Pseudospectral methods for large-scale bioacoustic models

Large-scale simulations of ultrasonic waves in heterogeneous tissue models are useful in biomedical R&D for imaging and therapeutics. The scale of bioacoustic models is hundreds of wavelengths. Typical 2D wave solvers are not practical at this scale, and 3D is out of the question, because of numerical errors and/or computer limits. To achieve much higher performance we use the periodic pseudospectral (PS) method, where spatial derivatives are calculated from FFTs over Cartesian grids. With a 4th order explicit time integrator, the PS method yields the necessary accuracy and efficiency. However, the domain must be periodic. We show how to circumvent this intrinsic limitation with Berenger's perfectly matched layer (PML) on the boundaries. High accuracy, computational efficiency, and parallelism are demonstrated and a large-scale bioacoustic model is calculated. Generalizations of the method are described, including attenuation and nonlinearity.