Subspace Acceleration for a Sequence of Linear Systems and Application to Plasma Simulation
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| Format: | Preprint |
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2023
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| _version_ | 1866911817334259712 |
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| author | Guido, Margherita Kressner, Daniel Ricci, Paolo |
| author_facet | Guido, Margherita Kressner, Daniel Ricci, Paolo |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_02156 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Subspace Acceleration for a Sequence of Linear Systems and Application to Plasma Simulation Guido, Margherita Kressner, Daniel Ricci, Paolo Numerical Analysis Plasma Physics 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. |
| title | Subspace Acceleration for a Sequence of Linear Systems and Application to Plasma Simulation |
| topic | Numerical Analysis Plasma Physics |
| url | https://arxiv.org/abs/2309.02156 |