Dealing with periodic boundary conditions for 1D, 2D and 3D isogeometric finite element method

Marcin Łoś, Maciej Paszyński, Lisandro Dalcin, Victor M. Calo

Research output: Contribution to journalArticlepeer-review


In this paper we analyze the problem of implementing periodic boundary conditions in the isogeometric finite element method (ISO-FEM). The ISO-FEM method uses the B-spline-based basis functions, which facilitates usage of the same basis functions for approximation of the geometry as well as for the numerical solution of the modeled physical phenomena. The usage of the B-spline based basis functions results in C^(p-1) global continuity of the solution. The drawback is a difficulty in implementing the periodic boundary conditions, and special dedicated methods are necessary. In this paper we present two algorithms implementing the periodic boundary conditions. The first one is an iterative algorithm that utilizes widely available block-diagonal LAPACK solver. The second one is a modification of the multi-frontal solver algorithm itself, and it requires a dedicated solver with its source code modified accordingly. The presented methods can be applied in one, two or three-dimensional isogeometric finite element method.
Original languageEnglish (US)
Pages (from-to)213-218
Number of pages6
JournalComputer Methods in Materials Science
Issue number1
StatePublished - Jan 1 2015

Bibliographical note

KAUST Repository Item: Exported on 2020-10-06
Acknowledgements: The work presented in this paper has been supported by the National Science Center, project 2012/07/B/ST6/01229.


  • Direct solvers
  • Finite element method
  • Isogeomtric analysis
  • Periodic boundary conditions

ASJC Scopus subject areas

  • Computer Science Applications
  • General Materials Science


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