Approximate Solutions Of Wave Equation Research Articles

Spatial domain decomposition-based physics-informed neural networks for practical acoustic propagation estimation under ocean dynamics.

Practical acoustic propagation modeling is significantly affected by ocean dynamics, and then can be exploited in numerous oceanic applications, where "practical" refers to modeling acoustic propagation in simulations that mimic real-world ocean environments. Physics-based numerical models provide approximate solutions of wave equation and rely on accurate prior environmental knowledge while the environment of practical scenarios is largely unknown. In contrast, data-driven machine learning offers a promising avenue to estimate practical acoustic propagation by learning from dataset. However, collecting such a high-quality, noise-free, and dense dataset remains challenging. Under the practical hurdle posed by the above approaches, the emergence of physics-informed neural network (PINN) presents an alternative to integrate physics and data but with limited representation capacity. In this work, a framework, termed spatial domain decomposition-based physics-informed neural networks (SPINNs), is proposed to enhance the representation capacity in spatially dependent oceanic scenarios and effectively learn from incomplete and biased prior physics and noisy dataset. Experiments demonstrate SPINNs' advantages over PINN in practical acoustic propagation estimation. The learning capacity of SPINNs toward physics and dataset during training is further analyzed. This work holds promise for practical applications and future expansion.

Approximate Solution of Wave Equation using Fuzzy Number

In this paper, the fuzzy solution of the initial boundary value problem of hyperbolic one-dimensional wave equation is considered. The solution by finite difference method is observed by using fuzzy intervals.

On approximate symmetry and approximate solutions of the nonlinear wave equation with a small parameter

The concept of approximate symmetry is introduced. The authors describe all nonlinearities F(u) with which the nonlinear wave equation Square Operator u+ lambda u3+ epsilon F(u)=0 with a small parameter epsilon is approximately scale and conformally invariant. Some approximate solutions of wave equations in question are obtained using the approximate symmetry.

Use Of Gaussian Beams To Study The Effects Of Interface Irregularities On Love Waves

Gaussian beam summation is applied to study the effects of dipping and irregular interfaces on Love waves. Gaussian beams are approximate solutions of wave equation under the parabolic approximation. Closely related to ray theory, this approach is free of some limitations of ray solutions. For instance, it is possible to compute the wave field near to caustics because of the intrinsic smoothing effects of Gaussian beams. Given a source expansion in terms of beams and a simple ray tracing scheme that considers appropriate reflexion coefficients, the solution is computed in the frequency domain for a series of receivers along the surface of a simple layered structure. A frequency-wavenumber analysis allows to identify dispersion curves of Love waves. The procedure is tested for a flat layer case and excellent agreement with exact solution is found. The effects of upand down-dip propagation on dispersion characteristics of Love waves are presented. Some cases of smooth and sharp transitions between different structures are also described. INTRODUCTION Locally generated surface waves play a significant role in the local site response of sediment filled geological structures during earthquakes. Several approaches that explicitly take this fact into account have been recently proposed (see e g Calderon et al [1], Hisada et al. [2], Fujiwara and Takenaka [3] and Sanchez-Sesma et al. [4]). In these studies, however, one basic assumption is that the layered structure of the sediment is flat. Earlier studies of lateral effects on the propagation of surface waves include the work of Boore [5] Transactions on the Built Environment vol 3, © 1993 WIT Press, www.witpress.com, ISSN 1743-3509