An accelerated alternating iterative algorithm for data completion problems connected with Helmholtz equation

Statistics, Optimization and Information Computing

article

Karzan AhmadBerdawood¹  Abdeljalil Nachaoui¹  Mourad Nachaoui² 

[1] Laboratoire de Mathematiques Jean Leray, Nantes Universite;Faculté de Sciences et Technique, Université Sultan Moulay Slimane

关键词: Inverse Cauchy problem;    Helmholtz equation;    Relaxed iterative method;    Dynamical relaxation;    Numerical simulation.;   

DOI  :  10.19139/soic-2310-5070-1702

来源: Istituto Superiore di Sanita

【 摘 要 】

This paper deals with an inverse problem governed by the Helmholtz equation. It consists in recovering lackingdata on a part of the boundary based on the Cauchy data on the other part. We propose an optimal choice of the relaxationparameter calculated dynamically at each iteration. This choice of relaxation parameter ensures convergence without priordetermination of the interval of the relaxation factor required in our previous work. The numerous numerical example showsthat the number of iterations is drastically reduced and thus, our new relaxed algorithm guarantees the convergence for allwavenumber k and gives an automatic acceleration without any intervention of the user.

【 授权许可】

Unknown