用直接方法和希耳伯变换计算二维瞬态势及其梯度(英文)

CALCULATIONS OF TWO-DIMENSIONAL TRANSIENT POTENTIAL AND ITS GRADIENT BY COMBINING DIRECT METHOD AND HILBERT TRANSFORM

本文用直接方法和希耳伯变换给出了计算二维瞬态势及其梯度的新方法 .这种方法可以计算复杂度从传统的 O(N2t)降低到 O(Nt) .在计算势及其梯度时 ,该方法的直接计算中所用的权重因子不随时间变化 ,因此它们只需在第一个时间步长时计算一次 .所以 ,当用于二维瞬态散射的时间推进算法中时 ,该方法可节省大量的 CPU时间 .数值结果表明该方法的精度非常高 .

This paper presents a new method to calculate the two dimensional transient potential and its gradient by combining the direct method and Hilbert transform.This method can reduce the computational complexity to O(N t) from conventional O(N 2 t) The weight factors used in the direct computations are not functions of time for both the potential and its gradient,so they need to be calculated only once at the first time step.Therefore,this method can save a lot of CPU time when it is applied in the march on in time based algorithm for the two dimensional transient scattering.Numerical results show that this method can provide very high accuracies.