Speaker
Description
POD and POD combined with interpolation and regression methods like DEIM are popular model order reduction technologies for time-dependent partial differential equations. In this talk, first, we investigate the numerical properties of POD for large-scale advection-dominated problems. We investigate the stability properties of the time-stepping schemes for the Euler equations of compressible fluids. We explore the largest stable stepsizes and conclude with much larger stable CFL numbers. We shall investigate the cone-preservation property for POD. To this aim, we prove mathematical theorems for the cone-preservation of SVD and the best approximating low-rank matrices. Finally, we investigate the consistency property of the DEIM methods and propose a modification that improves the stability of the POD-DEIM procedure for the input-output systems.
