Speaker
Description
Constructing low-order approximations to a high-dimensional manifold is a well-studied field as these types of problems arise naturally from the solution of parametric partial differential equations in multi-query or optimization contexts. Full-order approximations, although the most accurate approach to reconstructing a solution manifold, incur too high of an expense in these scenarios. Results for reduced order modeling (ROM) procedures such as proper orthogonal decomposition (POD) and greedy reduced basis methods are often stated in a continuous, functional analysis setting; however, these algorithms are the continuous analog of well-known discrete linear algebra routines for matrix factorizations. In this talk, we compare widely used ROM techniques with their discrete counterparts: POD with SVD, reduced basis methods with column pivoted QR, and empirical interpolation with full pivoted LU. Results from the continuous and discrete settings are juxtaposed to highlights similarities and allow for the interpretation and development of continuous ROM results in light of their linear algebra decomposition analogs.