On iterative solvers in structural mechanics; separate displacement orderings and mixed variable methods

Mathematics and Computers in Simulation

Volumn 50, Issue 1-4, 1999, Pages 11-30

  Axelsson, Owe ^a  

^a RADBOUD UNIVERSITY NIJMEGEN   (Netherlands)

Author keywords

Displacement orderings; Mixed variable methods; Structural mechanics

Indexed keywords

EID: 0142078039     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0378-4754(99)00058-0     Document Type: Article

References (23)

1. O. Axelsson, Preconditioning of indefinite problems by regularization, SIAM J. Numer. Anal. 16 (1979) 58-69.
2. O. Axelsson, On algebraic multilevel iteration methods for selfadjoint elliptic problems with anisotropy, in: Rend. Sem. Mat. Univers. Politech. Torino, Fascicolo Speciale, Numerical Methods, Torino 1990, 1991, pp. 31-61.
3. O. Axelsson, Iterative Solution Methods, Cambridge University Press, Cambridge, 1994.
4. O. Axelsson, V.A. Barker, Finite Element Solution of Boundary Value Problems, Theory and Computation, Academic Press, Orlando, FL, 1984.
5. O. Axelsson, I. Gustafsson, Iterative methods for the solution of the Navier's equations of elasticity, Comput. Meth. Appl. Mech. Eng. 15 (1978) 241-258.
6. O. Axelsson, M. Neytcheva, Scalable algorithms for the solution of Navier's equations of elasticity, Comput. Appl. Math. 63 (1995) 149-178.
7. O. Axelsson, A. Padiy, On a robust and scalable linear elasticity solver based on a saddle point formulation, Int. J. Numer. Meth. Engng. 44 (1999) 801-818.
8. O. Axelsson, P. Vassilevski, A black-box generalized conjugate gradient solver with inner iterations and variable-step preconditioning, SIAM J. Matrix Anal. Appl. 12 (1991) 625-644.
9. O. Axelsson, P. Vassilevski, Construction of variable-step preconditioners for inner-outer iteration methods, in: R. Beauwens, P. de Groen (Eds.), Iterative Methods in Linear Algebra, North-Holland, Amsterdam, 1992, pp. 1-14.
10. I. Babuska, M. Suri, Locking effects in the finite approximation of elasticity problems, Numer. Math. 62 (1992) 439-463.
11. R. Blaheta, Displacement decomposition-incomplete factorization preconditioning techniques for linear elasticity problems, Numer. Linear Algebra Appl. 1 (1994) 107-128.
12. D. Braess, Finite Elements. Theory, Fast Solvers, and Applications in Solid Mechanics, Cambridge University Press, Cambridge, 1997.
13. F. Brezzi, M. Fortin, Mixed and Hybrid Finite Element Methods, Springer, New York, 1991.
14. D. Chapelle, K.-J. Bathe, Fundamental considerations for the finite element analysis of shell structures, Computers and Structures, to appear.
15. P.G. Ciarlet, Mathematical Elasticity, vol. 1, Three-dimensional Elasticity, North-Holland, Amsterdam, 1988.
16. K.O. Friedrichs, On the boundary value problems of the theory of elasticity and Korn's inequality, Ann. Math. 48 (1947) 441-471.
17. C.O. Horgan, Korn's inequalities and their applications in continuum mechanics, SIAM Rev. 37 (1995) 491-511.
18. A. Korn, Über einige Ungleichungen, welche in der Theorie der elastischen und elektrischen Schwingungen eine Rolle spielen, Bull. Int. Cracov. Acad. Umijet (1908) 706-724.
19. U. Langer, W. Queck, On the convergence factor of Uzawa's algorithm, J. Comput. Appl. Math. 15 (1986) 191-202.
20. J. Necǎs, I. Hlaváček, Mathematical Theory of Elastic and Elastico-plastic Bodies: An Introduction, Elsevier, Amsterdam, 1981.
21. P. Saint-Georges, G. Warzee, Y. Notay, R. Beauwens, High-performance PCG solver for FEM structural analysis, Int. J. Numer. Meth. Eng. 39 (1996) 1133-1160.
22. S. Shlafman, I. Efrat, Using Korn's inequality for an efficient iterative solution of structural analysis problems, in: R. Beauwens, P. de Groen (Eds.), Iterative Methods in Linear Algebra, North Holland, Amsterdam, 1992, pp. 575-581.
23. E.E. Ovtchinnikov, L.S. Xanthis, A new Korn's type inequality for thin domains and its application to iterative methods, Comput. Methods Appl. Mech. Eng. 138 (1996) 299-315.