论文标题
通过伴随方法从浅水方程从浅水方程恢复时间依赖的底部形象函数
Recovery of a Time-Dependent Bottom Topography Function from the Shallow Water Equations via an Adjoint Approach
论文作者
论文摘要
我们开发了一种伴随方法，用于恢复一维双曲平衡法的源项中包含的地形函数。我们专注于特定的系统，即浅水方程，以恢复河床的地形。这项工作的新颖性在于能够使用一个测量事件中的嘈杂边界数据来稳健地恢复底层，并在迭代更新方案中包含两个正则化项。伴随方案是根据向前系统的线性化确定的，用于计算成本函数的梯度。底部的地形函数是通过通过三操作员分裂方法给出的迭代过程恢复的，该方法允许可行性包括两个正则化项。许多数值测试都证明了该方法的鲁棒性，而不管最初的猜测选择如何，并且在向前问题的解决方案中存在不连续性。
We develop an adjoint approach for recovering the topographical function included in the source term of one-dimensional hyperbolic balance laws. We focus on a specific system, namely the shallow water equations, in an effort to recover the riverbed topography. The novelty of this work is the ability to robustly recover the bottom topography using only noisy boundary data from one measurement event and the inclusion of two regularization terms in the iterative update scheme. The adjoint scheme is determined from a linearization of the forward system and is used to compute the gradient of a cost function. The bottom topography function is recovered through an iterative process given by a three-operator splitting method which allows the feasibility to include two regularization terms. Numerous numerical tests demonstrate the robustness of the method regardless of the choice of initial guess and in the presence of discontinuities in the solution of the forward problem.
