An Efficient Hybrid Absorbing Edge Reflections for Fractional Laplacian Viscoacoustic Wave Equation

We propose an efficient scheme to absorb the reflections from the model boundaries in numerical solutions of fractional Laplacianviscoacoustic wave equations. The classical CPML obviously increases computational cost and cannot efficiently absorb the waves propagating into the absorbing layer at grazing incidence, and we cannot divide the accurate PML absorbing boundary for some special wave equations, such as the fractional laplacianviscoacoustic wave equations. This scheme divides the compuational domain into boundary, transition, and inner areas. The wavefields within the inner and boundary areas are computed by the wave equation and Liao’s boundary condition, respectively. The wavefields within the transition area are determined by a weighted combination of the wavefields computed by the wave equation and the Liao’s boundary condition to obtain a smooth variation within area to the boundary via the transition zone. The results show our method can greatly improve the computational efficiency of wave equations compared with the traditional CPML and Liu’s ABCs. Numerical experiments demonstrate that use of 5 grid points for absorbing edge reflections attains nearly perfect absorption, even for the complex fractional Laplacianviscoacoustic wave equations with small Q values.