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We propose a time-domain boundary integral method to model linear wave propagation with refractive, focusing, and Doppler effects arising from medium heterogeneities and moving obstacles. In contrast to existing techniques, our method…

Numerical Analysis · Mathematics 2026-05-13 Raaghav Ramani

Losses associated with nonlinear wave propagation and exhibited by acoustic wave distortion and shock formation compromise the efficiency of contactless acoustic energy transfer systems. As such, predicting the shock formation distance and…

Applied Physics · Physics 2021-02-03 Vamsi C. Meesala , Muhammad R. Hajj , Shima Shahab

The Westervelt equation models the propagation of nonlinear acoustic waves in a regime well-suited for applications such as medical ultrasound imaging. In this work, we prove that the nonlinear parameter, as well as the sound speed, can be…

Analysis of PDEs · Mathematics 2025-10-06 Mike Wendels

Nonlinear ultrasound imaging leverages harmonic wave generation to enhance contrast and spatial resolution beyond the capabilities of conventional linear techniques. This behavior is commonly modeled by the Westervelt equation, which…

Analysis of PDEs · Mathematics 2026-05-25 Benjamin Rainer , Barbara Kaltenbacher

We investigate the propagation of infinitesimal harmonic mechanical waves emitted from a boundary with variable velocity and arriving at a stationary observer. In the classical Doppler effect, $X_\mathrm{s}(t) = vt$ is the location of the…

Analysis of PDEs · Mathematics 2017-07-18 Ivan C. Christov , C. I. Christov

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

Nonlinearity parameter tomography leads to the problem of identifying a coefficient in a nonlinear wave equation (such as the Westervelt equation) modeling ultrasound propagation. In this paper we transfer this into frequency domain, where…

Numerical Analysis · Mathematics 2023-03-31 Barbara Kaltenbacher , William Rundell

We consider an inverse problem governed by the Westervelt equation with linear diffusivity and quadratic-type nonlinearity. The objective of this problem is to recover all the coefficients of this nonlinear partial differential equation. We…

Analysis of PDEs · Mathematics 2025-09-16 Sebastian Acosta , Benjamin Palacios

We theoretically propose a nonlinear spin-wave Doppler effect, in which the time-dependent motion of a magnetic energy boundary acts as an active frequency modulator, directly converting boundary-induced phase dynamics into instantaneous…

Applied Physics · Physics 2026-05-22 Jinchen Hou , Shaojie Hu , Long You

In this paper, we study the nonlinear periodic Westervelt equation with excitations located within a bounded domain in $\mathbb{R}^d$, where $d \in \{2,3\}$, subject to Robin boundary conditions. This problem is of particular interest for…

Analysis of PDEs · Mathematics 2026-01-06 Benjamin Rainer , Barbara Kaltenbacher

We propose a self-adaptive absorbing technique for quasilinear ultrasound waves in two- and three-dimensional computational domains. As a model for the nonlinear ultrasound propagation in thermoviscous fluids, we employ Westervelt's wave…

Numerical Analysis · Mathematics 2019-05-01 Markus Muhr , Vanja Nikolić , Barbara Wohlmuth

We present a numerical approach to efficiently calculate spin-wave dispersions and spatial mode profiles in magnetic waveguides of arbitrarily shaped cross section with any non-collinear equilibrium magnetization which is translationally…

Mesoscale and Nanoscale Physics · Physics 2024-06-12 Lukas Körber , Gwendolyn Quasebarth , Andreas Otto , Attila Kákay

High-frequency wave propagation is often modelled by nonlinear Friedrichs systems where both the differential equation and the initial data contain the inverse of a small parameter $\varepsilon$, which causes oscillations with wavelengths…

Analysis of PDEs · Mathematics 2024-02-21 Julian Baumstark , Tobias Jahnke

Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…

Numerical Analysis · Mathematics 2023-03-22 Cale Harnish , Luke Dalessandro , Karel Matous , Daniel Livescu

In this work, we present a conditionally stable finite-difference scheme that consistently approximates the solution of a general class of (3+1)-dimensional nonlinear equations that generalizes in various ways the quantitative model…

Numerical Analysis · Mathematics 2011-12-26 J. E. Macías-Díaz , A. Puri

We consider an inverse problem for a Westervelt type nonlinear wave equation with fractional damping. This equation arises in nonlinear acoustic imaging, and we show the forward problem is locally well-posed. We prove that the smooth…

Analysis of PDEs · Mathematics 2023-08-01 Li Li , Yang Zhang

A form of the conservation equations for fluid dynamics is presented, deduced using slightly less restrictive hypothesis than those necessary to obtain the Westervelt equation. This formulation accounts for full wave diffraction,…

Fluid Dynamics · Physics 2015-05-26 Roberto Velasco-Segura , Pablo L. Rendón

Diffraction is one of the universal phenomena of physics, and a way to overcome it has always represented a challenge for physicists. In order to control diffraction, the study of structured waves has become decisive. Here, we present a…

Optics · Physics 2013-02-26 Miguel A. Bandres , B. M. Rodríguez-Lara

Nonlinear distortion of infrasonic waves through atmospheres up to thermospheric altitudes govern large-range ground-level observations of explosive noise sources, causing large differences between the near and far field. Propagation…

Fluid Dynamics · Physics 2024-01-29 Liam J. Tope , Jae Wook Kim , Peter Spence

We analyze and develop numerical methods for time-harmonic wave scattering in metallic waveguide structures of infinite extent. We show that radiation boundary conditions formulated via projectors onto outgoing modes determine the…

Numerical Analysis · Mathematics 2025-09-26 Tristan Goodwill , Shidong Jiang , Manas Rachh , Kosuke Sugita
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