THE REDUCED BASIS TECHNIQUE AS A COARSE SOLVER FOR PARAREAL IN TIME SIMULATIONS

In this paper,we extend the reduced basis methods for parameter dependent problems to the parareal in time algorithm introduced by Lions et al.12] and solve a nonlinear evolutionary parabolic partial differential equation.The fine solver is based on the finite element method or spectral element method in space and a semi-implicit Runge-Kutta scheme in time.The coarse solver is based on a semi-implicit scheme in time and the reduced basis approximation in space.Offline-online procedures are developed,and it...