A bi-fidelity stochastic collocation method for transport equations with diffusive scaling and multi-dimensional random inputs

In this paper, we consider the development of efficient numerical methods for linear transport equations with random parameters and under diffusive scaling. We extend to present case bi-fidelity stochastic collocation method introduced in [33], [50], [51]. For high-fidelity model, asymptotic-preserving scheme [29] is used each sample. employ simple two-velocity Goldstein-Taylor equation as low-fidelity model accelerate convergence uncertainty quantification process. The choice motivated by fact that both models, high fidelity low fidelity, share same diffusion limit. Speed-up achieved proper selection points reasonable approximation solution. Extensive experiments are conducted show efficiency accuracy proposed method, even non regimes, empirical error bound estimations studied [16].