HAPOD - Fast, Simple and Reliable Distributed POD Computation

emgr—The Empirical Gramian Framework

“…hence this distributed empirical cross Gramian [72] (Section 4.2) is computable in parallel and communication-free on a distributed memory computer system, or sequentially in a memory-economical manner as a low-rank empirical cross Gramian [73] on a unified memory computer system. This column-wise computability translates also to the empirical joint Gramian and the non-symmetric variants of the empirical cross and joint Gramian.…”

“…This column-wise computability translates also to the empirical joint Gramian and the non-symmetric variants of the empirical cross and joint Gramian. Based on this partitioning, a low-rank representation can be obtained in a memory-bound or compute-bound setting together with the hierarchical approximate proper orthogonal decomposition (HAPOD) [72]. This POD variant allows to directly compute a Galerkin projection from an arbitrary column-wise partitioning of the empirical cross Gramian.…”

“…Together with a partitioned singular value decomposition, such as the HAPOD [72], an empirical-cross-Gramian-based Galerkin projection is computable with minimal communication in parallel on a distributed memory system, or sequentially on a shared memory system [73].…”