A parallel spectral element method for dynamic three-dimensional nonlinear elasticity problems

Computers and Structures

Volumn 87, Issue 1-2, 2009, Pages 59-72

  Dong, S ^a   Yosibash, Z ^b  

^a PURDUE UNIVERSITY   (United States)

^b BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

Author keywords

Exponential convergence; hp finite element method; Jacobi polynomial; Message passing interface; Nonlinear elasticity; Spectral element method

Indexed keywords

BEAMS AND GIRDERS; DOMAIN DECOMPOSITION METHODS; ELASTICITY; FINITE ELEMENT METHOD; FUNCTION EVALUATION; MESSAGE PASSING; POLYNOMIAL APPROXIMATION; PROBABILITY DENSITY FUNCTION; THREE DIMENSIONAL;

EXPONENTIAL CONVERGENCE; HP FINITE ELEMENT METHOD; JACOBI POLYNOMIAL; MESSAGE PASSING INTERFACE; NONLINEAR ELASTICITY; SPECTRAL ELEMENT METHOD;

CONVERGENCE OF NUMERICAL METHODS;

EID: 55749102696     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruc.2008.08.008     Document Type: Article

References (35)

1. Armero E., and Romero I. On the formulation of high-frequency dissipative time-stepping algorithms for nonlinear dynamics. Part II: Second-order methods. Comput Methods Appl Mech Eng 190 (2001) 6783-6824
2. Babuska I., Elman H.C., and Markley K. Parallel implementation of the hp-version of the finite element method on a shared-memory architecture. SIAM J Sci Statist Comput 13 6 (1992) 1433-1459
3. Bathe K.J. Finite element procedures (1996), Prentice Hall
4. Bathe K.J. Conserving energy and momentum in nonlinear dynamics: a simple implicit time integration scheme. Comput Struct 85 (2007) 437-445
5. Bathe K.J., and Cimento A.P. Some practical procedures for the solution of nonlinear finite element equations. Comput Methods Appl Mech Eng 22 (1980) 59-85
6. Bittencourt M.L., Vazquez M.G., and Vazquez T.G. Construction of shape functions for the h- and p-versions of the FEM using tensorial product. Int J Numer Methods Eng 71 (2007) 529-563
7. Dey S., and Datta D.K. A parallel hp-FEM infrastructure for three-dimensional structural acoustics. Int J Numer Methods Eng 68 (2006) 583-603
8. Dong S. Direct numerical simulation of turbulent Taylor-Couette flow. J Fluid Mech 587 (2007) 373-393
9. Dong S., Insley J., Karonis N.T., Papka M., Binns J., and Karniadakis G.E. Simulating and visualizing human arterial system on the TeraGrid. Future Gener Comput Syst 22 (2006) 1011-1017
10. Dong S., and Karniadakis G.E. DNS of flow past a stationary and oscillating cylinder at Re = 10,000. J Fluid Struct 20 (2005) 519-531
11. Dong S., Karniadakis G.E., Ekmekci A., and Rockwell D. A combined DNS-PIV study of the turbulent near wake. J Fluid Mech 569 (2006) 185-207
12. Dong S., Triantafyllou G.S., and Karniadakis G.E. Elimination of vortex streets in bluff-body flows. Phys Rev Lett 100 (2008) 204501
13. Dubiner M. Spectral methods on triangles and other domains. J Sci Comput 6 (1991) 345
14. Düster A., Hartmann S., and Rank E. p-FEM applied to finite isotropic hyperelastic bodies. Comput Methods Appl Mech Eng 192 (2003) 5147-5166
15. 2 flow theory with non-linear isotropic hardening. Int J Numer Methods Eng 53 (2002) 49-63
16. Foster I.T. Designing and building parallel programs (1995), Addison-Wesley
17. Guo X., and Myers K. A parallel solver for the hp-version of the finite element methods. Comput Methods Appl Mech Eng 133 (1996) 229-246
18. Heisserer U. Solution of the semidiscrete equations of structural dynamics by the generalized-α method and its implementation in a p-FEM code. PhD thesis, Technical University of Munich, Institute of Computer Sciences in Civil Engineering, Munich, Germany; 2001.
19. Heisserer U, Hartmann S, Düster A, Yosibash Z. On volumetric locking-free behavior of p-version finite elements under finite deformations. Commun Numer Methods Eng; in press.
20. Holzer S.M., and Yosibash Z. The p-version of the finite element method in incremental elasto-plastic analysis. Int J Numer Methods Eng 39 (1996) 1859-1878
21. Humar J.L. Dynamics of structures (2002), A.A. Balkema Publishers
22. Janik T.J. Parallel implementation of the p-version of the finite element method for elliptic equations on a shared-memory architecture. Adv Comput Math 8 (1998) 97-110
23. Karniadakis G.E., and Sherwin S.J. Spectral/hp element methods for computational fluid dynamics. 2nd ed. (2005), Oxford University Press, New York (NY), USA
24. Karypis G., and Kumar V. A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J Sci Comput 20 (1998) 359-392
25. Laszloffy A., Long J., and Patra A.K. Simple data management, scheduling and solution strategies for managing the irregularities in parallel adaptive hp finite element simulations. Parallel Comput 26 (2000) 1765-1788
26. Noel A.T., and Szabó B.A. Formulation of geometrically non-linear problems in the spatial reference frame. Int J Numer Methods Eng 40 (1997) 1263-1280
27. Oden J.T., Patra A., and Feng Y. Parallel domain decomposition solver for adaptive hp finite element methods. SIAM J Numer Anal 34 (1997) 2090-2118
28. Rank E., Rücker M., Düster A., and Bröker H. The efficiency of the p-version finite element in a distributed computing environment. Int J Numer Methods Eng 52 (2001) 589-604
29. Ribeiro P. A p-version first order shear deformation finite element for geometrically non-linear vibration of curved beams. Int J Numer Methods Eng 61 (2004) 2696-2715
30. Scholz D, Düster A, Rank E. Model-adaptive structural FEM computations for fluid-structure interaction. In: Third MIT conference on computational fluid and solid mechanics, Cambridge, USA; 2005.
31. Scholz D., Kollmannsberger S., Düster A., and Rank E. Thin solids for fluid-structure interaction. Lect Notes Comput Sci Eng 53 (2006) 294-335
32. Szabó B.A., and Babuška I. Finite element analysis (1991), John Wiley & Sons, New York
33. Szabó B.A., Düster A., and Rank E. The p-version of the finite element method. In: Hughes T.J.R., Stein E., and de Borst R. (Eds). Encyclopedia of computational mechanics vol. I (2004), John Wiley & Sons 119-139
34. Tufo H.M., and Fischer P.F. Fast parallel direct solvers for coarse grid problems. J Parallel Distr Comput 61 (2001) 151-177
35. Yosibash Z., Hartmann S., Heisserer U., Duester A., Rank E., and Szanto M. Axisymmetric pressure boundary loading for finite deformation analysis using p-FEM. Comput Methods Appl Mech Eng 196 (2007) 1261-1277