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Real‐time direct integration of reduced solid dynamics equations
Author(s) -
González David,
Cueto Elías,
Chinesta Francisco
Publication year - 2014
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.4691
Subject(s) - integrator , curse of dimensionality , sort , mathematics , control theory (sociology) , proper orthogonal decomposition , parametric statistics , displacement (psychology) , mathematical optimization , point of delivery , algorithm , computer science , psychology , computer network , statistics , arithmetic , control (management) , bandwidth (computing) , artificial intelligence , psychotherapist , agronomy , biology
SUMMARY A new method is developed here for the real‐time integration of the equations of solid dynamics based on the use of proper orthogonal decomposition (POD)–proper generalized decomposition (PGD) approaches and direct time integration. The method is based upon the formulation of solid dynamics equations as a parametric problem, depending on their initial conditions. A sort of black‐box integrator that takes the resulting displacement field of the current time step as input and (via POD) provides the result for the subsequent time step at feedback rates on the order of 1 kHz is obtained. To avoid the so‐called curse of dimensionality produced by the large amount of parameters in the formulation (one per degree of freedom of the full model), a combined POD–PGD strategy is implemented. Examples that show the promising results of this technique are included. Copyright © 2014 John Wiley & Sons, Ltd.