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在众多的数值计算方法中,有限差分方法大概算是最早提出的方法之一.其简便、灵活、易于实现的特点使该方法在大型科学计算中仍然占有一席之地.完全多重网格方法(FMG方法)能够有效地解决有限差分方法中存在的收敛速度慢的缺陷.本文运用完全多重网格方法结合有限差分法和共形映射法求解Helmholtz波动方程,计算了几个实际电磁问题并取得了良好的结果.具体算例说明这种方法是一种在现代数值计算领域中十分实用、简单、高效的新方法,在现代科技计算领域中有着广泛的应用前景和发展潜力.
Among the many numerical methods, the finite difference method is probably one of the earliest proposed methods, and its simple, flexible and easy-to-implement characteristics make the method still occupy a place in large-scale scientific computing.Fully multi-grid method (FMG method) Which can effectively solve the problem of slow convergence in the finite difference method.In this paper, the Helmholtz wave equation is solved by a fully multigrid method combined with finite difference method and conformal mapping method, and several practical electromagnetic problems are calculated and good results are obtained The concrete example shows that this method is a new method which is very practical, simple and efficient in the field of modern numerical computation. It has a wide range of applications and potentials in the field of modern scientific computing.