HIERARCHICAL APPROXIMATE PROPER ORTHOGONAL DECOMPOSITION

Proper Orthogonal Decomposition (POD) is a widely used technique for the construction of low-dimensional approximation spaces from high-dimensional input data. For large-scale applications and an increasing number of input data vectors, however, computing the POD often becomes prohibitively expensive. This work presents a general, easy-to-implement approach to compute an approximate POD based on arbitrary tree hierarchies of worker nodes, where each worker computes a POD of only a small number of input vectors. The tree hierarchy can be freely adapted to optimally suit the available computational resources. In particular, this hierarchical approximate POD (HAPOD) allows for both simple parallelization with low communication overhead, as well as incremental POD computation under constrained memory capacities. Rigorous error estimates ensure the reliability of our approach, and extensive numerical examples underline its performance.