Real-time direct integration of reduced solid dynamics equations

David González (1) , Elías Cueto (1) , Francisco Chinesta (2)

1 I3A - Aragón Institute of Engineering Research [Zaragoza]
2 GeM - Institut de Recherche en Génie Civil et Mécanique

A new method is developed here for the real-time integration of the equations of solid dynamics based on the use of POD-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 is obtained 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. 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 are included that show the promising results of this technique.

Mots clés: solid dynamics; PGD; POD; model order reduction; real-time simulation

Domaines: Mécanique des structures [physics.class-ph]

David González, Elías Cueto, Francisco Chinesta. Real-time direct integration of reduced solid dynamics equations. International Journal for Numerical Methods in Engineering, 2014, 99 (9), pp.633-653. ⟨10.1002/nme.4691⟩. ⟨hal-01857307⟩