.. _MecaSequentialLinear: MecaSequentialLinear ==================== This use case aims to validate the methodology POD + ECM for uniform isotropic elactic material computations with Z-set, see Section :ref:`Publications`, article 1. In this linear case, the ECM should find a trivial quadrature formula, since the operators can be completely precomputed in the offline stage. No optional prerequisite. The data needed to execute the tutorials below can be loaded here: :download:`exampleMecaSequentialLinear.zip ` Features: linear material ------------------------- The physical setting, workflow and reduction strategy are the same as in the tutorial :ref:`MecaSequential` , hence we only point out the differences here. The difference is the use of a uniform isotropic elactic material. Even if the data is generated by Z-set, a constitutive law solver has been implemented in ``Containers/ConstitutiveLaws/MecaUniformLinearElasticity.py``, hence Z-mat is not required to run the *offline* and *online* stages of this tutorial. Results ------- The ECM selects 3 reduced integration points in this example (this can slightly vary due the probabilistic nature of our implementation for ECM) In :numref:`cube-lin-res`, the quality of the reduced model is illustrated by comparing it to the high-fidelity reference. The comparison is done on the displacement, since no internal variable is available with the simple considered material. .. figure:: res.jpg :name: cube-lin-res :align: center :width: 75% Illustration of the ROM accuracy on the displacement ``U`` (left) HFM, (right) pointwise difference between the ROM and the HFM.