This study numerically solves inhomogeneous Helmholtz equations modeling acoustic wave propagation in homogeneous and lossless, absorbing and dispersive, and inhomogeneous and nonlinear media. The traditional Born series (TBS) method has been employed to solve such equations. Simulated pressure field patterns for a linear array of acoustic sources (a line source) estimated by the TBS procedure exhibit excellent agreement with that of a standard time domain approach (the k-wave toolbox). For instance, the maximum absolute error of normalized pressure amplitude made by the proposed technique for the homogeneous and lossless medium is ≈2% with respect to the latter method. The TBS scheme, though iterative, is a very fast method. For example, the graphics processing unit (GPU)-enabled cuda c code implementing the TBS procedure for calculating the pressure field for the homogeneous and lossless medium is 102× faster than the k-wave module and also 4× faster than the corresponding central processing unit C code for the computational domain considered in this study (4096×4096). The findings of this study demonstrate the effectiveness of the TBS method for solving inhomogeneous Helmholtz equation, while the GPU-based implementation significantly reduces the computation time. In this work, the capability and performance of the method have been tested in two dimensions only.
Mandal et al. (Sun,) studied this question.