论文标题
一项针对汉堡方程式应用的非线性系统的基于伴随的优化的全面研究
A Comprehensive Study of Adjoint-Based Optimization of Non-Linear Systems with Application to Burgers' Equation
论文作者
论文摘要
在基于伴随的优化的背景下，非线性保护定律在直接和伴随解决方案的存在和唯一性以及问题的敏感性分析和基于梯度的优化算法方面构成了重大问题。在本文中，我们将分析伴随方程式的收敛到各种数值方案的Inviscid Burgers方程的已知确切解。将讨论基本近似求解器的非差异性的影响，将讨论离散方案的完整与不完整的分化和及时的不一致性。
In the context of adjoint-based optimization, nonlinear conservation laws pose significant problems regarding the existence and uniqueness of both direct and adjoint solutions, as well as the well-posedness of the problem for sensitivity analysis and gradient-based optimization algorithms. In this paper we will analyze the convergence of the adjoint equations to known exact solutions of the inviscid Burgers' equation for a variety of numerical schemes. The effect of the non-differentiability of the underlying approximate Riemann solver, complete vs. incomplete differentiation of the discrete schemes and inconsistencies in time advancement will be discussed.
