Saifon Chaturantabut

TL;DR: A dimension reduction method called discrete empirical interpolation is proposed and shown to dramatically reduce the computational complexity of the popular proper orthogonal decomposition (POD) method for constructing reduced-order models for time dependent and/or parametrized nonlinear partial differential equations (PDEs).

TL;DR: A greatly simplified description of EIM in a finite dimensional setting that possesses an error bound on the quality of approximation and extends to arbitrary systems of nonlinear ODEs with minor modification.

TL;DR: In this article, the authors derived state space error bounds for the solutions of reduced systems constructed using proper orthogonal decomposition (POD) together with the discrete empirical interpolation method (DEIM) recently developed for nonlinear dynamical systems.

TL;DR: Numerical results demonstrate that the dynamics of the viscous fingering in the full-order system of Dimension 15,000 can be captured accurately by the POD–DEIM reduced system of dimension 40 with the computational time reduced by factor of .

TL;DR: A structure-preserving model reduction approach applicable to large-scale, nonlinear port-Hamiltonian systems that ensures the retention of port- Hamiltonian structure which assures the stability and passivity of the reduced model.