ALE有限元方法中的网格运动算法

基于新的网格单元畸变度量体系，设计了一种新的网格运动算法。该算法将求解节点位移（速度）的问题转化成求解无约束最优化问题。通过偏导数等于零，得到求解位移向量的显式表达式，算法具有设计合理、实现简便、计算量小等特点。该算法可由二维情形推广到三维的情形。二维和三维算例验证了算法的有效性。

Algorithm of Mesh-Moving in ALE Finite Element Method

Mesh-moving is one of the most important characters of the ALE finite element method. This paper proposed a new algorithm of mesh-moving on the ground of a new framework to measure the distortion of meshes. It converts computing the displacement or velocity of grid to solving an optimal problem without constraints. One can obtain the explicit formulation to calculate the displacement through setting the partial derivative of object function to zero. So it greatly facilitates the computation of mesh-moving when implementing the ALE finite element. Moreover, the new algorithm can be easily extended to the three dimensional case. Finally, the examples show its effectiveness.