Model reduction & manifold learning — Based parametric computational electromagnetism: Fundamentals & applications

Abstract

Techniques based on the use of separated representations, are at the heart of the so-called Proper Generalized Decomposition methods. Such separated representations were employed for solving multidimensional models suffering the so-called curse of dimensionality, transient models within a non-incremental integration schema and in the context of uncertainty propagation. Then, its use was extended for separating space coordinates making possible the solution of models defined in degenerated domains, e.g. plate, shells or laminates, and finally for addressing parametric models where model parameters were considered as problem extra-coordinates.