Isogeometric analysis and proper orthogonal decomposition for the acoustic wave equation

Discretization methods such as finite differences or finite elements were usually employed to provide high fidelity solution approximations for reduced order modeling of parameterized partial differential equations. In this paper, a novel discretization technique-Isogeometric Analysis (IGA) is used in combination with proper orthogonal decomposition (POD) for model order reduction of the time parameterized acoustic wave equations. We propose a new fully discrete IGA-Newmark-POD approximation and we analyze the associated numerical error, which features three components due to spatial discretization by IGA, time discretization with the Newmark scheme, and modes truncation by POD. We prove stability and convergence. Numerical examples are presented to show the effectiveness and accuracy of IGA-based POD techniques for the model order reduction of the acoustic wave equation.