Comprehensive Memory-Bound Simulations on Single Board Computers

Numerical simulations of increasingly complex models, demand growing amounts of (main) memory. Typically, large quantities of memory are provided by workstation- and server-type computers, but in turn consume massive amounts of power. Model order reduction can reduce the memory requirements of simulations by constructing reduced order models, yet the assembly of these surrogate models itself often requires memory-rich compute environments. We resolve this deadlock by careful algorithmic design of the model reduction technique. The presented empirical-cross-Gramian-based model reduction comprises two phases; in a first phase the empirical cross Gramian matrix is computed, secondly, a singular value decomposition of this system Gramian matrix reveals a low-rank projection, which can be applied to the original full order model. This model reduction approach can be realized economically memory-wise using the HAPOD algorithm, and we demonstrate its applicability on a low-end single board computer device.