Inspired by medical applications of high-intensity ultrasound, we study a coupled elasto-acoustic problem with general acoustic nonlinearities of quadratic type as they arise, for example, in the Westervelt and Kuznetsov equations of nonlinear acoustics. We derive convergence rates in the energy norm of a finite element approximation to the coupled problem in a setting that involves different acoustic materials and hence jumps within material parameters. A subdomain-based discontinuous Galerkin approach realizes the acoustic-acoustic coupling of different materials. At the same time, elasto-acoustic interface conditions are used for a mutual exchange of forces between the different models. Numerical simulations back up the theoretical findings in a three-dimensional setting with academic test cases as well as in an application-oriented simulation, where the modeling of human tissue as an elastic versus an acoustic medium is compared.

翻译：在高强度超声波医学应用的启发下,我们研究一种伴生声学问题,随着诸如Westervelt和Kuznetsov等非线性声学等方程式的出现,它们与一般的声学非线性二次类型非线性声学问题同时出现。我们从一个包含不同声学材料并因此在物质参数范围内跳跃的环境下,定点元素近似于并存问题的能量标准中得出趋同率。一种亚面不连续的Galerkin方法认识到不同材料的声学-声学组合。同时,在不同的模型之间相互交换力量时,也使用电磁共声界面条件。数字模拟在三维环境中以学术测试案例和以应用为导向的模拟中支持理论结论,在模拟中将人体组织建模作为弹性与声学媒介进行比较。