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Relaxation procedures for an iterative algorithm for solving the Cauchy problem for the Laplace equation

机译：求解Laplace方程Cauchy问题的迭代算法的松弛程序

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摘要

In this paper an iterative alternating algorithm for solving the Cauchy problem for the Laplace equation is considered. Three relaxation procedures are developed in order to increase the rate of convergence of the algorithm and selection criteria for the variable relaxation factors are provided. These procedures are analysed and compared both theoretically and numerically. The boundary element method is used in order to implement numerically the iterative algorithm and to show that the ill-posed Cauchy problem is regularized by using an appropriate stopping criterion. The numerical results obtained show that by using the relaxation procedures proposed in this paper, the number of iterations required to achieve convergence may be drastically reduced.
机译：本文考虑了求解Laplace方程Cauchy问题的迭代交替算法。为了提高算法的收敛速度，开发了三种松弛程序，并提供了可变松弛因子的选择标准。这些程序在理论上和数值上都进行了分析和比较。使用边界元方法是为了在数字上实现迭代算法，并表明通过使用适当的停止准则对不适定柯西问题进行了正则化。数值结果表明，通过使用本文提出的松弛程序，可以大大减少实现收敛所需的迭代次数。

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