Scalable robust physics simulator via reduced order modeling and domain decomposition

Tuesday 6 Feb 2024, 16:00 → 20:00 UTC

Abstract: Numerous cutting-edge scientific technologies originate at the laboratory scale, but transitioning them to practical industry applications can be a formidable challenge. Traditional pilot projects at intermediate scales are costly and time-consuming. Alternatives such as E-pilots can rely on high-fidelity numerical simulations, but even these simulations can be computationally prohibitive at larger scales. To overcome these limitations, we propose a scalable, component reduced order model (CROM) method. We employ Discontinuous Galerkin Domain Decomposition (DG-DD) to decompose the physics governing equation for a large-scale system into repeated small-scale unit components. Critical physics modes are identified via proper orthogonal decomposition (POD) from small-scale unit component samples. The computationally expensive, high-fidelity discretization of the physics governing equation is then projected onto these modes to create a reduced order model (ROM) that retains essential physics details. The combination of DG-DD and POD enables ROMs to be used as building blocks comprised of unit components and interfaces, which can then be used to construct a global large-scale ROM without data at such large scales. This method is demonstrated on the Poisson and Stokes flow equations, showing that it can solve equations about 15−40 times faster with only ∼ 1% relative error, even at scales 1000 times larger than the unit components. This research is ongoing, with efforts to apply these methods to more complex physics such as Navier-Stokes equation, highlighting their potential for transitioning laboratory-scale technologies to practical industrial use.

More info : https://mfem.org/seminar/