Proper generalized decomposition of time-multiscale models

International Journal for Numerical Methods in Engineering

Volumn 90, Issue 5, 2012, Pages 569-596

  Ammar, Amine ^a   Chinesta, Francisco ^b   Cueto, Elías ^c   Doblaré, Manuel ^c  

^a ARTS ET MÉTIERS PARISTECH   (France)

^b AIRBUS GROUP INNOVATIONS   (Germany)

^c UNIVERSITY OF ZARAGOZA   (Spain)

Author keywords

Proper generalized decomposition; Separated representations; Time multiscale; Transient models

Indexed keywords

ALTERNATIVE APPROACH; COMPUTING TIME; CURSE OF DIMENSIONALITY; EVOLUTION MODELS; FAST SOLUTIONS; MULTIDIMENSIONAL TIME; MULTISCALES; PROPER GENERALIZED DECOMPOSITIONS; SEPARATED REPRESENTATION; SOLUTION PROCEDURE; TIME AXIS; TIME INTERVAL; TIME STEP; TIME-SCALES; TRANSIENT MODEL;

COMPUTATIONAL MECHANICS;

SEPARATION;

EID: 84859862487     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.3331     Document Type: Article

References (22)

1. Ladeveze P. Nonlinear Computational Structural Mechanics. Springer: NY, 1999.
2. Ladeveze P, Nouy A. On a multiscale computational strategy with time and space homogenization for structural mechanics. Computer Methods in Applied Mechanics and Engineering 2003; 192: 3061-3087.
3. Nouy A, Ladeveze P. Multiscale computational strategy with time and space homogenization: a radial-type approximation technique for solving microproblems. International Journal of Multiscale Computational Engineering 2004; 170(2): 557-574.
4. Ladeveze P, Passieux J-C, Neron D. The LATIN multiscale computational method and the proper generalized decomposition. Computer Methods in Applied Mechanics and Engineering 2010; 199(21-22): 1287-1296.
5. Ammar A, Normandin M, Daim F, Gonzalez D, Cueto E, Chinesta F. Non-incremental strategies based on separated representations: applications in computational rheology. Communications in Mathematical Sciences 2010; 8(3): 671-695.
6. Ammar A, Mokdad B, Chinesta F, Keunings R. A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids. Journal of Non-Newtonian Fluid Mechanics 2006; 139: 153-176.
7. Ammar A, Mokdad B, Chinesta F, Keunings R. A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids. Part II: transient simulation using space-time separated representations. Journal of NonNewtonian Fluid Mechanics 2007; 144: 98-121.
8. Nouy A. A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations. Computer Methods in Applied Mechanics and Engineering 2007; 196: 4521-4537.
9. Chinesta F, Ammar A, Lemarchand F, Beauchene P, Boust F. Alleviating mesh constraints: model reduction, parallel time integration and high resolution homogenization. Computer Methods in Applied Mechanics and Engineering 2008; 197(5): 400-413.
10. Chinesta F, Ammar A, Cueto E. Recent advances and new challenges in the use of the proper generalized decomposition for solving multidimensional models. Archives of Computational Methods in Engineering 2010; 17(4): 327-350.
11. Ammar A, Chinesta F, Joyot P. The nanometric and micrometric scales of the structure and mechanics of materials revisited: an introduction to the challenges of fully deterministic numerical descriptions. International Journal for Multiscale Computational Engineering 2008; 6(3): 191-213.
12. Chinesta F, Ammar A, Cueto E. Proper generalized decomposition of multiscale models. International Journal of Numerical Methods in Engineering 2010; 83(8-9): 1114-1132.
13. Yu Q, Fish J. Temporal homogenization of viscoelastic and viscoplastic solids subjected to locally periodic loading. Computational Mechanics 2002; 29: 199-211.
14. Frantziskonis G, Muralidharan K, Deymier P, Simunovic S, Nukala P, Pannala S. Time-parallel multiscale/multiphysics framework. Journal of Computational Physics 2009; 228(21): 8085-8092.
15. Baffico L, Bernard S, Maday Y, Turinici G, Zérah G. Parallel-in-time molecular-dynamics simulations. Physical Review E 2002; 66(5): 057701.
16. Bottasso CL. Multiscale temporal integration. Computer Methods in Applied Mechanics and Engineering 2002; 191(25-26): 2815-2830.
17. Neron D, Dureisseix D. A computational strategy for poroelastic problems with a time interface between coupled physics. International Journal for Numerical Methods in Engineering 2008; 73(6): 783-804.
18. Neron D, Dureisseix D. A computational strategy for thermo-poroelastic structures with a time-space interface coupling. International Journal for Numerical Methods in Engineering 2008; 75(9): 1053-1084.
19. Pruliere E, Chinesta F, Ammar A. On the deterministic solution of multidimensional parametric models using the proper generalized decomposition. Mathematics and Computers in Simulation 2010; 81: 791-810.
20. Gonzalez D, Ammar A, Chinesta F, Cueto E. Recent advances on the use of separated representations. International Journal for Numerical Methods in Engineering 2010; 81(5): 637-659.
21. Beylkin G, Mohlenkamp M. Algorithms for numerical analysis in high dimensions. SIAM Journal on Scientific Computing 2005; 26(6): 2133-2159.
22. Szabo B, Babuska I. Introduction to Finite Element Analysis. John Wiley and Sons: New York, 1989.