We introduce and study a BDDC (Balancing Domain Decomposition by Constraints) method for the Naghdi shell problem discretized with MITC (Mixed Interpolation of Tensorial Components) elements. Compared with the Kirchhoff model, the Naghdi model uses both displacement and rotation as variables, and therefore is more accurate but also more complicated at the numerical level. The severe difficulties of finite element shell analysis are also reflected in the condition number of the problem, which quickly diverges as the thickness of the shell and/or the finite element mesh size tend to zero. The proposed BDDC preconditioner is based on a proper selection of primal continuity constraints, the implicit elimination of the interior degrees of freedom in each subdomain, and the iterative solution of the resulting shell Schur complement by a preconditioned conjugate gradient method. The preconditioner is built from the solutions of local shell problems on each subdomain with clamping conditions at the primal degrees of freedom and on the solution of a coarse shell problem for the primal degrees of freedom. Three choices of primal constraints, hence coarse spaces, are considered, yielding three BDDC preconditioner of increasing strength and cost. Several numerical tests are performed for cylindrical, hyperbolic and elliptic shells. The results show that the proposed BDDC preconditioners are scalable in the number of subdomains, quasi-optimal in the ratio subdomain/element sizes, robust with respect to discontinuities of the shell material properties, and almost robust with respect to the shell thickness

Beirao da Veiga, L., Chinosi, C., Lovadina, C., & Pavarino, L. (2012). BDDC preconditioners for Naghdi shell problems and MITC9 elements. COMPUTERS & STRUCTURES, 102-103, 28-41 [10.1016/j.compstruc.2012.03.015].

BDDC preconditioners for Naghdi shell problems and MITC9 elements

BEIRAO DA VEIGA, LOURENCO
Primo
;
2012

Abstract

We introduce and study a BDDC (Balancing Domain Decomposition by Constraints) method for the Naghdi shell problem discretized with MITC (Mixed Interpolation of Tensorial Components) elements. Compared with the Kirchhoff model, the Naghdi model uses both displacement and rotation as variables, and therefore is more accurate but also more complicated at the numerical level. The severe difficulties of finite element shell analysis are also reflected in the condition number of the problem, which quickly diverges as the thickness of the shell and/or the finite element mesh size tend to zero. The proposed BDDC preconditioner is based on a proper selection of primal continuity constraints, the implicit elimination of the interior degrees of freedom in each subdomain, and the iterative solution of the resulting shell Schur complement by a preconditioned conjugate gradient method. The preconditioner is built from the solutions of local shell problems on each subdomain with clamping conditions at the primal degrees of freedom and on the solution of a coarse shell problem for the primal degrees of freedom. Three choices of primal constraints, hence coarse spaces, are considered, yielding three BDDC preconditioner of increasing strength and cost. Several numerical tests are performed for cylindrical, hyperbolic and elliptic shells. The results show that the proposed BDDC preconditioners are scalable in the number of subdomains, quasi-optimal in the ratio subdomain/element sizes, robust with respect to discontinuities of the shell material properties, and almost robust with respect to the shell thickness
Articolo in rivista - Articolo scientifico
BDDC preconditioning; Domain decomposition; MITC finite elements; Shells
English
28
41
14
Beirao da Veiga, L., Chinosi, C., Lovadina, C., & Pavarino, L. (2012). BDDC preconditioners for Naghdi shell problems and MITC9 elements. COMPUTERS & STRUCTURES, 102-103, 28-41 [10.1016/j.compstruc.2012.03.015].
BEIRAO DA VEIGA, L; Chinosi, C; Lovadina, C; Pavarino, L
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/98820
Citazioni
  • Scopus 4
  • ???jsp.display-item.citation.isi??? 3
Social impact