流体力学反命题变分有限元非线性规划法

Nonliner Programming Methods of Variational Finite Element for Inverse Problem of Fluid Mechanics

本文在用有限元法求解变域问题时,利用变域变分公式将问题化为求泛函的驻值,但该驻值常常是一个鞍点,因此给计算带来不便,我们在这里利用最小二乘法将求驻值的问题转化为求另一泛函的极值问题,然后采用LMF方法和共轭梯度法求解极值问题。

In this paper, in order to solve the variable domain problem, by using the variable domain variation formula and discrete the variation function by the self-adapting finite element, the extremum problem of algebraic function was introduced. But this extremum may be a saddle point, so that the general methods are inconvenient to solve the extremen. By using the least square method the other extremum problem was presented, then use LMF method and conjugate method to solve this problem.