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Proper generalized decomposition of time‐multiscale models
Author(s) -
Ammar Amine,
Chinesta Francisco,
Cueto Elías,
Doblaré Manuel
Publication year - 2011
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.3331
Subject(s) - curse of dimensionality , interval (graph theory) , decomposition , computer science , space time , algorithm , mathematical optimization , mathematics , spacetime , artificial intelligence , engineering , physics , chemical engineering , ecology , combinatorics , biology , quantum mechanics
SUMMARY Models encountered in computational mechanics could involve many time scales. When these time scales cannot be separated, one must solve the evolution model in the entire time interval by using the finest time step that the model implies. In some cases, the solution procedure becomes cumbersome because of the extremely large number of time steps needed for integrating the evolution model in the whole time interval. In this paper, we considered an alternative approach that lies in separating the time axis (one‐dimensional in nature) in a multidimensional time space. Then, for circumventing the resulting curse of dimensionality, the proper generalized decomposition was applied allowing a fast solution with significant computing time savings with respect to a standard incremental integration. Copyright © 2011 John Wiley & Sons, Ltd.