A component decomposition preconditioning for 3D stress analysis problems

Numerical Linear Algebra with Applications

Volumn 9, Issue 6-7, 2002, Pages 567-583

  Mihajlovic M D ^a   Mijalkovic S ^b  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

^b DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

3D linear elasticity; Algebraic multigrid; Krylov methods; Preconditioning; Stress analysis

Indexed keywords

EID: 0036391650     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/nla.298     Document Type: Conference Paper

References (36)

1. Ovtchinnikov EE, Xanthis LS. A new Korn's type inequality for thin domains and its application to iterative methods. Computer Methods in Applied Mechanics and Engineering 1996; 138:299-315.
2. Ovtchinnikov EE, Xanthis LS. The Korn's type inequality in subspaces and thin elastic structures. Proceedings of the Royal Society (London) 1997; A 453, Series A, 2003-2016.
3. Ovtchinnikov EE, Xanthis LS. Iterative subspace correction methods for thin elastic structures and Korn's type inequality in subspaces. Proceedings of the Royal Society (London), Series A 1998; A 454:2023-2039.
4. Ovtchinnikov EE, Xanthis LS. Effective dimensional reduction algorithm for eigenvalue problems for thin elastic structures: A paradigm in three dimensions. Proceedings of the National Academy of Science USA 2000; 97(3):967-971.
5. Hughes TJR. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Prentice-Hall: Englewood Cliffs, NJ, 1987.
6. Malkus DS, Hughes TJR. Mixed finite element methods - reduced and selective integration techniques: A Unification of Concepts. Compututer Methods in Applied Mechanics and Engineering 1978; 15(1):63-81.
7. Achchab B, Axelsson O, Laayouni L, Souissi A. Strenghtened Cauchy-Bunyakowski-Schwarz inequality for a three-dimensional elasticity system. Numerical Linear Algebra with Applications 2001; 8:191-205.
8. Axelsson O. On iterative solvers in structural mechanics; separate displacement orderings and mixed variable methods. Mathematics and Computers in Simulation 1999; 50:11-30.
9. Padiy A. On a robust multilevel method applied for solving large-scale linear elasticity problems. Communications in Numerical Methods in Engineering 1999; 15:153-165.
10. Stüben K. Algebraic multigrid (AMG): experiences and comparisons. Applied Mathematics and Computation 1983; 13:419-452.
11. Stüben K. Algebraic Multigrid (AMG): An Introduction with Applications. In Multigrid, Trottenberg U, Oosterlee CW, Schüler A. (eds). Academic Press: New York, 2000.
12. Stüben K. A review of algebraic multigrid. Journal of Computational and Applied Mathematics 2001; 128: 281-309.
13. Füllenbach T, Stüben K, Mijalković S. Application of an algebraic multigrid solver to process simulation problems. Proceedings of the 2000 International Conference on Simulation of Semiconductor Processes and Devices, Seattle, WA, 2000: 225-228.
14. Hu SM. Stress related problems in silicon technology. Journal of Applied Physics 1991; 15:R53-R80.
15. Axelsson O, Gustafsson I. Iterative methods for the solution of the Navier equations of elasticity. Computer Methods in Applied Mechanics and Engineering 1978; 15:241-258.
16. Blaheta R. Displacement decomposition - incomplete factorisation preconditioning techniques for linear elasticity problems. Numerical Linear Algebra with Applications 1994; 1:107-128.
17. Horgan CO. Korn's inequalities and their applications in continuum mechanics. SIAM Review 1995; 37: 491-511.
18. Fichera G. Existence theorems in elasticity. In Handbuch der Physik, vol. 6a/2, Flüge S. Truesdell C (eds). Springer: Berlin, 1972; 347-389.
19. Dongarra JJ, Duff IS, Sorensen DC, van der Vorst HA. Numerical Linear Algebra for High-Performance Computers. SIAM: Philadelphia, PA, 1998.
20. Golub G, Van Loan CF. Matrix Computations (2nd edn). The Johns Hopkins University Press: Baltimore, MD, 1989.
21. Saad Y. Iterative Methods for Sparse Linear Systems. PWS Publishing Company: Boston, 1996.
22. Xu J. Iterative methods by space decomposition and subspace correction. SIAM Review 1992; 34:581-613.
23. Arnold D, Falk R, Winther R. Preconditioning in H(div) and applications. Mathematics of Computation 1997; 66:957-984.
24. Mijalković S, Mihajlović MD. Component-wise algebraic multigrid preconditioning for the iterative solution of stress analysis problems from microfabrication technology. Communications in Numerical Methods in Engineering 2001, 17(10):737-747.
25. Kondratiev VA, Oleinik OA. On Korn's inequalities. Comptes Rendus de l'Académie des Sciences. Paris Série I 1989; 308:483-487.
26. Ovtchinnikov EE, Xanthis LS. Effective dimensional reduction for elliptic problems. Comptes Rendus de l'Académie des Sciences, Paris Série I 1995; 320:879-884.
27. Mijalković S. A piecewise linear Galerkin approach to stress analysis of nearly incompressible materials. Communications in Numerical Methods in Engineering 2000, 16:537-543.
28. Joe B. Geompack - a software package for the generation of meshes using geometric algorithms. Advances in Engineering Software 1991: 13:325-331.
29. Saad Y, Schultz MH. GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Statistical and Scientific Computing 1986; 7:856-869.
30. Balay S, Gropp W, McInnes LC, Smith B. PETSc 2.0 Users Manual. ANL-95/11-Revision 2.0.28. Argonne National Laboratory, Argonne, 1999.
31. Golub GH, Van Loan CF. Matrix Computations. John Hopkins University Press: Baltimore, MD, 1983.
32. Numerical Analysis Group. NAG Manual, Fortran Library Mark 19. Oxford, 1999.
33. Axelsson O, Padiy A. On the additive version of the algebraic multilevel iteration method for anisotropic elliptic problems. SIAM Journal on Scientific Computing 1999; 20(5): 1807-1830.
34. Axelsson O, Vassilevski PS. Algebraic multilevel preconditioning methods. I. Numerische Mathematik 1989; 56:157-177.
35. Axelsson O, Vassilevski PS. Algebraic multilevel preconditioning methods. II. SIAM Journal on Numerical Analysis 1990; 27(6): 1569-1590.
36. Joppich W, Mijalković S. Semiconductor process modeling. In Wiley Encyclopedia of Electrical and Electronics Engineering, vol. 19, Webster JG (ed.). Wiley: New York, 1999; 127-139.