A Domain Decomposition Approach to POD

Abstract

The proper orthogonal decomposition (POD) is a popular approach for building reduced-order models for nonlinear distributed parameter systems. The approach is based on developing a reduced basis by post-processing one, and often multiple, high fidelity simulations of a nonlinear partial differential equation. The computational overhead required to perform just one simulation may involve the need to distribute the data and the use of parallel computing architectures. For these problems, the size of the discretization and the number of simulations may preclude 'typical' POD algorithms that are based on accessing all of the information on a single processor. In this paper, we present an algorithm for extracting the dominant POD basis from distributed time history data with low communication overhead. A singular value decomposition of a (spatial) subdomain time history is calculated locally on the resident processor followed by the exchange of a small number of dominant (local) right singular vectors with other processors. Numerical experiments demonstrate that an iterated application of this step works well for two complex fluid flow simulations, taking advantage of relatively homogeneous frequency content of subdomain time histories