弹性波场数值模拟的隐式差分多重网格算法

MULTI-GRID ALGORITHM FOR NUMERICAL MODELING OF ELASTIC WAVE FIELD USING FINITE-DIFFERENCE METHOD

为了得到稳定的弹性波数值模拟 ,而不得不选择隐式差分方程 ;为了提高解的精度 ,又不得不增加节点数目 ,但同时也降低了隐式迭代求解的收敛速度 .为此 ,本文使用隐式差分的多重网格算法进行弹性波数值模拟 ,多重网格算法通过粗网格收敛较快的迭代过程求出近似解 ,以近似解为初值使用细网格进行精确的迭代求解 ,从而加速了隐式迭代求解的过程 ,能够以较高计算速度、精度。

Improving the efficiency, precision and stability of calculation is the key to numerical modeling of elastic wave propagation. For stabilizing the results of wavefield simulation by the finite difference method, the implicit algorithm has to be used ; On the other hand, for improving precision of the results, the number of nodes must be increased, and thus the efficiency of iterative calculation is decrease. This paper introduces multi grid algorithm into the calculation . The approximat result can be obtained in coarse grids by the iterative method,and then these result is used as the initial values of iterative calculation in fine grids,and the calculated result for fine grids is more accurate than that from coarse grids, thus the efficiency is improved.