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Mathematics > Numerical Analysis
Title: Subspace Acceleration for a Sequence of Linear Systems and Application to Plasma Simulation
(Submitted on 5 Sep 2023 (v1), last revised 28 Mar 2024 (this version, v3))
Abstract: We 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.
Submission history
From: Margherita Guido [view email][v1] Tue, 5 Sep 2023 11:48:37 GMT (1193kb)
[v2] Thu, 5 Oct 2023 09:20:03 GMT (1708kb)
[v3] Thu, 28 Mar 2024 17:26:32 GMT (944kb)
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