基于Fortran90的自动微分算法

Automatic Differentiation Fundamental and Program

为了得到高效准确的数值微分运算工具,根据自动微分技术的基本原理,利用Fortran90语言开发了自动微分计算模块MADF(Module of Automatic Differentiation with Function),引入ADF(Automatic Differentiationwith Function)数据类型,按照求导规则对运算符及基本函数进行重载,在计算函数值的同时实现了其导数值的自动计算。利用此方法计算了长柱形天然气储运罐的应力对载荷和材料特性参数的导数,其结果与解析解完全一致。

In order to obtain a high effective calculating tool of numerical differentiation, according to the fundamental of automatic differentiation, an automatic differentiation computing module--MADF （ Module of Automatic Differentiation with Function） is programmed with Fortran90 language in which a new variable type-ADF （Automatic Differentiation with Function） is defined, and the overloading mechanism of operators and functions is provided according to the differentiation rule. With this method, the derivative of long cylindrical high pressure container＇s stress respects to loads and material specific property is calculated, the result is equivalaent to analytic value.