Endre søk
RefereraExporteraLink to record
Permanent link

Direct link
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Annet format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annet språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf
Numerical Solution of a Nonlinear Inverse Heat Conduction Problem
Linköpings universitet, Matematiska institutionen. Linköpings universitet. (Scientific Computing)
2010 (engelsk)Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
Abstract [en]

 The inverse heat conduction problem also frequently referred as the sideways heat equation, in short SHE, is considered as a mathematical model for a real application, where it is desirable for someone to determine the temperature on the surface of a body. Since the surface itself is inaccessible for measurements, one is restricted to use temperature data from the interior measurements. From a  mathematical point of view, the entire situation leads to a non-characteristic Cauchy problem, where by using recorded temperature one can solve a well-posed nonlinear problem in the finite region for computing heat flux, and consequently obtain the Cauchy data [u, ux]. Further by using these data and by performing an appropriate method, e.g. a space marching method, one can eventually achieve the desired temperature at x = 0.

The problem is severely ill-posed in the sense that the solution does not depend continuously on the data. The problem solved by two different methods, and for both cases we stabilize the computations by replacing the time derivative in the heat equation by a bounded operator. The first one, a spectral method based on finite Fourier space is illustrated to supply an analytical approach for approximating the time derivative. In order to get a better accuracy in the numerical computation, we use cubic spline function for approximating the time derivative in the least squares sense.

The inverse problem we want to solve, by using Cauchy data, is a nonlinear heat conduction problem in one space dimension. Since the temperature data u = g(t) is recorded, e.g. by a thermocouple, it usually contains some perturbation in the data. Thus the solution can be severely ill-posed if the Cauchy data become very noisy. Two experiments are presented to test the proposed approach.

sted, utgiver, år, opplag, sider
2010. , s. 71
Emneord [en]
inverse problem, ill-posed, Cauchy problem, heat conduction, well-posed, nonlinear problem, spline derivative, spectral method.
HSV kategori
Identifikatorer
URN: urn:nbn:se:liu:diva-57486ISRN: LiTH - MAT - EX - 2010 / 10 - SEOAI: oai:DiVA.org:liu-57486DiVA, id: diva2:325988
Presentation
2010-06-10, Kompakta rummet, MAI, 13:15 (engelsk)
Uppsök
Physics, Chemistry, Mathematics
Veileder
Examiner
Tilgjengelig fra: 2010-06-22 Laget: 2010-06-21 Sist oppdatert: 2010-06-22bibliografisk kontrollert

Open Access i DiVA

fulltekst(1126 kB)2481 nedlastinger
Filinformasjon
Fil FULLTEXT01.pdfFilstørrelse 1126 kBChecksum SHA-512
54dbac5b9167bae9d9bf9a02b35ce6d034d25bfe8e3176b65dfaeeef32581749b1819e2a6a03fd2ce3678db05def8d688c8cfd15f5b32c02d99ce72f3392ffbf
Type fulltextMimetype application/pdf

Søk i DiVA

Av forfatter/redaktør
Hussain, Muhammad Anwar
Av organisasjonen

Søk utenfor DiVA

GoogleGoogle Scholar
Totalt: 2487 nedlastinger
Antall nedlastinger er summen av alle nedlastinger av alle fulltekster. Det kan for eksempel være tidligere versjoner som er ikke lenger tilgjengelige

urn-nbn

Altmetric

urn-nbn
Totalt: 380 treff
RefereraExporteraLink to record
Permanent link

Direct link
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Annet format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annet språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf