Stochastic calculations in connection with FE-simulations

In my current research, I am investigating non-linear finite element (FE) calculations involving random variables and random fields.

For this purpose, elasto-plastic calculations and damage calculations are performed using the FE software Abaqus. In order to model the dependence of damage evolution on inhomogeneities in the material more realistically, random fields are used to model material properties. Thus, the material properties vary not only from realisation to realisation, but also in space within the model.

Hereby, high stochastic dimensions arise easily, even if a random field is approximated with a Karhunen-Loeve expansion (KLE). To investigate certain output quantities of a stochastic system, Monte-Carlo simulations can be performed, which can lead to very high computational costs for high-dimensional problems. For this reason, the goal of this research project is to investigate more effective sampling methods in the application to non-linear problems.

So far, sparse Polynomial Chaos Expansion (sparse PCE) has been investigated as a surrogate model sampling method. Currently, Multi-Fidelity Monte Carlo (MFMC) calculations are under investigation. Here, models with higher and lower accuracy are combined to save computational costs.