Computing and communication structure design for fast mass-parallel numerical solving PDE

Partial differential equations and systems with certain boundary conditions specify continuous processes significant for both large-scale simulations in computer-aided design using HPC and subsequent real-time control of embedded applications using dedicated hardware. The paper develops a spectrum of techniques based on a family of place-transition nets aimed at the computing and communication structure design for fast mass-parallel numerical solving of PDEs. For the HPC domain, we develop models of interconnects in the form of infinite nets and graphical programs in the form of Sleptsov nets. For the embedded control domain, we develop specialized lattices for fast numerical solving PDE based on integer number approximation specified with Sleptsov-Salwicki nets to be implemented on dedicated hardware, which we prototype on FPGAs. For mass-parallel solving of PDEs, we employ ad-hoc finite-difference schemes and iteration methods that allow us to recalculate the lattice values in a single time cycle suitable for control of hypersonic objects and thermonuclear reactions.