Linear Reduced Order Models for Parameterized Partial Differential Equations

This thesis develops a framework for linear reduced order modeling (ROM) of parameterized PDEs, targeting multi-query forward problems where full-order solvers are computationally expensive. Using the reduced basis (RB) method, the work proposes novel ROMs with certified accuracy, including schemes for space- and time-dependent operators, integration of low-rank tensor decompositions, and RB approximations on parameter-dependent domains. A comprehensive Julia library implementing these methods is also developed, emphasizing both efficiency and usability, providing a high-level, performant tool for the scientific computing community. Numerical tests validate the proposed approaches.