An object-oriented framework for reduced-order models using proper orthogonal decomposition (POD)

This work presents an object-oriented design for reduced-order modeling using the proper orthogonal decomposition (POD) technique. Object-oriented design attributes such as data encapsulation, inheritance, and polymorphism are shown to produce efficient implementations that optimize code reuse and maintainability in reduced-order models. This paper demonstrates how existing finite element libraries can be used to efficiently carry out integration of field quantities and their gradients over complex domains for producing reduced-order models that are based on the weak-form Galerkin method and POD. Furthermore, numerical examples are used to show how reduced-order models are computationally feasible for reducing CPU time as long as the computational expense incurred in solving the associated systems of linear equations is significantly higher than the computational expense related to the assembly of the system of equations.