Proper orthogonal decomposition (POD) stabilized methods for the Navier--Stokes equations are considered and analyzed. We consider two cases: case in which snapshots based on a non inf-sup stable method an method. For both cases we construct approximations to velocity pressure. first case, analyze scheme with equal order polynomials pressure local projection stabilization (LPS) gradient of POD ...

Internal hydrodynamics and its coupling with structural dynamics are non-negligible processes in the design phase of aerospace systems. An improved understanding nature this would allow for greater flexibility modeling such systems, could lead eventually to development suitable active and/or passive control strategies enhanced performances. In manuscript we apply a number data analysis techniqu...

In order to reduce the computation time of a quasi-static problem solved by the finite element method, methods of model order reduction can be applied. In this context, two approaches, the Proper Orthogonal Decomposition and the Proper Generalized Decomposition, are applied to the vector potential formulation used to solve the quasi-static problem. The developped methods are compared on an acad...

The Proper Generalized Decomposition or, in short, PGD is a tensor decomposition based technique to solve PDE problems. It reduces calculation and storage cost drastically and presents some similarities with the Proper Orthogonal Decomposition, in short POD. In this work, we propose an efficient implementation to improve the convergence of the PGD, towards the numerical solution of a discretize...

The proper orthogonal decomposition (POD) is a model reduction technique for the simulation of physical processes governed by partial differential equations, e.g. fluid flows. It can also be used to develop reduced order control models. Fundamental is the computation of POD basis functions that represent the influence of the control action on the system in order to get a suitable control model....

Proper Orthogonal Decomposition (POD), also known as Karhunen-Loeve decomposition, is emerging as a useful experimental tool in dynamics and vibrations. The POD is a means of extracting spatial information from a set of time series data available on a domain. The use of Karhunen-Loeve (K-L) transform is of great help in nonlinear settings where traditional linear techniques such as modal testin...

The development and application of model reduction techniques have been widely investigated for problems in unsteady aerodynamic systems, driven mainly by the need to develop effective economical computational models capturing as much flow physics as possible. These techniques which have been based on a number of approaches such as balanced truncation, Arnoldi, proper orthogonal decomposition e...

Proper orthogonal decomposition (POD) technique (or the Karhunan Lo eve procedure) has been used to obtain low dimensional dynamical models of many applications in engineering and science. In principle, the idea is to start with an ensemble of data, called snapshots, collected from an experiment or a numerical procedure of a physical system. The POD technique is then used to produce a set of ba...