Absorbing boundary conditions for difference approximations to the multi-dimensional wave equation
Mathematics of Computation
Fourth order schemes for the heterogeneous acoustics equation
ICOSAHOM '89 Proceedings of the conference on Spectral and high order methods for partial differential equations
A perfectly matched layer for the absorption of electromagnetic waves
Journal of Computational Physics
Complementary boundary operators for wave propagation problems
Journal of Computational Physics
Mathematics and Computers in Simulation
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Acoustic pulse propagation requires the inclusion of attenuation and its causal companion, dispersion when propagation is through a non-ideal fluid medium. For acoustic propagation in a linear medium, Szabo [T.L. Szabo, J. Acoust. Soc. Am., 96 (1994) 491-500] introduced the concept of a convolutional propagation operator that plays the role of a casual propagation factor in the time domain. The resulting modified wave equation is solved via the method of finite differences. One aspect of the acoustic field that is of interest to researchers is the monostatic-backscattered field. This field which by definition is small compared to the forward-propagated field is challenging to isolate. Since the numerical grid is of finite size, the received signal has the possibility of being contaminated with spurious reflections coming from the walls of the computational grid even if absorbing boundary conditions (ABCs) are imposed. Therefore, a robust highly accurate absorbing boundary condition is developed. In addition, the finite difference description of the modified wave equation is developed having fourth-order accuracy in both time and space.