IFOSMONDI Co-simulation Algorithm with Jacobian-Free Methods in PETSc

Co-simulation is a widely used solution to enable global simulation of modular system via the composition black-boxed simulators. Among co-simulation methods, IFOSMONDI implicit iterative algorithm, previously introduced by authors, enables us solve non-linear coupling function while keeping smoothness interfaces without introducing delay. Moreover, it automatically adapts size steps between data exchanges among subsystems according difficulty solving constraint. The latter was solved fixed-point whereas this paper introduces Jacobian-Free Methods version. Most implementations Newton-like methods require jacobian matrix which, except in Zero-Order-Hold case, can be difficult compute context. As algorithm uses Hermite interpolation for enhancement, we propose hereafter new formulation including both values and time-derivatives variables. This well designed through jacobian-free Newton-type methods. Consequently, successive evaluations consist multiple simulations systems on time-step using rollback. orchestrator-workers structure combine PETSc framework orchestrator side solvers with parallel integrations workers’ thanks MPI processes. Different will compared one another original implementation newly proposed 2-system academic test case direct feedthrough sides. An industrial model also considered investigate performance method.