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abstract = {This paper presents a parallel-in-time multilevel iterative method for solving differential algebraic equation, arising from a discretization of linear time-dependent partial differential equation. The core of the method is the multilevel Krylov method, introduced by Erlangga and Nabben~{\it [SIAM J. Sci. Comput., 30(2008), pp. 1572--1595]}. In the method, special time restriction and interpolation operators are proposed to coarsen the time grid and to map functions between fine and coarse time grids. The resulting Galerkin coarse-grid system can be interpreted as time integration of an equivalent differential algebraic equation associated with a larger time step and a modified $\theta$-scheme. A perturbed coarse time-grid matrix is used on the coarsest level to decouple the coarsest-level system, allowing full parallelization of the method. Within this framework, spatial coarsening can be included in a natural way, reducing further the size of the coarsest grid problem to solve. Numerical results are presented for the 1- and 2-dimensional heat equation using {\it simulated} parallel implementation, suggesting the potential computational speed-up of up to 9 relative to the single-processor implementation and the speed-up of about 3 compared to the sequential $\theta$-scheme.},
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author = {Yogi A. Erlangga},
@@ -6973,18 +6961,6 @@ @article{DravinsEtAl2024
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year = {2024},
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}
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@report{DrewsEtAl2024,
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author = {Drews, Wiebke and Turek, Stefan and Lohmann, Christoph},
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doi = {10.17877/DE290R-24129},
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journal = {Ergebnisberichte des Instituts für Angewandte Mathematik;670},
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keywords = {610},
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language = {en},
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publisher = {TU Dortmund},
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title = {Improving Convergence of Time-Simultaneous Multigrid Methods for Convection-Dominated Problems using VMS Stabilization Techniques},
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