Modified method of fundamental solutions for the Cauchy problem connected with the Laplace equation
Modified method of fundamental solutions for the Cauchy problem connected with the Laplace equation
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DOI：
10.1080/00207160.2013.868447
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发表时间：
2014-10
影响因子：
1.8
通讯作者：
Yao Sun
中科院分区：
文献类型：
--
作者：
Yao Sun
本文提出了一种基于基本解方法的求解含拉普拉斯方程的柯西问题的数值算法。改进后的MFS的主要优点是保持了问题描述的一个非常基本的自然性质，即在微小坐标变化下的不变性。该方法结合牛顿法和经典的吉洪诺夫正则化来求解一个逆问题。在高噪声条件下，本文还分析了该方法在增加源点数量和减少输入数据中的噪声量方面的数值收敛性、精度和稳定性。
In this paper, a numerical algorithm is proposed based on the method of fundamental solutions (MFS) for the Cauchy problem connected with the Laplace equation in ℝ2. The major advantage of the modified MFS is to keep a very basic natural property, i.e. the invariance under trivial coordinate changes in the problem description. The method combines Newton's method and classic Tikhonov regularization to solve an inverse problem. The numerical convergence, accuracy, and stability of the method with respect to increasing the number of source points, and decreasing the amount of noise added into the input data, respectively, are also analysed with some examples, even for high noise levels.