论文标题
关于非线性系数的同时识别和Westervelt方程中的音速
On the simultanenous identification of the nonlinearity coefficient and the sound speed in the Westervelt equation
论文作者
论文摘要
本文认为Westervelt方程是非线性声学中最广泛使用的模型之一，并试图从时间跟踪边界测量值中恢复两个具有物理重要性的空间依赖性参数。具体来说，这些是声学文学中通常称为$ b/a $的非线性参数$κ（x）$，波速速度$ c_0（x）$。这些数量的空间变化的确定可以用作成像手段。我们考虑从一个或两个边界测量值中的可识别性，在这些应用中相关。要根据平方缓慢的$ \ mathfrak {s} = 1/c_0^2 $和组合系数$η= \ frac {b/a+2} {\ varrho_0 c_0^4} $，我们将其分解了一种newton方法，并证明其convermence。该迭代方案的有效性（和局限性）由数值示例证明。
This paper considers the Westervelt equation, one of the most widely used models in nonlinear acoustics, and seeks to recover two spatially-dependent parameters of physical importance from time-trace boundary measurements. Specifically, these are the nonlinearity parameter $κ(x)$ often referred to as $B/A$ in the acoustics literature and the wave speed $c_0(x)$. The determination of the spatial change in these quantities can be used as a means of imaging. We consider identifiability from one or two boundary measurements as relevant in these applications. For a reformulation of the problem in terms of the squared slowness $\mathfrak{s}=1/c_0^2$ and the combined coefficient $η=\frac{B/A+2}{\varrho_0 c_0^4}$ we devise a frozen Newton method and prove its convergence. The effectiveness (and limitations) of this iterative scheme are demonstrated by numerical examples.
