基于玻璃基质离子扩散方程的数值解研究

The Study on Numerical Calculation of Glasses Ion Diffusion Equation Equation

介绍了玻璃基质离子交换法制备变折射率光学器件中离子扩散方程的有限差分法模型.该方法把连续的扩散方程转化为离散的差分方程,将MATLAB程序中的矩阵运算用于迭代求解过程.通过对正方形边界条件下扩散结果校验表明,该方法可以得到了较为精确的数值解,所有数据计算误差小于0.2%,并且具有操作简单,解的输出形式多样的优点.对于正六边形和沟道边界扩散同样能给出较好的结果.

The Finite Difference Method model is used in the field of glass substrate ion exchange for producing the Gradient refractive index optical devices. The matrix of MATLAB program is used for the iteration process. The square boundary conditions proliferation calibration results show that this method can get a more accurate numerical solution, All data calculation error is less than 0. 2%, and is simple, the output solutions variety of advantages. For hexagonal borders and the proliferation of the same channel can provide better results.