![]() ![]() ![]() Mathematical Models and Methods in Applied Sciences 28 (13), 2018, 2557-2597 more… Fritz, Marvin Nikolić, Vanja Wohlmuth, Barbara: Well-posedness and numerical treatment of the Blackstock equation in nonlinear acoustics.Kaltenbacher, Barbara Nikolić, Vanja: Vanishing relaxation time limit of the Jordan-Moore-Gibson-Thompson wave equation with Neumann and absorbing boundary conditions.Mathematical Models and Methods in Applied Sciences 0 (ja), 2019, null more… Kaltenbacher, Barbara Nikolić, Vanja: On the Jordan-Moore-Gibson-Thompson Equation: Well-Posedness with Quadratic Gradient Nonlinearity and Singular Limit for Vanishing Relaxation Time.Wohlmuth, B.: A Priori Error Estimates for the Finite Element Approximation of Westervelt's Quasi-linear Acoustic Wave Equation. Journal of Computational Physics 388, 2019, 279-299 more… Muhr, Markus Nikolić, Vanja Wohlmuth, Barbara: Self-adaptive absorbing boundary conditions for quasilinear acoustic wave propagation.Evolution Equations & Control Theory 8 (1), 2019, 163-202 more… Muhr, Markus Nikolić, Vanja Wohlmuth, Barbara Wunderlich, Linus: Isogeometric shape optimization for nonlinear ultrasound focusing.Our self-adaptive method locally computes the incidence angle and updates the absorbing conditions on the fly, basing the local angle computation on the gradient of the wave field. Absorbing boundary conditions provide a simple, yet effective way of dealing with unwanted reflections. To accurately simulate ultrasound, we have to avoid spurious reflections of the wave at the boundary of the truncated domain. In numerical simulations of ultraounds, the large physical space often has to be truncated. ![]() Self-adaptive absorbing boundary conditions Westervelt's equation is a strongly damped quasilinear wave equation that provides challenges both in analysis and simulation. Propagation of high-intensity ultrasound through thermoviscous fluids can be modeled by Westervelt's equation $$\Large \psi_.$$ The goal of our work is to mathematically analyze, efficiently simulate, and in the end optimize sound waves. Accurate simulation of ultrasound offers a path to a better quality of numerous procedures in industry and medicine, from non-destructive detection of material damages to ultrasound imaging and non-invasive treatments of medical disorders. ![]()
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