In our former works we proposed different Model Order Reduction strategies for alleviating the complexity of computational simulations. In fact we proved that separated representations are specially appealing for addressing many issues, in particular, the treatment of 3D models defined in degenerated domains (those involving very different characteristic dimensions, like beams, plate and shells) as well as the solution of parametrized models for calculating their parametric solutions. However it was proved that the efficiency of solvers based on the construction of such separated representations strongly depends on the affine decompositions (separability) of operators, parameters and geometry. Even if our works proved that different techniques exists for performing such beneficial separation prior of applying the separated representation constructor, the complexity of the solver increases in certain circumstances too much, as the one involving the space separation of complex microstructures concerned by 3D woven fabrics. In this paper we explore an alternative route that allows circumventing the just referred difficulties. Thus, instead of following the standard procedure that consists of introducing the separated representation of the unknown field prior to discretize the models, the strategy here proposed consists of proceeding inversely: first the model is discretized and then the separated representation of the discrete unknown field is enforced. Such a procedure enables the consideration of very complex and non separable features, like complex domains, boundary conditions and microstructures as the ones concerned by homogenized models of complex and rich 3D woven fabrics. It will be proved that such a procedure can be also easily coupled with a non-intrusive treatment of the parametric dimensions by using a sparse hierarchical collocation technique.

中文翻译：

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涉及空间和参数的非侵入式适当广义分解：在3D机织物的机械建模中的应用

在我们以前的工作中，我们提出了不同的模型降阶策略来减轻计算仿真的复杂性。实际上，我们证明了分离表示法对于解决许多问题特别有吸引力，尤其是处理在退化域中定义的3D模型（这些特征涉及非常不同的特征尺寸，例如梁，板和壳）以及参数化模型的解决方案用于计算其参数解。然而，事实证明，基于这种分离表示的构造，求解器的效率很大程度上取决于算子，参数和几何形状的仿射分解（可分离性）。即使我们的工作证明存在应用分离表示构造器之前执行这种有益分离的不同技术，求解器的复杂性在某些情况下也会增加太多，因为涉及3D机织织物所涉及的复杂微结构的空间分离。在本文中，我们探索了一种替代方法，可以绕开上述困难。因此，代替遵循在离散化模型之前引入未知字段的分离表示的标准程序，这里提出的策略包括相反地进行：首先离散化模型，然后离散离散未知字段的分离表示为强制执行。这样的程序可以考虑非常复杂且不可分离的特征，复杂和丰富的3D机织织物均质化模型所关注的复杂领域，边界条件和微观结构。将会证明，通过使用稀疏的分级配置技术，这种过程也可以很容易地与参数尺寸的非侵入式处理结合起来。