Efficient solution for the diffraction of elastic SH waves by a wedge: Performance of various exact, asymptotic and simplified solutions

The diffraction of horizontally polarized shear waves by a semi-infinite wedge in frequency and time domains is studied. In particular, this work focus on the performance of different solutions, including the classical contributions from Macdonald, Sommerfeld and Kouyoumjian & Pathak. In addition, two fully analytical, simplified solutions are proposed using arguments from the so-called geometrical theory of diffraction. The main advantage of the two proposed solutions is the fact that the resulting solutions can be scaled to problems with arbitrary and complex geometries. Moreover, it is found that one of the proposed new solutions is highly efficient in terms of accuracy and computational speed as compared to alternative formulations (approximately 1000 times faster than the Macdonald and Kouyoumjian & Pathak solutions), thus, this important characteristic renders this solution ideal for implementation in GPUs (Graphics Processor Units) for multiscale modeling applications. [Display omitted] •The performance of different solutions for diffraction of SH waves in a wedge are studied.•Two simplified full analytics solutions are proposed for diffraction of SH waves in a wedge.•The ideas of Geometrical Theory of Diffraction (GTD) are used.•One of the simplified analytics solutions is an excellent option for representing the diffraction in wedges.