Efficient solvers for 3-D homogenized elasticity model

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 3732 LNCS, Issue , 2006, Pages 857-863

  Hoppe, Ronald H W ^a   Petrova, Svetozara I ^a  

^a UNIVERSITY OF AUGSBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; ELASTICITY; NUMERICAL ANALYSIS; OPTIMIZATION; PRODUCT DESIGN; TENSORS;

ALGEBRAIC MULTIGRID METHOD (AMG); EFFICIENT SOLVERS; ELASTICITY MODELS; INCOMPLETE CHOLESKY (IC);

MATERIALS SCIENCE;

EID: 33745314458     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11558958_103     Document Type: Conference Paper

References (13)

1. M.P. Bendsøe and N. Kikuchi. Generating optimal topologies in structural design using a homogenization method. Comput. Methods Appl. Mech. Eng., 71:197-224, 1988.
2. M.P. Bendsøe and O. Sigmund. Topology Optimization: Theory, Methods and Applications. Springer, Berlin-Heidelberg-New York, 2003.
3. A. Bensoussan, J. L. Lions, G. Papanicolaou. Asymptotic Analysis for Periodic Structures. North-Holland, Elsevier Science Publishers, Amsterdam, 1978.
4. R. Blaheta. Displacement decomposition - incomplete factorization preconditioning techniques for linear elasticity problems. Numer. Linear Algebra Appl., 1(2):107-128, 1994.
5. C. Carstensen and St. Funken. Averaging technique for FE-a posteriori error control in elasticity. Part II: λ-independcnt estimates. Comput. Methods Appl. Mech. Engrg., 190:4663-4675, 2001.
6. P. Greil, T. Lifka, A. Kaindl. Biomorphic cellular silicon carbide ceramics from wood: I. Processing and microstructure, and II. Mechanical properties. J. Europ. Cer. Soc., 18:1961-1973 and 1975-1983, 1998.
7. R.H.W. Hoppe and S.I. Petrova. Applications of primal-dual interior methods in structural optimization. Comput. Methods Appl. Math., 3(1):159-176, 2003.
8. R.H.W. Hoppe and S.I. Petrova. Optimal shape design in biomimetics based on homogenization and adaptivity. Math. Comput. Simul., 65(3):257-272, 2004.
9. V.V. Jikov, S.M. Kozlov, and O.A. Oleinik. Homogenization of Differential Operators and Integral Functionals, Springer, 1994.
10. R. Rodriguez. Some remarks on the Zienkiewicz-Zhu estimator. Numer. Meth. PDEs, 10:625-635, 1994.
11. M. Sarikaya and I.A. Aksay. Biomimetics: Design and Processing of Materials. AIP Series in Polymer and Complex Materials, Woodbury (New York), 1995
12. K. Stüben. A review of algebraic multigrid. J. Comput. Appl. Math., 128:281-309, 2001.
13. O.G. Zienkiewicz and J.Z. Zhu. A simple error estimator and adaptive procedure for practical engineering analysis. Intern. J. Numer. Methods Eng., 24:337-357, 1987.