Objectives and applied methods
The DFG Emmy-Noether-Group EMMA - Efficient Methods for Mechanical Analysis has the primary objective of significantly reducing the computational ressources (memory demand and CPU time) of simulations dealing with non-linear, dissipative, path-dependent, solid mechanical problems.
In order to achieve the anticipated savings, sophisticated model order reduction techniques are developed. More specifically the mechanical fields are approximated by problem-specific, global ansatz functions. These ansatz functions define a so-called reduced basis (RB). This RB is identified from a computationally intense training phase (offline phase). A snapshot proper orthogonal decomposition (snapshot POD) is applied which extracts a set of orthogonal basis functions minimizing the approximation error. The objectives of modern model order reduction techniques are:
- reduction of the CPU time
- reduction of the memory demand
- decoupling of the required computational ressources with respect to the dimension of the unreduced problem
- efficient identification of the reduced basis (low dimension and low number of preanalysis simulations)
The first two points represent primary objectives. In order to attain these primary objectives, the two seperately mentioned secondary objectives need to be solved. Additionally, the computational strategy (which preferably stems from physical principles) for the determination of the reduced degrees of freedom has a major influence on the overall numerical cost.
Within the Emmy-Noether-Group EMMA a specific interdisciplinary approach is pursued in order to address the afore-mentioned points. Other than in many general model order reduction techniques usually based on mathematically motivated projection rules, micromechanically supported methods are developed in EMMA. These techniques combine cleverly chosen restrictions regarding the modeling. In particular, it is required that the constitutive equations of the underlying materials derive from potential structures (GSM [Halphen, Nguyen (1975)], SD-CZ [Leuschner et al. 2015]).
Four different main projects define the main research activities of EMMA:
- project P.1 - potential based model reduction for large deformations
- project P.2 - potential based model reduction for structural simulations
- project A.1 - error estimation and robust time integration
- project A.2 - high performance implementation and parallel algorithms