Related papers: On parabolic-equation model verification for under…
Acoustic wave propagation in a one-dimensional waveguide connected with Helmholtz resonators is studied numerically. Finite amplitude waves and viscous boundary layers are considered. The model consists of two coupled evolution equations: a…
We prove the convergence of the solutions of the parabolic wave equation to that of the Gaussian white-noise model widely used in the physical literature. The random medium is isotropic and is assumed to have integrable correlation…
Numerical methods are developed to simulate the wave propagation in heterogeneous 2D fluid / poroelastic media. Wave propagation is described by the usual acoustics equations (in the fluid medium) and by the low-frequency Biot's equations…
A mode parabolic equation method for resonantly interacted modes was developed. The flow of acoustic energy is conserved for the derived equations with an accuracy adequate to the used approximation. The testing calculations were done for…
This paper provides a methodology of verified computing for solutions to 1-dimensional advection equations with variable coefficients. The advection equation is typical partial differential equations (PDEs) of hyperbolic type. There are few…
Isogeometric analysis with the boundary element method (IGABEM) has recently gained interest. In this paper, the approximability of IGABEM on 3D acoustic scattering problems will be investigated and a new improved BeTSSi submarine will be…
Acoustic propagation models are widely used in numerous oceanic and other underwater applications. Most conventional models are approximate solutions of the acoustic wave equation, and require accurate environmental knowledge to be…
This work deals with the convergence analysis of parabolic perturbations to quasilinear wave equations on smooth bounded domains. In particular, we consider wave equations with nonlinearities of quadratic type, which cover the two classical…
A recently developed method has been extended to a nonlocal equation arising in steady water wave propagation in two dimensions. We obtain analyic approximation of steady water wave solution in two dimensions with rigorous error bounds for…
Efficient and accurate numerical simulation of 3D acoustic wave propagation in heterogeneous media plays an important role in the success of seismic full waveform inversion (FWI) problem. In this work, we employed the combined scheme and…
A traditional approach to the analysis of mode coupling in a fluctuating underwater waveguide is based on solving the system of coupled equations for the second statistical moments of mode amplitudes derived in the Markov approximation…
The article explores the acoustic equations in inhomogeneous media and the linearized shallow water equations. Two methods for integrating these equations are proposed. The first method is based on the of the Laplace cascade method, while…
We consider a parameter dependent family of damped hyperbolic equations with interesting limit behavior: the system approaches steady states exponentially fast and for parameter to zero the solutions converge to that of a parabolic limit…
To analyze seismic wave propagation in geological structures, it is possible to consider various numerical approaches: the finite difference method, the spectral element method, the boundary element method, the finite element method, the…
We consider the numerical approximation of the mild solution to a semilinear stochastic wave equation driven by additive noise. For the spatial approximation we consider a standard finite element method and for the temporal approximation, a…
We analyze planar electromagnetic waves confined by a slab waveguide formed by two perfect electrical conductors. Remarkably, 2D Maxwell equations describing transverse electromagnetic modes in such waveguides are exactly mapped onto…
Inferring electromagnetic propagation characteristics within the marine atmospheric boundary layer (MABL) from data in real time is crucial for modern maritime navigation and communications. The propagation of electromagnetic waves is well…
First-order systems of hyperbolic partial differential equations (PDEs) occur ubiquitously throughout computational physics, commonly used in simulations of fluid turbulence, shock waves, electromagnetic interactions, and even general…
Parabolic partial differential equations (PDEs) appear in many disciplines to model the evolution of various mathematical objects, such as probability flows, value functions in control theory, and derivative prices in finance. It is often…
We present a simple systematic construction and analysis of solutions of the two-dimensional parabolic wave equation that exhibit far-field localisation near a given algebraic plane curve. Our solutions are complex contour integral…