Numerical solution of inverse problem for 2D acoustic system of conservation laws by gradient type method requires storage of $O(N^3)$ elements which is crucial on large grids with $O(N)$ points in single dimension. In this article we present an approach to save twice memory on the stage of adjoint problem and gradient calculation and compare it with usual approach in memory and CPU time cost. Numerical comparison for CPU time and memory of one step of iteration process which consists of direct problem solution, adjoint problem solution and calculation of the gradient are presented.

中文翻译：

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使用基于梯度的方法优化CPU时间和RAM内存以解决动态逆问题

梯度法对二维守恒律声学系统反问题的数值解需要存储 $Ø（{ñ}^3）$ 在大型网格上至关重要的元素 $Ø（ñ）$单一维度中的点。在本文中，我们提出了一种在伴随问题和梯度计算阶段节省两次内存的方法，并将其与常规方法在内存和CPU时间成本方面进行了比较。给出了由直接问题解，伴随问题解和梯度计算组成的迭代过程的第一步的CPU时间和内存的数值比较。