Speaker
Description
Model order reduction has become an established tool to reduce costs in computational engineering. It is based on the idea that potential solutions to parameterized problems possess a certain kind of similarity, i.e. that the actual solution vectors reside in a lower-dimensional solution manifold. Vice versa, a certain solution can represented in terms of a low-dimensional solution vector.
This approach has been used widely for multiscale simulations, where the microscale FE solutions on the RVE level exhibit a high level of repetitiveness, so that the microscale kinematics can be lowered drastically using a reduced basis. On the kinetic side, the respective equations of motions can be derived by means of Galerkin projection from the original internal force vector. Computing the latter by numerical integration in the elements is, however, still an expensive task.
Different hyperintegration methods have been proposed to reduce the number of quadrature points and thus the computation costs. Hyperintegration methods identify quadrature points and their weights based on least-squares error minimization on training data, incorporating certain criteria like the internal forces in the empirical cubature method (ECM) or the elastic free energy in the reduced energy optimal cubature (REOC), while preserving the integration of the volume.
The present contribution formulates additional generalized criteria for hyperintegration. Their individual and combined effects on the computational cost is evaluated for a number of reduced order FE² problems. This way, the computational online costs can be further decreased if the criteria are combined, caused by the better generalization of the resulting hyperintegration scheme. This scheme is implemented in an element-wise manner as Empirical Hyper Element Integration Method (EHEIM), enabling a modular integration into existing FE² codes.
