一维非线性弦平衡方程的有限元两重网格算法

针对一维非线性弦的平衡方程,构造了有限元两重网格算法,该算法只需要在粗网格上进行非线性迭代,而在所需要求解的细网格上进行一次线性运算即可。与非线性迭代直接求解结果进行对比可知,有限元两重网格算法在保持了计算精度的前提下,所用的时间更短,从而证明了该算法是一种求解非线性问题的高效方法。

Finite-Element Two-Grid Algorithm of 1D Nonlinear Chord Balance Equation

For one dimensional nonlinear chord balance equation,a two-grid method of finite-element algorithm is constructed.This algorithm needs only to have the nonlinear iteration executed on the coarse grid,while only one linear operation should be carried out on the fine-grid solution required.It can be known from the contrast with the results obtained from the non-linear direct iterative solution that in the prerequisite of maintaining calculation accuracy,the finite-element two-grid algorithm can use the shorter time,whereby proving that this algorithm is a kind of high-efficient method for obtaining the nonlinear solution to the problems.