Sensitivity based Proper Orthogonal Decomposition for nonlinear parameter dependent systems

Parameter dependent systems are found in many complex coupled systems. When applying optimization techniques, using full order models for the solution of parameter dependent systems may simply be intractable. Therefore we investigate methods for generating reduced order models that can be applied to nonlinear parameter dependent systems. The development of these reduced order models is made possible by sensitivity analysis of the basis functions. We also introduce a new method using piecewise cubic Hermite interpolating polynomials of the basis functions.