Geodesic
On validity of Gaussian beams summation method in problems with corner points on boundaries
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 13, Tome 128 (1983), pp. 65-71 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is shown the GBS method is available for the problems with corner points on boundaries. It is found that the largest errors about $5\%$ arise in a vicinity of shadow-light boundaries only. 
@article{ZNSL_1983_128_a6,
     author = {A. P. Katchalov and M. M. Popov and I. Pshenchik},
     title = {On validity of {Gaussian} beams summation method in problems with corner points on boundaries},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {65--71},
     year = {1983},
     volume = {128},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1983_128_a6/}
}
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A. P. Katchalov; M. M. Popov; I. Pshenchik. On validity of Gaussian beams summation method in problems with corner points on boundaries. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 13, Tome 128 (1983), pp. 65-71. http://geodesic.mathdoc.fr/item/ZNSL_1983_128_a6/