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This study develops a theoretical framework for modeling acoustic pulse propagation in a non-ideal shallow-water waveguide. We derive an {\epsilon}-pseudodifferential operator ({\epsilon}-PDO) formulation from the general three-dimensional…

Mathematical Physics · Physics 2025-12-16 Aleksandr Kaplun , Boris Katsnelson

Seismic tomography has long been an effective tool for constructing reliable subsurface structures. However, simultaneous inversion of P- and S-wave velocities presents a significant challenge for conventional seismic tomography methods,…

Geophysics · Physics 2024-07-24 Chao Song , Hang Geng , Umair bin Waheed , Cai Liu

We describe and evaluate a numerical solution strategy for simulating surface acoustic waves through semiconductor devices with complex geometries. This multi-physics problem is of particular relevance to the design of quantum electronic…

Computational Physics · Physics 2007-05-23 S. Rahman , H. P. Langtangen , C. H. W. Barnes

Eikonal tomography has become a popular methodology for deriving phase velocity maps from surface wave phase delay measurements. Its high efficiency makes it popular for handling datasets deriving from large-N arrays, in particular in the…

Geophysics · Physics 2023-02-21 Jack B. Muir

Estimating the travel time of ultrasound in an inhomogeneous medium is crucial for high-quality imaging, as with an accurate estimate of the distribution of speed of sound, phase aberration, which is normally viewed as one of the reasons…

Medical Physics · Physics 2023-12-12 Feixiao Long , Weiguang Zhang

The eikonal equation has become an indispensable tool for modeling cardiac electrical activation accurately and efficiently. In principle, by matching clinically recorded and eikonal-based electrocardiograms (ECGs), it is possible to build…

Optimization and Control · Mathematics 2023-12-06 Thomas Grandits , Jan Verhülsdonk , Gundolf Haase , Alexander Effland , Simone Pezzuto

This article proposes a novel approach for determining exact solutions to nonlinear ordinary differential equations. The recommended iterative method provides the solution via a rapidly converging series that readily approaches a closed…

Analysis of PDEs · Mathematics 2025-07-15 Prakash Kumar Das

We propose a computationally efficient technique for extrapolating seismic waves in an arbitrary isotropic elastic medium. The method is based on factorizing the full elastic wave equation into a product of pseudo-differential operators.…

Geophysics · Physics 2012-06-05 Musa Maharramov

This paper presents a novel method for evaluating second-order consistent hydrodynamic loads, which employs nonlinear wave and body kinematics. The pseudo-spectral formulation of nonlinear potential flow wave solvers is exploited,…

The Physics-Informed Neural Network (PINN) framework introduced recently incorporates physics into deep learning, and offers a promising avenue for the solution of partial differential equations (PDEs) as well as identification of the…

Machine Learning · Computer Science 2021-08-04 Ehsan Haghighat , Ali Can Bekar , Erdogan Madenci , Ruben Juanes

We develop a numerical hydrodynamics code using a pseudo-Newtonian formulation that uses the weak field approximation for the geometry, and a generalized source term for the Poisson equation that takes into account relativistic effects. The…

High Energy Astrophysical Phenomena · Physics 2015-06-04 Jinho Kim , Hee Il Kim , Matthew William Choptuik , Hyung Mok Lee

The aim of this paper is to give an account of some applications of pseudodifferential calculus for solving linear wave equations in the limit of high frequency/short wavelength waves. More specifically, on using as a benchmark the case of…

Mathematical Physics · Physics 2007-05-23 Omar Maj

A deep learning approach to numerically approximate the solution to the Eikonal equation is introduced. The proposed method is built on the fast marching scheme which comprises of two components: a local numerical solver and an update…

Computer Vision and Pattern Recognition · Computer Science 2019-03-20 Moshe Lichtenstein , Gautam Pai , Ron Kimmel

We present algorithms for solving high-frequency acoustic scattering problems in complex domains. The eikonal and transport partial differential equations from the WKB/geometric optic approximation of the Helmholtz equation are solved…

Numerical Analysis · Mathematics 2023-05-03 Samuel F. Potter , Maria K. Cameron , Ramani Duraiswami

In this contribution, we generalize the concept of \textit{optimally accurate operators} proposed and used in a series of studies on the simulation of seismic wave propagation, particularly based on Geller \& Takeuchi (1995). Although these…

Geophysics · Physics 2025-05-06 Nobuaki Fuji , Thibault Duretz

In this paper we establish the orbital stability of periodic traveling waves for a general class of dispersive equations. We use the Implicit Function Theorem to guarantee the existence of smooth solutions depending of the corresponding…

Analysis of PDEs · Mathematics 2019-09-17 Fábio Natali

Correct prediction of particle transport by surface waves is crucial in many practical applications such as search and rescue or salvage operations and pollution tracking and clean-up efforts. Recent results have indicated transport by…

Fluid Dynamics · Physics 2023-01-26 D. Eeltink , R. Calvert , J. E. Swagemakers , Qian Xiao , T. S. van den Bremer

The fast marching algorithm, and its variants, solves numerically the generalized eikonal equation associated to an underlying riemannian metric. A major challenge for these algorithms is the non-isotropy of the riemannian metric.…

Numerical Analysis · Mathematics 2012-05-25 J. -M. Mirebeau

The paper is concerned with modeling and simulating approaches of wall distance functions based on Partial Differential Equations (PDE). The distance to the nearest wall is required for many industrial problems in Computational Fluid…

Fluid Dynamics · Physics 2025-04-11 Niklas Kühl

We propose a time-adaptive predictor/multi-corrector method to solve hyperbolic partial differential equations, based on the generalized-$\alpha$ scheme that provides user-control on the numerical dissipation and second-order accuracy in…

Numerical Analysis · Mathematics 2022-10-11 Nicolas A. Labanda , Pouria Behnoudfar , Victor M. Calo