三维双调和方程的高阶紧致差分格式及其多重网格方法

High-order compact difference format of three-dimensional double-harmonic equation and its solution with multi-grid approach

提出一类求解三维双调和方程的高精度紧致差分格式.该类格式是以泊松方程的高精度格式为基础的四阶精度19点紧致差分格式和六阶精度27点紧致差分格式.采用多重网格方法求解由高精度紧致差分格式所形成的代数方程组,并与低精度方法进行比较.讨论多重网格方法中不同松驰算子的迭代收敛效果.数值实验结果验证四阶紧致差分格式和六阶紧致差分格式的精度以及多重网格方法的可靠性和高效性.

Based on high-accuracy compact difference format,the solution of three-dimensional double-harmonic equation with a class of high-order compact difference formats was proposed.Two kinds of formats were those with fourth-order difference approximation on 19 points and sixth-order difference approximation on 27 points,which were based on the high-accuracy format of the Poisson equation.The multigrid method was used to solve a set of algebraic equations formed with the high-accuracy compact difference format and the computing result was compared with that computed with low-accuracy method.The iterative convergence effect of different relaxation operators in the multigrid method was aslo discussed.Numerical simulation was carried out to verify the accuracy of the fourth-order and sixth-order compact formats as well as the stability and efficiency of the multigrid method.