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In this paper, systematic wave-equation finite difference time domain (WE-FDTD) formulations are presented for modeling electromagnetic wave-propagation in linear and nonlinear dispersive materials. In the proposed formulations, the complex conjugate pole residue (CCPR) pairs model is adopted in deriving a unified dispersive WE-FDTD algorithm that allows modeling different dispersive materials, such as Debye, Drude and Lorentz, in the same manner with the minimal additional auxiliary variables. Moreover, the proposed formulations are incorporated with the wave-equation perfectly matched layer (WE-PML) to construct a material independent mesh truncating technique that can be used for modeling general frequency-dependent open region problems. Several numerical examples involving linear and nonlinear dispersive materials are included to show the validity of the proposed formulations.

Backscattered wave acoustic tomography using wideband probing signals makes it possible to obtain three-dimensional (3D) images of scattering inhomogeneities. Signal processing based on the reverse time migration (RTM) method allows one to take into account the influence of background refractive obstacles of the medium to minimize distortions of reconstructed tomographic images. We propose a noniterative method of acoustic tomography in an immersion medium based on RTM approach supplemented with linear signal preprocessing to enhance resolution of reconstructing tomography images. The visualization of scattering objects is based on wave inversion from the measurement area considering the probing wave field specially distorted to perform regularized back convolution. The applicability of the proposed method for visualizing scattering objects in water is shown analytically, numerically and experimentally. The proposed method is resistant to noise according to regularization. The results obtained show the agreement between the numerical and analytical solution. Using the example of sounding with linear frequency modulation signals, it is demonstrated that the proposed method allows increasing the resolution of tomographic images in comparison with conventional RTM. The novelty of the proposed method is the preliminary filtration of the forward propagation wave in the course of solving the inverse problem. This approach improves the resolution of tomographic images and allows considering the influence of obstacles.

The complex nature of the ocean environment requires advanced computational acoustic models to gain insights into the dominating physical factors controlling the underwater sound propagation and scattering in the ocean. In this study, we explore the “ab-initio” approach to solve wave equations with numerical algorithms that can be implemented in distributed memory parallel computers. The goal is to improve the calculation speed so long-range global scale hydroacoustic wave propagation can be studied more efficiently and effectively. Two major algorithms: the finite difference time domain (FDTD) method and the Parabolic Equation (PE) method are investigated. Two PE-based numerical models are considered. One is the Split-Step-Fourier Parabolic Equation (SSFPE) model using split-step Fourier schemes in three-dimensional (3D) environments. The second PE model is a multi-frequency implementation of the Range-dependent Acoustic Model (RAM) that computes two-dimensional (2D) sound pressure fields.

One of the primary challenges in global-scale hydroacoustic propagation modeling with the “ab-initio” approach is the demand for significant computational resources on both memories and computational speeds. To address this, we employed parallel computing techniques using directive-based programming languages, such as OpenACC and XscalableACC, to leverage the power of multiple Graphics Processing Unit (GPU) systems and Central Processing Unit (CPU) cluster computers. Our performance evaluation revealed substantial speedup gains. For the FDTD method, we achieved approximately 3.5-fold and 4-fold speedups with four GPUs and four CPU cluster nodes, respectively. With the 3D SSFPE model, we obtained a speedup of 3.7-fold using four CPU cluster nodes. A significant result was observed with the 2D broadband multi-frequency RAM model, where we achieved a 110-fold speedup compared to one core original implementation.

These results demonstrate the promising potential of massively parallel computers for ocean acoustic propagation modeling and highlight the significant performance benefits of utilizing parallel computing techniques. Our findings emphasize the importance of efficient computational strategies.