Iterative strong coupling of dimensionally heterogeneous models

International Journal for Numerical Methods in Engineering

Volumn 81, Issue 12, 2010, Pages 1558-1580

  Leiva, Jorge S ^a   Blanco, Pablo J ^b   Buscaglia, Gustavo C ^c  

^a INSTITUTO BALSEIRO   (Argentina)

^b LABORATÓRIO NACIONAL DE COMPUTAÇÃO CIENTÍFICA   (Brazil)

^c UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

Complex systems; Coupled problems; Dimensionally heterogeneous models; Partitioned analysis; Strong coupling

Indexed keywords

COMPLEX SYSTEMS; COUPLED PROBLEMS; DECOMPOSITION STRATEGY; DIRICHLET-TO-NEUMANN; DOMAIN DECOMPOSITIONS; FINITE TERMINATION PROPERTY; FUNCTION VALUES; GAUSS SEIDEL ITERATION; HETEROGENEOUS MODELS; ITERATIVE PROCEDURES; ITERATIVE SOLVERS; LINEAR PROBLEMS; NOVEL METHODOLOGY; NUMERICAL EXPERIMENTS; STRONG COUPLING; SUB-DOMAINS; SUBMODELS; SYSTEM OF EQUATIONS;

COMPLEXATION; DOMAIN DECOMPOSITION METHODS; NONLINEAR EQUATIONS;

ALGORITHMS;

EID: 75649108203     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2741     Document Type: Article

References (24)

1. Felippa C, Park K, Farhat C. Partitioned analysis of coupled mechanical systems. Computer Methods in Applied Mechanics and Engineering 2001; 190:3247-3270.
2. Blanco P, Feijóo R, Urquiza S. A unified variational approach for coupling 3D-1D models and its blood flow applications. Computer Methods in Applied Mechanics and Engineering 2007; 196:4391-4410.
3. Formaggia L, Gerbeau JF, Nobile F, Quarteroni A. Numerical treatment of defective boundary conditions for the Navier-Stokes equations. SIAM Journal on Numerical Analysis 2002; 40:376-401.
4. Formaggia L, Gerbeau JF, Nobile F, Quarteroni A. On the coupling of 3D and 1D Navier-Stokes equations for flow problems in compliant vessels. Computer Methods in Applied Mechanics and Engineering 2001; 191:561-582.
5. Urquiza S, Blanco P, Vénere M, Feijóo R. Multidimensional modelling for the carotid artery blood flow. Computer Methods in Applied Mechanics and Engineering 2006; 195:4002-4017.
6. Aufranc M. Numerical study of a junction between a three-dimensional elastic structure and a plate. Computer Methods in Applied Mechanics and Engineering 1989; 74:207-222.
7. Blanco P, Feijóo R, Urquiza S. A variational approach for coupling kinematically incompatible structural models. Computer Methods in Applied Mechanics and Engineering 2008; 197:1577-1602.
8. Ciarlet P, Dret HL, Nzengwa R. Junctions between three-dimensional and two-dimensional linearly elastic structures. Journal de Mathématiques Pures et Apptiquées 1989; 68:261-295.
9. Kozlov V, Maz'ya V, Movchan A. Fields in non-degenerate 1D-3D elastic multi-structures. Quarterly Journal of Mechanics and Applied Mathematics 2001; 54:177-212.
10. Deparis S, Discacciati M, Fourestey G, Quarteroni A. Fluid-structure algorithm based on Steklov-Poincaré operators. Computer Methods in Applied Mechanics and Engineering 2006; 195:5797-5812.
11. Mandel J. Balancing domain decomposition. International Journal for Numerical Methods in Engineering 1993; 9:233-241.
12. Farhat C, Pierson K, Lesoinne M. The second generation FETI methods and their application to the parallel solution of large-scale linear and geometrically non-linear structural analysis problems. Computer Methods in Applied Mechanics and Engineering 2000; 184:333-374.
13. Veneziani A, Vergara C. An approximate method for solving incompressible Navier-Stokes problems with flow rate conditions. Computer Methods in Applied Mechanics and Engineering 2007; 196:1685-1700.
14. Veneziani A, Vergara C. Flow rate defective boundary conditions in haemodynamics simulations. International Journal for Numerical Methods in Fluids 2005; 47:803-816.
15. Park K, Felippa C. A variational principle for the formulation of partitioned structural systems. International Journal for Numerical Methods in Engineering 2000; 47:395-418.
16. Matthies H, Niekamp R, Steindorf J. Algorithms for strong coupling procedures. Computer Methods in Applied Mechanics and Engineering 2006; 195:2028-2049.
17. Incropera F, DeWitt D. Introduction to Heat Transfer. Wiley: New York, 1985.
18. Houzeaux G, Codina R. An overlapping iteration-by-subdomain Dirichlet/Robin domain decomposition method for advection-diffusion problems. Journal of Computational and Applied Mathematics 2003; 158:243-276.
19. Quarteroni A, Valli A. Domain Decomposition Methods for Partial Differential Equations, Chapter 8. Oxford University Press: Oxford, 1999.
20. Nobile F, Vergara C. An effective fluid-structure interaction formulation for vascular dynamics by generalized Robin conditions. SIAM Journal on Scientific Computing 2008; 30:731-763.
21. Kelley C. Iterative methods for linear and nonlinear equations, Frontiers in Applied Mathematics, Chapter 6. SIAM: Philadelphia, PA, 1995.
22. Dennis J, Schnabel R. Numerical methods for unconstrained optimization and nonlinear equations, Classics in Applied Mathematics, Chapter 8. SIAM: Philadelphia, PA, 1996.
23. Leiva J. Ph.D. Thesis, Instituto Balseiro, Bariloche, 2009. In preparation.
24. Storti M, Nigro N, Paz R, Dalcín L. Dynamic boundary conditions in computational fluid dynamics. Computer Methods in Applied Mechanics and Engineering 2008; 197:1219-1232.