TY - JOUR
T1 - Dealing with periodic boundary conditions for 1D, 2D and 3D isogeometric finite element method
AU - Łoś, Marcin
AU - Paszyński, Maciej
AU - Dalcin, Lisandro
AU - Calo, Victor M.
N1 - 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.
PY - 2015/1/1
Y1 - 2015/1/1
N2 - 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.
AB - 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.
KW - Direct solvers
KW - Finite element method
KW - Isogeomtric analysis
KW - Periodic boundary conditions
UR - http://hdl.handle.net/10754/665442
UR - https://www.researchgate.net/profile/Maciej_Paszynski/publication/318949616_Dealing_with_periodic_boundary_conditions_for_1D_2D_and_3D_isogeometric_finite_element_method/links/598e02cea6fdcc10d8ebb974/Dealing-with-periodic-boundary-conditions-for-1D-2D-and-3D-isogeometric-finite-element-method.pdf
UR - http://www.scopus.com/inward/record.url?scp=85026296231&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:85026296231
SN - 1641-8581
VL - 15
SP - 213
EP - 218
JO - Computer Methods in Materials Science
JF - Computer Methods in Materials Science
IS - 1
ER -