Change search
ReferencesLink to record
Permanent link

Direct link
Numerical Methods for the PDES on Curves and Surfaces
Umeå University, Faculty of Science and Technology, Department of Computing Science.
2013 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

Curves and surfaces are manifolds that can be represented using implicit and parametric methods. With a representation in hand, one can define a partial differential equation on the manifold using differential tangential calculus. The solution of these PDEs is quite interesting because they have many applications in a variety of areas including fluid dynamics, solid mechanics, biology and image processing.In this thesis, we examine two numerical methods for the solution of PDEs on manifolds: a so called cut finite element method and isogeometric analysis. We review the theoretical framework of the two methods and implement them to solve example problems in two and three dimensions: the Laplace-Beltrami problem, the Laplace-Beltrami eigenvalue problem, the biharmonic problem and the time-dependent advection diffusion problem. We compare the methods and we confirm that the numerical results agree with the exact solutions and that they obey the theoretical a priori error estimates.

Place, publisher, year, edition, pages
, UMNAD, 971
National Category
Engineering and Technology
URN: urn:nbn:se:umu:diva-81124OAI: diva2:652933
Educational program
Master's Programme in Computational Science and Engineering
Available from: 2013-10-02 Created: 2013-10-02 Last updated: 2013-10-02Bibliographically approved

Open Access in DiVA

fulltext(8144 kB)558 downloads
File information
File name FULLTEXT01.pdfFile size 8144 kBChecksum SHA-512
Type fulltextMimetype application/pdf

By organisation
Department of Computing Science
Engineering and Technology

Search outside of DiVA

GoogleGoogle Scholar
Total: 558 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 521 hits
ReferencesLink to record
Permanent link

Direct link