论文标题
伴随状态的方法用于杂交不连续的Galerkin离散化，应用于逆声波问题
Adjoint-state method for Hybridizable Discontinuous Galerkin discretization, application to the inverse acoustic wave problem
论文作者
论文摘要
在本文中，我们使用杂交不连续的Galerkin方法（HDG）进行非线性最小化，以实现向前问题的离散化，并实施伴随状态方法来计算功能衍生物。与连续和不连续的Galerkin离散化相比，HDG通过使用数值痕迹来降低计算成本，从而消除了细胞内部的自由度。对于大规模的时间谐波定量逆问题，它特别有吸引力，这些逆问题使它们依赖于迭代最小化程序，因此可以重复使用正向离散化。 HDG基于两个线性问题的两个级别：一个用于查找数值轨迹的全局系统，其次是局部系统来构建音量解决方案。我们在本文中解决了这种技术性，需要仔细推导伴随状态方法。我们与频域中的声波方程一起使用，并使用局部反射数据进行了三维实验，在此实验中，我们进一步采用了类似DG的方法的特征，以P-适应性有效地处理地形。
In this paper, we perform non-linear minimization using the Hybridizable Discontinuous Galerkin method (HDG) for the discretization of the forward problem, and implement the adjoint-state method for the computation of the functional derivatives. Compared to continuous and discontinuous Galerkin discretizations, HDG reduces the computational cost by working with the numerical traces, hence removing the degrees of freedom that are inside the cells. It is particularly attractive for large-scale time-harmonic quantitative inverse problems which make repeated use of the forward discretization as they rely on an iterative minimization procedure. HDG is based upon two levels of linear problems: a global system to find the numerical traces, followed by local systems to construct the volume solution. This technicality requires a careful derivation of the adjoint-state method, that we address in this paper. We work with the acoustic wave equations in the frequency domain and illustrate with a three-dimensional experiment using partial reflection-data, where we further employ the features of DG-like methods to efficiently handle the topography with p-adaptivity.
