Numerical simulations of dynamical systems are a successful tool to study complex physical phenomena. However, to describe the complete physical behaviour of such models requires massive amounts of storage and computational resources, particularly in the case of 3D continuum mechanics. Model Order Reduction (MOR) techniques have been developed to reduce the complexity of these models whilst retaining information for specific purposes, such as control or diagnosis. The POD-DEIM is a reduction method that has been proven to be efficient for reducing non-linear systems. The non-linearity could be a result the system dynamics or non-constant material properties of the system. In this thesis the POD-DEIM approach is tested on the FitzHugh–Nagumo non-linear system, In addition to two industrial use cases (Bridgman furnace, the Vacuum Furnace). Besides, A 2D thermal block with non-constant material property. Model order reduction for non-linearities emerging from temperature-dependent material properties like thermal conductivity are addressed, and a matrix interpolation approach is proposed to tackle this problem.     «

Numerical simulations of dynamical systems are a successful tool to study complex physical phenomena. However, to describe the complete physical behaviour of such models requires massive amounts of storage and computational resources, particularly in the case of 3D continuum mechanics. Model Order Reduction (MOR) techniques have been developed to reduce the complexity of these models whilst retaining information for specific purposes, such as control or diagnosis. The POD-DEIM is a reductio...     »