使用伴随方法的逆边界值识别的数学方面与数值计算
Mathematical Aspects and Numerical Computations of an Inverse Boundary Value Identification Using the Adjoint Method
AI总结：
本文研究了伴随方法在柯西问题（逆边界值问题）中的数学性质，通过变分公式和最速下降法最小化目标泛函，并提出了收敛性和最优步长的显式条件，数值实验验证了理论的有效性。
摘要：
本研究的目的是展示伴随方法的一些数学方面，该方法是针对柯西问题（一种逆边界值问题）的数值方法。伴随方法是一种基于变分公式的迭代方法，最速下降法最小化由原始问题导出的目标泛函。传统的伴随方法由于使用Armijo准则数值确定最速下降法的步长，在数值计算中耗时。找到收敛性和最优步长的显式条件很重要。获得了关于数值方法收敛性的一些理论结果。通过数值实验，得出结论我们的理论是有效的。
英文摘要：
The purpose of this study is to show some mathematical aspects of the adjoint method that is a numerical method for the Cauchy problem, an inverse boundary value problem. The adjoint method is an iterative method based on the variational formulation, and the steepest descent method minimizes an objective functional derived from our original problem. The conventional adjoint method is time-consuming in numerical computations because of the Armijo criterion, which is used to numerically determine the step size of the steepest descent method. It is important to find explicit conditions for the convergence and the optimal step size. Some theoretical results about the convergence for the numerical method are obtained. Through numerical experiments, it is concluded that our theories are effective.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
