We aim at a step change in numerical modeling for science and engineering by developing two methodologies: reduced-order models (ROMs) and hierarchical grid schemes.
- ROMs are small-dimensional mathematical models derived from the full set of PDEs governing the physical phenomenon. With this approach the solution space of the PDE is obtained from existing simulations or experimental data, realizing a convergence between the data and the modeling approach. With ROMs one counteracts the curse of dimension by significantly reducing the computational complexity.
- Hierarchical Cartesian numerical models allow the multi-scale solution of PDEs on non body-fitted meshes with a drastic reduction of the computational setup overhead. These methods are based on i) a monolithic multi-physics model; ii) implicit representation of the geometry via level sets; iii) octree hierarchical meshes. These methods are natively parallel and they can efficiently be mapped to high-performance computer architectures.
Thanks to these enablers it will be possible to transfer complexity handling from engineers to computers, providing fast, on-line numerical models for design and control.