Sensitivity Theory for General Systems of Nonlinear Equations
Sensitivity Theory for General Systems of Nonlinear Equations
复制标题
一般非线性方程组的灵敏度理论
DOI：
10.13182/nse75-88
复制
发表时间：
1980
影响因子：
1.2
通讯作者：
J. Marable
中科院分区：
文献类型：
--
作者：
D. Cacuci;C. Weber;E. Oblow;J. Marable
本文提出了一般灵敏度理论，用于处理由具有非线性响应的非线性方程组描述的问题。Frechet导数的概念被证明是微分和变分方法的基本概念。这两种方法通过Frechet导数统一起来，形成了灵敏度理论的算子观点，导致了伴随方程和灵敏度函数的相同表达式。还给出了非线性矩阵方程组的另一种灵敏度公式，例如在许多实际问题中应用数值方法所产生的灵敏度公式。这种方法大大扩展了灵敏度理论的范围和通用性，因为它允许直接处理纯粹源于数值方法的参数。为了证明算子和矩阵形式的有效性和实际应用，我们考虑了快堆热工水力学中的一个显著的非线性暂态问题。Fo..。
AbstractGeneral sensitivity theory is presented for treating problems characterized by systems of nonlinear equations with nonlinear responses. The concept of the Frechet derivative is shown to be fundamental to both differential and variational approaches. These two approaches, unified through the Frechet derivative, form an operator viewpoint of sensitivity theory, leading to identical expressions for the adjoint equations and for the sensitivity functions. Also presented is an alternative sensitivity formalism for systems of nonlinear matrix equations, such as those arising from the application of numerical methods to many practical problems. This approach significantly enlarges the scope and versatility of sensitivity theory as it allows direct treatment of parameters that are purely of numerical-methods origin.To demonstrate the usefulness and practical applications of both operator and matrix formalisms, a significantly nonlinear transient problem in fast reactor thermal hydraulics is considered. Fo...