基于模式的伴随方程推导——一种懒人方法
Mode-based derivation of adjoint equations - a lazy man's approach
AI总结：
本文提出一种基于模态表示的伴随方程推导方法，用于求解大规模偏微分方程的伴随解，通过动态Arnoldi方法处理非对称耦合方程，应用于Burgers方程和欧拉方程的优化问题。
摘要：
本文讨论了一种计算大规模偏微分方程伴随解的方法。该方法不同于已知的连续和离散伴随方程，包括自动微分，代表了一种替代的第三种方法。它基于 governing (primal) 系统线性化算子的模态表示。为了近似算子，引入了扩展版的Arnoldi分解，即动态Arnoldi方法（DAM）。DAM允许推导非对称耦合方程的算子近似，这些算子无法通过经典Arnoldi分解获得。该方法应用于Burgers方程和欧拉方程在周期性和非周期性域上的计算。最后，它在优化问题上进行了测试。
英文摘要：
A method to calculate the adjoint solution for a large class of partial differential equations is discussed. It differs from the known continuous and discrete adjoint, including automatic differentiation. Thus, it represents an alternative, third method. It is based on a modal representation of the linearized operator of the governing (primal) system. To approximate the operator an extended version of the Arnoldi factorization, the dynamical Arnoldi method (DAM) is introduced. The DAM allows to derive approximations for operators of non-symmetric coupled equations, which are inaccessible by the classical Arnoldi factorization. The approach is applied to the Burgers equation and to the Euler equations on periodic and non-periodic domains. Finally, it is tested on an optimization problem.
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。
