A block FETI-DP/BDDC preconditioner for mixed formulations of almost incompressible elasticity is constructed and analyzed; FETI-DP (Finite Element Tearing and Interconnecting Dual-Primal) and BDDC (Balancing Domain Decomposition by Constraints) are two very successful domain decomposition algorithms for a variety of elliptic problems. The saddle point problems of the mixed problems are discretized with mixed isogeometric analysis with continuous pressure fields. As in previous work by Tu and Li (2015) for finite element discretizations of the incompressible Stokes system, the proposed preconditioner is applied to a reduced positive definite system involving only the pressure interface variable and the Lagrange multiplier of the FETI-DP algorithm. In this work, we extend the theory to a wider class of saddle point problems and we propose a novel block-preconditioning strategy, which consists in using BDDC with deluxe scaling for the interface pressure block as well as deluxe scaling for the FETI-DP preconditioner for the Lagrange multiplier block. A convergence rate analysis is presented with a condition number bound for the preconditioned operator which depends on the inf-sup parameter of the fully assembled problem and the condition number of a closely related BDDC algorithm for compressible elasticity. This bound is scalable in the number of subdomains, poly-logarithmic in the ratio of subdomain and element sizes, and robust with respect to material incompressibility. Parallel numerical experiments validate the theory, demonstrate robustness in the presence of discontinuities of the Lamé parameters, and indicate how the rate of convergence varies with respect to the spline polynomial degree and regularity and the deformation of the domain.

Block FETI-DP/BDDC preconditioners for mixed isogeometric discretizations of three-dimensional almost incompressible elasticity / O.B. Widlund, S. Zampini, S. Scacchi, L.F. Pavarino. - In: MATHEMATICS OF COMPUTATION. - ISSN 0025-5718. - 90:330(2021 Jul), pp. 1773-1797. [10.1090/mcom/3614]

Block FETI-DP/BDDC preconditioners for mixed isogeometric discretizations of three-dimensional almost incompressible elasticity

S. Zampini
Secondo
;
S. Scacchi
Penultimo
;
L.F. Pavarino
Ultimo
2021

Abstract

A block FETI-DP/BDDC preconditioner for mixed formulations of almost incompressible elasticity is constructed and analyzed; FETI-DP (Finite Element Tearing and Interconnecting Dual-Primal) and BDDC (Balancing Domain Decomposition by Constraints) are two very successful domain decomposition algorithms for a variety of elliptic problems. The saddle point problems of the mixed problems are discretized with mixed isogeometric analysis with continuous pressure fields. As in previous work by Tu and Li (2015) for finite element discretizations of the incompressible Stokes system, the proposed preconditioner is applied to a reduced positive definite system involving only the pressure interface variable and the Lagrange multiplier of the FETI-DP algorithm. In this work, we extend the theory to a wider class of saddle point problems and we propose a novel block-preconditioning strategy, which consists in using BDDC with deluxe scaling for the interface pressure block as well as deluxe scaling for the FETI-DP preconditioner for the Lagrange multiplier block. A convergence rate analysis is presented with a condition number bound for the preconditioned operator which depends on the inf-sup parameter of the fully assembled problem and the condition number of a closely related BDDC algorithm for compressible elasticity. This bound is scalable in the number of subdomains, poly-logarithmic in the ratio of subdomain and element sizes, and robust with respect to material incompressibility. Parallel numerical experiments validate the theory, demonstrate robustness in the presence of discontinuities of the Lamé parameters, and indicate how the rate of convergence varies with respect to the spline polynomial degree and regularity and the deformation of the domain.
almost incompressible linear elasticity; BDDC deluxe; continuous pressure fields; Domain decomposition; FETI-DP; isogeometric analysis; NURBS;
Settore MAT/08 - Analisi Numerica
24-mar-2021
Article (author)
File in questo prodotto:
File Dimensione Formato  
AIE_IGA_210217.pdf

accesso aperto

Tipologia: Pre-print (manoscritto inviato all'editore)
Dimensione 529.05 kB
Formato Adobe PDF
529.05 kB Adobe PDF Visualizza/Apri
S0025-5718-2021-03614-5.pdf

accesso riservato

Tipologia: Publisher's version/PDF
Dimensione 1.36 MB
Formato Adobe PDF
1.36 MB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

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/2434/869796
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 4
  • ???jsp.display-item.citation.isi??? 2
social impact