Guido, MargheritaKressner, DanielRicci, Paolo2024-06-052024-06-052024-06-052024-06-0110.1007/s10915-024-02525-1https://infoscience.epfl.ch/handle/20.500.14299/208327WOS:001220314000001We present an acceleration method for sequences of large-scale linear systems, such as the ones arising from the numerical solution of time-dependent partial differential equations coupled with algebraic constraints. We discuss different approaches to leverage the subspace containing the history of solutions computed at previous time steps in order to generate a good initial guess for the iterative solver. In particular, we propose a novel combination of reduced-order projection with randomized linear algebra techniques, which drastically reduces the number of iterations needed for convergence. We analyze the accuracy of the initial guess produced by the reduced-order projection when the coefficients of the linear system depend analytically on time. Extending extrapolation results by Demanet and Townsend to a vector-valued setting, we show that the accuracy improves rapidly as the size of the history increases, a theoretical result confirmed by our numerical observations. In particular, we apply the developed method to the simulation of plasma turbulence in the boundary of a fusion device, showing that the time needed for solving the linear systems is significantly reduced.Physical SciencesInitial GuessIterative SolversPartial Differential EquationsProjectionRandomized Linear AlgebraPlasma SimulationTokamaktext::journal::journal article::research article