Application of a reduced basis method for an efficient treatment of structural mechanics problems

For numerous problems in structural mechanics, a repeated solution of partial differential equations (PDEs), varying certain input parameters, is necessary. Solving the PDE for a large number of different input parameter sets using a full‐dimensional finite element method, requires repeated solving of large systems of equations and, thus, leads to a high computational effort. The aim of model order reduction techniques is to reduce the computational complexity in such calculations. In order to achieve this, the idea of the reduced basis method [1–3] is to replace the high‐dimensional model with a lower dimensional model, which is realized by forming a basis of solutions of the full problem for selected parameter sets. Key to determining suitable parameter sets is an appropriate error estimator.