liu.seSök publikationer i DiVA
Ändra sökning
RefereraExporteraLänk till posten
Permanent länk

Direktlänk
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Annat format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annat språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf
Numerical Solution of Cauchy Problems for Elliptic Equations in "Rectangle-like" Geometries
Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Beräkningsvetenskap.
Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Beräkningsvetenskap.ORCID-id: 0000-0003-2281-856X
2005 (Engelska)Ingår i: FEMLAB Conference,2005, Stockholm: Comsol AB , 2005Konferensbidrag, Publicerat paper (Övrigt vetenskapligt)
Abstract [en]

We consider two dimensional inverse steady state heat conduction problems in complex geometries. The coefficients of the elliptic equation are assumed to be non-constant. Cauchy data are given on one part of the boundary and we want to find the solution in the whole domain. The problem is ill--posed in the sense that the solution does not depend continuously on the data. Using an orthogonal coordinate transformation the domain is mapped onto a rectangle. The Cauchy problem can then be solved by replacing one derivative by a bounded approximation. The resulting well--posed problem can then be solved by a method of lines. A bounded approximation of the derivative can be obtained by differentiating a cubic spline, that approximate the function in the least squares sense. This particular approximation of the derivative is computationally efficient and flexible in the sense that its easy to handle different kinds of boundary conditions. This inverse problem arises in iron production, where the walls of a melting furnace are subject to physical and chemical wear. Temperature and heat--flux data are collected by several thermocouples located inside the walls. The shape of the interface between the molten iron and the walls can then be determined by solving an inverse heat conduction problem. In our work we make extensive use of Femlab for creating test problems. By using Femlab we solve relatively complex model problems for the purpose of creating numerical test data used for validating our methods. For the types of problems we are intressted in numerical artefacts appear, near corners in the domain, in the gradients that Femlab calculates. We demonstrate why this happen and also how we deal with the problem.

Ort, förlag, år, upplaga, sidor
Stockholm: Comsol AB , 2005.
Nyckelord [en]
Ill-posed, Cauchy Problem, Elliptic Equation
Nationell ämneskategori
Matematik
Identifikatorer
URN: urn:nbn:se:liu:diva-29471Lokalt ID: 14820OAI: oai:DiVA.org:liu-29471DiVA, id: diva2:250286
Tillgänglig från: 2009-10-09 Skapad: 2009-10-09 Senast uppdaterad: 2013-08-30

Open Access i DiVA

Fulltext saknas i DiVA

Personposter BETA

Berntsson, FredrikElden, Lars

Sök vidare i DiVA

Av författaren/redaktören
Berntsson, FredrikElden, Lars
Av organisationen
Tekniska högskolanBeräkningsvetenskap
Matematik

Sök vidare utanför DiVA

GoogleGoogle Scholar

urn-nbn

Altmetricpoäng

urn-nbn
Totalt: 455 träffar
RefereraExporteraLänk till posten
Permanent länk

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