequency electromagnetic fields computations near fold caustics. I
The authors deal with the propagation of a laser wave in a material medium. They present a new method for the direct Eulerian computation of the multivalued solution of the Hamilton-Jacobi equation in the case of a fold caustic. The authors show that the accuracy of the usual method degenerates near the caustic and provide a numerical formula to close the system while maintaining a first-order accuracy. Moreover, they give a systematic initialization procedure of the system when the Cauchy data are only available for the incident wave.
scientific article; zbMATH DE number 1956161
scientific article