Model reduction of multidimensional dynamical systems by tensor decompositions

This paper investigates different methods for multi dimensional POD reduction. The POD basis functions will be obtained from a tensor decomposition method. Multiple methods are available and will be compared for their use in model reduction. These methods will be applied to a dynamical system described by Partial Differential Equations, PDEs. The methods are well defined on functions on Cartesian domains, several methods to apply them on non Cartesian domains are treated as well.