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We consider the ultrasound imaging problem governed by a nonlinear wave equation of Westervelt type with variable wave speed. We show that the coefficient of nonlinearity can be recovered uniquely from knowledge of the Dirichlet-to-Neumann…

Analysis of PDEs · Mathematics 2022-02-04 Sebastian Acosta , Gunther Uhlmann , Jian Zhai

This thesis deals with shape optimization for contact mechanics. More specifically, the linear elasticity model is considered under the small deformations hypothesis, and the elastic body is assumed to be in contact (sliding or with Tresca…

Optimization and Control · Mathematics 2022-08-30 Bastien Chaudet-Dumas

In this study, we investigate the inverse source problem arising in bioluminescence tomography, the objective of which is to reconstruct both the support and the intensity of an internal light source from boundary measurements governed by…

Numerical Analysis · Mathematics 2025-11-25 Qianqian Wu , Rongfang Gong , Wei Gong , Ziyi Zhang , Shengfeng Zhu

We build a new mathematical model of shape optimization for maximizing ionic concentration governed by the multi-physical coupling steady-state Poisson-Nernst-Planck system. Shape sensitivity analysis is performed to obtain the Eulerian…

Optimization and Control · Mathematics 2025-05-13 Jiajie Li , Shenggao Zhou , Shengfeng Zhu

Ultrasound imaging is a widely used, non-invasive diagnostic tool in modern medicine. A crucial assumption is a constant sound speed in the observed medium. For large scale sound speed variations, this assumption leads to blurred and…

Numerical Analysis · Mathematics 2025-10-08 Simon Hackl , Simon Hubmer , Ronny Ramlau

We develop mathematical models for shape design and topology optimization in structural contact problems involving friction between elastic and rigid bodies. The governing mechanical constraint is a nonlinear, non-smooth, and non-convex…

Optimization and Control · Mathematics 2025-12-17 Yixin Tan , Fang Feng , Shengfeng Zhu

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 objective of this study is to address the difficulty of simplifying the geometric model in which a differential problem is formulated, also called defeaturing, while simultaneously ensuring that the accuracy of the solution is…

Numerical Analysis · Mathematics 2023-06-09 Jochen Hinz , Ondine Chanon , Alessandra Arrigoni , Annalisa Buffa

Heating generated by high-intensity focused ultrasound waves is central to many emerging medical applications, including non-invasive cancer therapy and targeted drug delivery. In this study, we aim to gain a fundamental understanding of…

Numerical Analysis · Mathematics 2025-10-03 Julio Careaga , Benjamin Dörich , Vanja Nikolić

Shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations. Here we consider a class of shape optimization problems constrained by nonlocal equations which involve…

Optimization and Control · Mathematics 2022-07-26 Volker Schulz , Matthias Schuster , Christian Vollmann

In this paper, we consider a control/shape optimization problem of a nonlinear acoustics-structure interaction model of PDEs, whereby acoustic wave propagation in a chamber is governed by the Westervelt equation, and the motion of the…

Optimization and Control · Mathematics 2025-08-12 Barbara Kaltenbacher , Amjad Tuffaha

This paper presents an efficient gradient projection-based method for structural topological optimization problems characterized by a nonlinear objective function which is minimized over a feasible region defined by bilateral bounds and a…

Computational Engineering, Finance, and Science · Computer Science 2020-06-16 Zhi Zeng , Fulei Ma

Motivated by simulations of ultrasound-enhanced drug delivery, this work presents the numerical analysis of a mathematical model that captures the influence of ultrasound waves on the diffusivity of the drug. The system under study consists…

Numerical Analysis · Mathematics 2026-03-10 Femke de Wit , Vanja Nikolić

An algorithm is devised for solving minimization problems with equality constraints. The algorithm uses first-order derivatives of both the objective function and the constraints. The step is computed as a sum between a steepest-descent…

Numerical Analysis · Mathematics 2017-11-15 Cristian Barbarosie , Sérgio Lopes , Anca-Maria Toader

In this work, the trailing-edge shape of an airfoil is optimized to reduce the acoustic noise based on large-eddy simulation (LES). It is achieved by the ensemble Kalman method, which can enhance the optimization efficiency by using the…

Fluid Dynamics · Physics 2025-09-18 Qingyong Luo , Xin-Lei Zhang , Guowei He

Topology optimization is a valuable tool in engineering, facilitating the design of optimized structures. However, topological changes often require a remeshing step, which can become challenging. In this work, we propose an isogeometric…

Numerical Analysis · Mathematics 2026-05-01 Guilherme Henrique Teixeira , Nepomuk Krenn , Peter Gangl , Benjamin Marussig

A functional for joint variational object segmentation and shape matching is developed. The formulation is based on optimal transport w.r.t. geometric distance and local feature similarity. Geometric invariance and modelling of…

Computer Vision and Pattern Recognition · Computer Science 2014-12-30 Bernhard Schmitzer , Christoph Schnörr

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

For shape optimization problems, governed by elliptic equations with Dirichlet boundary condition and random coefficients, we utilize a penalization technique to get the approximate problem. We consider that uncertainties exists in the…

Optimization and Control · Mathematics 2025-08-26 Xiaowei Pang

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