Parallelisation and multiscale reduced order modelling

The macroscopic behaviour of a material is often governed by its underlying micro-structure. Due to the heterogeneities in the material it can be challenging to find constitutive laws to find a constitutive relation for the stress on the macro-scale. Therefore it is beneficial to model the micro-structure in the material to determine the stress-response to deduce the stiffness of the material.

PhD Candidate: Rody van Tuijl
Supervisor: J.J.C. Remmers
Promotor: M.G.D. Geers
Project Financing: ERC Advanced Grant 2013
Project Period: December 2014 - December 2018

In computational homogenisation a finite element simulation of the micro-structure is performed on each integration point of the macro-scale model to derive its tangent stiffness. This methodology is commonly denoted as FE2. Due to their O(N2) nature, computational homogenisation schemes are generally expensive. Therefore applying computational homogenisation to large-scale industrial problems on desktop computers is not yet feasible .

In this Ph.D. project reduced order modelling schemes are studied to reduce the computational effort required to compute the stress-response of the micro-structure. The reduced basis is used to efficiently solve the micro-scale problem. Using reduced order modelling the computationally feasible range of simulations is expanded such that a broad class of heterogeneous materials can be tackled.

The knowledge gained during this Ph.D. project can be used to make computational homogenisation a suitable modelling-tool for larger problems. In term, the application of model order reduction to computational homogenisation schemes may open the way to run large-scale simulations on a conventional desktop computers.