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Accurate simulation of nonlinear acoustic waves is essential for the continued development of a wide range of (high-intensity) focused ultrasound applications. This article explores mixed finite element formulations of classical strongly…

Numerical Analysis · Mathematics 2022-09-08 Mostafa Meliani , Vanja Nikolić

Exterior sound field interpolation is a challenging problem that often requires specific array configurations and prior knowledge on the source conditions. We propose an interpolation method based on Gaussian processes using a point source…

Audio and Speech Processing · Electrical Eng. & Systems 2026-02-06 Juliano G. C. Ribeiro , Ryo Matsuda , Jorge Trevino

We study the time-harmonic Maxwell equations on bounded Lipschitz domains with an impedance boundary condition. The impedance coefficient can be matrix valued such that, in particular, a polarization dependent impedance is modeled. We…

Analysis of PDEs · Mathematics 2025-10-17 Ben Schweizer , David Wiedemann

This paper investigates the inverse scattering problem of time-harmonic plane waves incident on a perfectly reflecting random periodic structure. To simulate random perturbations arising from manufacturing defects and surface wear in…

Numerical Analysis · Mathematics 2025-07-29 Zhiqi Sun , Yiwen Lin

We study the Blackstock equation which models the propagation of nonlinear sound waves through dissipative fluids. Global well-posedness of the model with homogeneous Dirichlet boundary conditions is shown for small initial data. To this…

Analysis of PDEs · Mathematics 2018-12-21 Marvin Fritz , Vanja Nikolić , Barbara Wohlmuth

Multichannel frequency estimation with incomplete data and miscellaneous noises arises in array signal processing, modal analysis, wireless communications, and so on. In this paper, we consider maximum-likelihood(-like) optimization methods…

Signal Processing · Electrical Eng. & Systems 2023-07-18 Xunmeng Wu , Zai Yang , Zongben Xu

Based upon elements of the modern Pseudoanalytic Function Theory, we analyse a new method for numerically approaching the solution of the Dirichlet boundary value problem, corresponding to the two-dimensional Electrical Impedance Equation.…

Mathematical Physics · Physics 2012-02-23 M. P. Ramirez T. , C. M. A. Robles G. , R. A. Hernandez-Becerril

Webster's horn equation (1919) offers a one-dimensional approximation for low-frequency sound waves along a rigid tube with a variable cross-sectional area. It can be thought as a wave equation with a source term that takes into account the…

Fluid Dynamics · Physics 2013-11-19 Rogério Jorge

A problem of reconstruction of the topology and the respective edge resistance values of an unknown circular planar passive resistive network using limitedly available resistance distance measurements is considered. We develop a multistage…

Systems and Control · Electrical Eng. & Systems 2026-04-29 Shivanagouda Biradar , Deepak U Patil

Nonlinear hydroelastic waves along a compressed ice sheet lying on top of a two-dimensional fluid of infinite depth are investigated. Based on a Hamiltonian formulation of this problem and by applying techniques from Hamiltonian…

Analysis of PDEs · Mathematics 2025-01-15 Philippe Guyenne , Adilbek Kairzhan , Catherine Sulem

It is often possible to perform reduced order modelling by specifying linear subspace which accurately captures the dynamics of the system. This approach becomes especially appealing when linear subspace explicitly depends on parameters of…

Machine Learning · Computer Science 2026-04-17 Vladimir Fanaskov , Vladislav Trifonov , Alexander Rudikov , Ekaterina Muravleva , Ivan Oseledets

In many applications, knowledge of the sound pressure transfer to the eardrum is important. The transfer is highly influenced by the shape of the ear canal and its acoustic properties, such as the acoustic impedance at the eardrum. Invasive…

Optimization and Control · Mathematics 2023-05-24 Nick Wulbusch , Reinhild Roden , Alexey Chernov , Matthias Blau

An efficient method for solving large nonlinear problems combines Newton solvers and Domain Decomposition Methods (DDM). In the DDM framework, the boundary conditions can be chosen to be primal, dual or mixed. The mixed approach presents…

Numerical Analysis · Mathematics 2018-02-07 Camille Negrello , Pierre Gosselet , Christian Rey

We prove the optimal convergence estimate for first order interpolants used in finite element methods based on three major approaches for generalizing barycentric interpolation functions to convex planar polygonal domains. The Wachspress…

Numerical Analysis · Mathematics 2012-06-19 Andrew Gillette , Alexander Rand , Chandrajit Bajaj

In this contribution we introduce a mixed interpolation-regression operator for functions defined in some domains of the plane. We focus the attention on the ellipse, an annulus and a polygon. An upper bound for such an operator is…

Numerical Analysis · Mathematics 2026-04-28 Ruymán Cruz-Barroso , Lidia Fernández , Francisco Marcellán , Juan Antonio Villegas

We consider an undetermined coefficient inverse problem for a nonlinear partial differential equation describing high intensity ultrasound propagation as widely used in medical imaging and therapy. The usual nonlinear term in the standard…

Numerical Analysis · Mathematics 2022-04-13 Barbara Kaltenbacher , William Rundell

Westervelt's equation is a nonlinear wave equation that is widely used to model the propagation of sound waves in a compressible medium, with one important application being ultra-sound in human tissue. Two fundamental aspects of this…

Mathematical Physics · Physics 2023-06-14 Stephen C. Anco , Almudena P. Marquez , Tamara M. Garrido , Maria L. Gandarias

The tone hole geometry of a clarinet is optimized numerically. The instrument is modeled as a network of one dimensional transmission line elements. For each (non-fork) fingering, we first calculate the resonance frequencies of the input…

We consider the application of the WaveHoltz iteration to time-harmonic elastic wave equations with energy conserving boundary conditions. The original WaveHoltz iteration for acoustic Helmholtz problems is a fixed-point iteration that…

Numerical Analysis · Mathematics 2022-09-28 Daniel Appelö , Fortino Garcia , Allen Alvarez Loya , Olof Runborg

We introduce an interpolation--regression operator for polynomial approximation on the unit sphere $\mathbb{S}^2$ from discrete samples. The approximant is a spherical polynomial of degree $r$ which interpolates the data on a prescribed…

Numerical Analysis · Mathematics 2026-05-14 Francesco Dell'Accio , Federico Nudo , Teresa E. Pérez , Miguel A. Piñar