Abstract:
We are interested in studying complex multi-scale systems that, in certain limits, are described by models of significantly less complexity and possibly with fewer uncertain parameters. Kinetic equations and their various fluid approximations are a prototypical example. Applications include radiation transport with linear/nonlinear diffusion limit, electron transport in materials with drift diffusion limit, or the Boltzmann equation with Euler/Navier-Stokes limit. These limits occur when collisions dominate the dynamics of the kinetic equation, but also in transition regimes (collisional, but not equilibrium), fluid models may have “reasonable accuracy”. We use this idea to design a two-level sampling strategy. Our approach is based on the sparse grid philosophy. Roughly speaking, balance deterministic and stochastic errors: sample the reduced model frequently, sample the full model sparingly. |