非线性Poisson方程在化学、化工及生物等领域有着广泛的应用.本文发展了一种基于格子演化的新算法-格子Poisson方法(LPM),并且给出了Dirichlet边界条件和Neumann边界条件的实现方法.本方法不需要对方程进行线化处理,直接求解非线性方程,适用范围广泛.Dirichlet边界与Neumann边界的数值模拟结果与多重网格法等结果符合很好,验证了该方法在求解非线性Poisson方程的正确性与有效性.本方法非常适合并行计算,并方便扩展到三维情况.
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