Irene Gómez-Bueno

University of Malaga - Spain

Title: Well-balanced POD-PID-DEIM reduced-order models for nonlinear parametric hyperbolic problems

Authors: Irene Gómez-Bueno, Enrique D. Fernández-Nieto, Samuele Rubino

Abstract

We present a reduced-order modelling strategy for nonlinear parametric hyperbolic systems that combines Proper Orthogonal Decomposition (POD) with Discrete Empirical Interpolation (DEIM) for an efficient approximation of nonlinear terms, and introduces PID (Principal-Interval Decomposition) together with a time-averaging approach. The time domain is split into subintervals used for basis construction, and time-averaged states over these subintervals are used to approximate the variables appearing in the nonlinear terms. In addition, the reduced formulation preserves the well-balanced property of the underlying full-order discretisation. Numerical experiments on nonlinear benchmark problems confirm the robustness and efficiency of the proposed reduced-order framework.