Um estudo sobre Proper Orthogonal Decomposition: fundamentação teórica - Cunha, Daniel Ammirante Da [UNIFESP] (2020)
The main objective of this work is to study the mathematical foundations of the Proper Orthogonal Decomposition (POD) method, the essence of which is to provides an orthogonal basis for representing a given set of data in a certain least-squares optimal sense. This method can be used to create low-order models. Its foundation is based on results of functional analysis and spectral theory in Hilbert spaces. The main results related to POD are linked to the spectral representation of compact and self-adjoint operators. These theorems are used in the description of the POD method. At the end of the work, it is presented two illustrative examples as application of the method; the first in the wave equation, and the second in the undamped free vibration of a structure.