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Numerical solution of a Cauchy problem for the Laplace equationPrimeFaces.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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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2001 (English)In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 17, no 4, p. 839-853Article in journal (Refereed) Published
##### Abstract [en]

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

2001. Vol. 17, no 4, p. 839-853
##### National Category

Engineering and Technology
##### Identifiers

URN: urn:nbn:se:liu:diva-47296DOI: 10.1088/0266-5611/17/4/316OAI: oai:DiVA.org:liu-47296DiVA, id: diva2:268192
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Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2017-12-13
##### In thesis

We consider a two-dimensional steady state heat conduction problem. The Laplace equation is valid in a domain with a hole. Temperature and heat-flux data are specified on the outer boundary, and we wish to compute the temperature on the inner boundary. This Cauchy problem is ill-posed, i.e. the solution does not depend continuously on the boundary data, and small errors in the data can destroy the numerical solution. We consider two numerical methods for solving this problem. A standard approach is to discretize the differential equation by finite differences, and use Tikhonov regularization on the discrete problem, which leads to a large sparse least squares problem. We propose to use a conformal mapping that maps the region onto an annulus, where the equivalent problem is solved using a technique based on the fast Fourier transform. The ill-posedness is dealt with by filtering away high frequencies in the solution. Numerical results using both methods are given.

1. Numerical methods for inverse heat conduction problems$(function(){PrimeFaces.cw("OverlayPanel","overlay255742",{id:"formSmash:j_idt705:0:j_idt709",widgetVar:"overlay255742",target:"formSmash:j_idt705:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
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