From f92bf8f06f236e1d485e7ecfe5d48b54e55e0b5e Mon Sep 17 00:00:00 2001 From: pancetta Date: Thu, 4 Jan 2024 06:22:18 +0000 Subject: [PATCH] updated pint.bib using bibbot --- _bibliography/pint.bib | 9 +++++++++ 1 file changed, 9 insertions(+) diff --git a/_bibliography/pint.bib b/_bibliography/pint.bib index 8a13ed9d..a83f1528 100644 --- a/_bibliography/pint.bib +++ b/_bibliography/pint.bib @@ -6425,6 +6425,15 @@ @unpublished{DanieliEtAl2023 year = {2023}, } +@unpublished{Erlangga2023, + abstract = {This paper presents a parallel-in-time multilevel iterative method for solving differential algebraic equation, arising from a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.}, + author = {Yogi A. Erlangga}, + howpublished = {arXiv:2401.00228v1 [math.NA]}, + title = {Parallel-in-time Multilevel Krylov Methods: A Prototype}, + url = {http://arxiv.org/abs/2401.00228v1}, + year = {2023}, +} + @article{FangEtAl2023, author = {Liang Fang and Stefan Vandewalle and Johan Meyers}, doi = {10.1016/j.jcp.2023.111927},