A comprehensive scheme for reduction of nonlinear dynamical systems

Model order reduction (MOR) also known as dimension reduction is a computational tool to obtain cost-effective lower order approximations of large scale dynamical systems. This paper presents a detailed yet simplified MOR approach using nonlinear moment matching (NLMM) in conjuncture with the Discrete Empirical Interpolation Method (DEIM). NLMM avoids the expensive simulation of the underlying nonlinear Sylvester partial differential equation by reducing it to a system of nonlinear algebraic equations using proper step-by-step simplifications. This reduces the offline computational cost of generating the orthonormal projection basis substantially. This is followed by the DEIM algorithm, resulting in comprehensive savings in computational resources. The proposed algorithms are tested on two benchmark problems and the results so obtained are compared with proper orthogonal decomposition for different test inputs.