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##### By author/editor

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

Computational Methods in Applied Mathematics
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Fluid Mechanics and Acoustics
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Reconstruction of the Radiation Condition and Solution for the Helmholtz Equation in a Semi-infinite Strip from Cauchy Data on an Interior SegmentPrimeFaces.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: Computational Methods in Applied Mathematics, ISSN 1609-4840, E-ISSN 1609-9389Article in journal (Refereed) Epub ahead of print
##### Abstract [en]

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

WALTER DE GRUYTER GMBH , 2023.
##### Keywords [en]

Helmholtz Equation; Inverse Problem; Cauchy Problem; Ill-Posed Problem; Well-Posed Problem; Landweber Method
##### National Category

Fluid Mechanics and Acoustics
##### Identifiers

URN: urn:nbn:se:liu:diva-196637DOI: 10.1515/cmam-2022-0244ISI: 001035412500001OAI: oai:DiVA.org:liu-196637DiVA, id: diva2:1788778
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt565",{id:"formSmash:j_idt565",widgetVar:"widget_formSmash_j_idt565",multiple:true}); Available from: 2023-08-17 Created: 2023-08-17 Last updated: 2023-11-13
##### In thesis

We consider an inverse problem for the Helmholtz equation of reconstructing a solution from measurements taken on a segment inside a semi-infinite strip. Homogeneous Neumann conditions are prescribed on both side boundaries of the strip and an unknown Dirichlet condition on the remaining part of the boundary. Additional complexity is that the radiation condition at infinity is unknown. Our aim is to find the unknown function in the Dirichlet boundary condition and the radiation condition. Such problems appear in acoustics to determine acoustical sources and surface vibrations from acoustic field measurements. The problem is split into two sub-problems, a well-posed and an ill-posed problem. We analyse the theoretical properties of both problems; in particular, we show that the radiation condition is described by a stable non-linear problem. The second problem is ill-posed, and we use the Landweber iteration method together with the discrepancy principle to regularize it. Numerical tests show that the approach works well.

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_idt883:0:j_idt888",widgetVar:"overlay1811372",target:"formSmash:j_idt883:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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