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Non-linear inverse geothermal problemsPrimeFaces.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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2017 (English)Licentiate thesis, comprehensive summary (Other academic)
##### Abstract [en]

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

Linköping: Linköping University Electronic Press, 2017. , p. 21
##### Series

Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1791
##### National Category

Computational Mathematics
##### Identifiers

URN: urn:nbn:se:liu:diva-143031DOI: 10.3384/lic.diva-143031ISBN: 9789176854044 (print)OAI: oai:DiVA.org:liu-143031DiVA, id: diva2:1157497
##### Presentation

2017-12-04, Ada Lovelace, B-huset, Campus Valla, Linköping, 13:15 (English)
##### Opponent

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#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt476",{id:"formSmash:j_idt476",widgetVar:"widget_formSmash_j_idt476",multiple:true}); Available from: 2017-11-16 Created: 2017-11-16 Last updated: 2017-11-16Bibliographically approved
##### List of papers

The inverse geothermal problem consist of estimating the temperature distribution below the earth’s surface using temperature and heat-flux measurements on the earth’s surface. The problem is important since temperature governs a variety of the geological processes including formation of magmas, minerals, fosil fuels and also deformation of rocks. Mathematical this problem is formulated as a Cauchy problem for an non-linear elliptic equation and since the thermal properties of the rocks depend strongly on the temperature, the problem is non-linear. This problem is ill-posed in the sense that it does not satisfy atleast one of Hadamard’s definition of well-posedness.

We formulated the problem as an ill-posed non-linear operator equation which is defined in terms of solving a well-posed boundary problem. We demonstrate existence of a unique solution to this well-posed problem and give stability estimates in appropriate function spaces. We show that the operator equation is well-defined in appropriate function spaces.

Since the problem is ill-posed, regularization is needed to stabilize computations. We demostrate that Tikhonov regularization can be implemented efficiently for solving the operator equation. The algorithm is based on having a code for solving a well- posed problem related to the operator equation. In this study we demostrate that the algorithm works efficiently for 2*D *calculations but can also be modified to work for 3D calculations.

1. An efficient regularization method for a large scale ill-posed geothermal problem$(function(){PrimeFaces.cw("OverlayPanel","overlay1117637",{id:"formSmash:j_idt538:0:j_idt542",widgetVar:"overlay1117637",target:"formSmash:j_idt538:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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