pint.bib updates

_bibliography/pint.bib

@@ -6999,6 +6999,15 @@ @article{HuangEtAl2024
 	year = {2024},
 }
 
+@unpublished{HuangEtAl2024b,
+	abstract = {In this study, the $\theta$-method is used for discretizing a class of evolutionary partial differential equations. Then, we transform the resultant all-at-once linear system and introduce a novel one-sided preconditioner, which can be fast implemented in a parallel-in-time way. By introducing an auxiliary two-sided preconditioned system, we provide theoretical insights into the relationship between the residuals of the generalized minimal residual (GMRES) method when applied to both one-sided and two-sided preconditioned systems. Moreover, we show that the condition number of the two-sided preconditioned matrix is uniformly bounded by a constant that is independent of the matrix size, which in turn implies that the convergence behavior of the GMRES method for the one-sided preconditioned system is guaranteed. Numerical experiments confirm the efficiency and robustness of the proposed preconditioning approach.},
+	author = {Yuan-Yuan Huang and Po Yin Fung and Sean Y. Hon and Xue-Lei Lin},
+	howpublished = {arXiv:2408.03535v1 [math.NA]},
+	title = {An efficient preconditioner for evolutionary partial differential equations with $θ$-method in time discretization},
+	url = {http://arxiv.org/abs/2408.03535v1},
+	year = {2024},
+}
+
 @unpublished{IbrahimEtAl2024,
 	abstract = {Iterative parallel-in-time algorithms like Parareal can extend scaling beyond the saturation of purely spatial parallelization when solving initial value problems. However, they require the user to build coarse models to handle the inevitably serial transport of information in time.This is a time consuming and difficult process since there is still only limited theoretical insight into what constitutes a good and efficient coarse model. Novel approaches from machine learning to solve differential equations could provide a more generic way to find coarse level models for parallel-in-time algorithms. This paper demonstrates that a physics-informed Fourier Neural Operator (PINO) is an effective coarse model for the parallelization in time of the two-asset Black-Scholes equation using Parareal. We demonstrate that PINO-Parareal converges as fast as a bespoke numerical coarse model and that, in combination with spatial parallelization by domain decomposition, it provides better overall speedup than both purely spatial parallelization and space-time parallelizaton with a numerical coarse propagator.},
 	author = {Abdul Qadir Ibrahim and Sebastian Götschel and Daniel Ruprecht},