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Achieng, PaulineBerntsson, FredrikKozlov, Vladimir
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Achieng, PaulineBerntsson, FredrikKozlov, Vladimir
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Analysis and Mathematics EducationFaculty of Science & EngineeringApplied Mathematics
##### In the same journal

Journal of Inverse and Ill-Posed Problems
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Computational Mathematics
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Robin-Dirichlet alternating iterative procedure for solving the Cauchy problem for Helmholtz equation in an unbounded domainPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2023 (English)In: Journal of Inverse and Ill-Posed Problems, ISSN 0928-0219, E-ISSN 1569-3945, Vol. 31, no 5Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

WALTER DE GRUYTER GMBH , 2023. Vol. 31, no 5
##### Keywords [en]

Helmholtz equation; Cauchy problem; inverse problem ill-posed problem
##### National Category

Computational Mathematics
##### Identifiers

URN: urn:nbn:se:liu:diva-192481DOI: 10.1515/jiip-2020-0133ISI: 000940871600001OAI: oai:DiVA.org:liu-192481DiVA, id: diva2:1744860
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##### In thesis

We consider the Cauchy problem for the Helmholtz equation with a domain in with N cylindrical outlets to infinity with bounded inclusions in . Cauchy data are prescribed on the boundary of the bounded domains and the aim is to find solution on the unbounded part of the boundary. In 1989, Kozlov and Mazya proposed an alternating iterative method for solving Cauchy problems associated with elliptic, selfadjoint and positive-definite operators in bounded domains. Different variants of this method for solving Cauchy problems associated with Helmholtz-type operators exists. We consider the variant proposed by Berntsson, Kozlov, Mpinganzima and Turesson (2018) for bounded domains and derive the necessary conditions for the convergence of the procedure in unbounded domains. For the numerical implementation, a finite difference method is used to solve the problem in a simple rectangular domain in R-2 that represent a truncated infinite strip. The numerical results shows that by appropriate truncation of the domain and with appropriate choice of the Robin parameters mu(0) and mu(1), the Robin-Dirichlet alternating iterative procedure is convergent.

1. Reconstruction of solutions of Cauchy problems for elliptic equations in bounded and unbounded domains using iterative regularization methods$(function(){PrimeFaces.cw("OverlayPanel","overlay1811372",{id:"formSmash:j_idt1521:0:j_idt1525",widgetVar:"overlay1811372",target:"formSmash:j_idt1521:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
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