Windowed space-time least-squares Petrov-Galerkin method for nonlinear model order reduction

Understand

This work presents the windowed space-time least-squares Petrov-Galerkin method (WST-LSPG) for model reduction of nonlinear parameterized dynamical systems.

• WST-LSPG is a generalization of the space-time least-squares Petrov-Galerkin method (ST-LSPG).
• The main drawback of ST-LSPG is that it requires solving a dense space-time system with a space-time basis that is calculated over the entire global time domain, which can be unfeasible for large-scale applications.
• Instead of using a temporally-global space-time trial subspace and minimizing the discrete-in-time full-order model (FOM) residual over an entire time domain, the proposed WST-LSPG approach addresses this weakness by (1) dividing the time simulation into time windows, (2) devising a unique low-dimensional space-time trial subspace for each window, and (3) minimizing the discrete-in-time space-time residual of the dynamical system over each window.