论文标题
在有限域中双曲线逆边界值问题的数值解上
On the numerical solution of a hyperbolic inverse boundary value problem in bounded domains
论文作者
论文摘要
我们考虑重建嵌入在有限域中的腔的边界曲线的反问题。该问题是在波方程的两个维度中提出的。我们将Laguerre转换与积分方程方法结合在一起，并将反问题减少到边界积分方程系统。我们提出了一种迭代方案，该方案使用正向操作员的Fréchet导数线性化方程。特殊正交规则的应用导致我们使用Tikhonov正则化解决的条件不良的线性系统。数值结果表明，所提出的方法会产生准确稳定的重建。
We consider the inverse problem of reconstructing the boundary curve of a cavity embedded in a bounded domain. The problem is formulated in two dimensions for the wave equation. We combine the Laguerre transform with the integral equation method and we reduce the inverse problem to a system of boundary integral equations. We propose an iterative scheme that linearizes the equation using the Fréchet derivative of the forward operator. The application of special quadrature rules results to an ill-conditioned linear system which we solve using Tikhonov regularization. The numerical results show that the proposed method produces accurate and stable reconstructions.
