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Publications (7 of 7) Show all publications
Sticko, S. & Kreiss, G. (2019). Higher order cut finite elements for the wave equation. Journal of Scientific Computing, 80, 1867-1887
Open this publication in new window or tab >>Higher order cut finite elements for the wave equation
2019 (English)In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 80, p. 1867-1887Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-301820 (URN)10.1007/s10915-019-01004-2 (DOI)
Projects
eSSENCE
Available from: 2019-07-17 Created: 2016-08-25 Last updated: 2019-08-30Bibliographically approved
Schoeder, S., Sticko, S., Kronbichler, M. & Kreiss, G. (2018). High order cut discontinuous Galerkin methods with local time stepping for acoustics.
Open this publication in new window or tab >>High order cut discontinuous Galerkin methods with local time stepping for acoustics
2018 (English)In: Article in journal (Other academic) Submitted
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-347423 (URN)
Projects
eSSENCE
Available from: 2018-04-01 Created: 2018-04-01 Last updated: 2018-04-10Bibliographically approved
Sticko, S., Ludvigsson, G. & Kreiss, G. (2018). High order cut finite elements for the elastic wave equation. Computing Research Repository (1804.00332)
Open this publication in new window or tab >>High order cut finite elements for the elastic wave equation
2018 (English)In: Computing Research Repository, no 1804.00332Article in journal (Other academic) Submitted
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-347421 (URN)
Projects
eSSENCE
Available from: 2018-04-01 Created: 2018-04-01 Last updated: 2018-04-10Bibliographically approved
Ludvigsson, G., Steffen, K. R., Sticko, S., Wang, S., Xia, Q., Epshteyn, Y. & Kreiss, G. (2018). High-order numerical methods for 2D parabolic problems in single and composite domains. Journal of Scientific Computing, 76, 812-847
Open this publication in new window or tab >>High-order numerical methods for 2D parabolic problems in single and composite domains
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2018 (English)In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 76, p. 812-847Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-339130 (URN)10.1007/s10915-017-0637-y (DOI)000436253800006 ()
Available from: 2018-01-10 Created: 2018-01-16 Last updated: 2018-09-09Bibliographically approved
Joffre, T., Isaksson, P., Dumont, P. J. J., Rolland du Roscoat, S., Sticko, S., Orgéas, L. & Gamstedt, E. K. (2016). A method to measure moisture induced swelling properties of a single wood cell. Experimental mechanics, 56, 723-733
Open this publication in new window or tab >>A method to measure moisture induced swelling properties of a single wood cell
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2016 (English)In: Experimental mechanics, ISSN 0014-4851, E-ISSN 1741-2765, Vol. 56, p. 723-733Article in journal (Refereed) Published
National Category
Applied Mechanics Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-229210 (URN)10.1007/s11340-015-0119-9 (DOI)000375727600005 ()
External cooperation:
Projects
eSSENCE
Available from: 2016-01-05 Created: 2014-08-05 Last updated: 2017-12-05Bibliographically approved
Sticko, S. & Kreiss, G. (2016). A stabilized Nitsche cut element method for the wave equation. Computer Methods in Applied Mechanics and Engineering, 309, 364-387
Open this publication in new window or tab >>A stabilized Nitsche cut element method for the wave equation
2016 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 309, p. 364-387Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-298112 (URN)10.1016/j.cma.2016.06.001 (DOI)000383828400015 ()
Projects
eSSENCE
Available from: 2016-06-21 Created: 2016-06-29 Last updated: 2018-04-10Bibliographically approved
Sticko, S. (2016). Towards higher order immersed finite elements for the wave equation. (Licentiate dissertation). Uppsala University
Open this publication in new window or tab >>Towards higher order immersed finite elements for the wave equation
2016 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

We consider solving the scalar wave equation using immersed finite elements. Such a method might be useful, for instance, in scattering problems when the geometry of the domain is not known a priori. For hyperbolic problems, the amount of computational work per dispersion error is generally lower when using higher order methods. This serves as motivation for considering a higher order immersed method.

One problem in immersed methods is how to enforce boundary conditions. In the present work, boundary conditions are enforced weakly using Nitsche's method. This leads to a symmetric weak formulation, which is essential when solving the wave equation. Since the discrete system consists of symmetric matrices, having real eigenvalues, this ensures stability of the semi-discrete problem.

In immersed methods, small intersections between the immersed domain and the elements of the background mesh make the system ill-conditioned. This ill-conditioning becomes increasingly worse when using higher order elements. Here, we consider resolving this issue using additional stabilization terms. These terms consist of jumps in higher order derivatives acting on the internal faces of the elements intersected by the boundary.

Place, publisher, year, edition, pages
Uppsala University, 2016
Series
Information technology licentiate theses: Licentiate theses from the Department of Information Technology, ISSN 1404-5117 ; 2016-008
National Category
Computational Mathematics
Research subject
Scientific Computing with specialization in Numerical Analysis
Identifiers
urn:nbn:se:uu:diva-301937 (URN)
External cooperation:
Supervisors
Projects
eSSENCE
Available from: 2016-08-26 Created: 2016-08-25 Last updated: 2016-08-26Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-4694-4731

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