An alternating iterative algorithm for the Cauchy problem associated to the Helmholtz equation

L. Marin; L. Elliott; P.J. Heggs; D.B. Ingham; D. Lesnic; X. Wen

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An alternating iterative algorithm for the Cauchy problem associated to the Helmholtz equation

机译：与Helmholtz方程相关的Cauchy问题的交替迭代算法

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摘要

In this paper, the iterative algorithm proposed by Kozlov et al. [Comput. Maths. Math. Phys. 31 (1991) 45] for obtaining approximate solutions to the ill-posed Cauchy problem for the Helmholtz equation is analysed. The technique is then numerically implemented using the boundary element method (BEM). The numerical results confirm that the iterative BEM produces a convergent and stable numerical solution with respect to increasing the number of boundary elements and decreasing the amount of noise added into the input data. An efficient stopping regularising criterion is also proposed.

机译：本文中，由Kozlov等人提出的迭代算法。 [计算机。数学。数学。物理[31（1991）45]为Helmholtz方程分析了不适定柯西问题的近似解。然后使用边界元素方法（BEM）在数字上实现该技术。数值结果证实，对于增加边界元素的数量和减少添加到输入数据中的噪声量，迭代BEM产生了收敛且稳定的数值解。还提出了一种有效的停车正则化准则。

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来源
《Computer Methods in Applied Mechanics and Engineering》 |2003年第6期|p.709-722|共14页
作者
L. Marin; L. Elliott; P.J. Heggs; D.B. Ingham; D. Lesnic; X. Wen;
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作者单位

School of the Environment, University of Leeds, Leeds LS2 9JT, UK;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类自动化基础理论;工程基础科学;
关键词
iterative BEM; cauchy problem; helmholtz equation; inverse problem;

机译：迭代边界元法;柯西问题;亥姆霍兹方程;反问题;

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机译：与修正的亥姆霍兹方程相关的柯西问题的交替迭代算法的松弛
2. An alternating iterative MFS algorithm for the Cauchy problem for the modified Helmholtz equation [J] . Marin L Computational Mechanics: Solids, Fluids, Fracture Transport Phenomena and Variational Methods . 2010,第6期

机译：修正的Helmholtz方程的Cauchy问题的交替迭代MFS算法
3. An alternating iterative MFS algorithm for the Cauchy problem for the modified Helmholtz equation [J] . Liviu Marin Computational Mechanics . 2010,第6期

机译：修正的Helmholtz方程的Cauchy问题的交替迭代MFS算法
4. Scale Invariant forms of Cauchy, Euler, Navier-Stokes and Modified Equation of Motion and Helmholtz Vorticity Equation [C] . SIAVASH H. SOHRAB Advances in fluid mechanics amp; heat amp; mass transfer . 2012

机译：Cauchy，Euler，Navier-Stokes的尺度不变形式以及运动的修正方程和亥姆霍兹涡度方程
5. Iterative solution of exterior Helmholtz equation with exact non-reflecting boundary conditions on distributed memory systems. [D] . Ianculescu, Cristian Daniel. 2003

机译：具有精确非反射边界条件的外部Helmholtz方程在分布式存储系统上的迭代解。
6. A new Sumudu transform iterative method for time-fractional Cauchy reaction–diffusion equation [O] . Kangle Wang, Sanyang Liu -1

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7. An alternating iterative algorithm for the Cauchy problem associated to the Helmholtz equation [O] . L. Marin A, L. Elliott B, P. J. Heggs C, 2002

机译：与亥姆霍兹方程相关的Cauchy问题的交替迭代算法

An alternating iterative algorithm for the Cauchy problem associated to the Helmholtz equation

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