Merge pull request #807 from Parallel-in-Time/bibtex-bibbot-806-620de09

pint.bib updates

_bibliography/pint.bib

@@ -6951,6 +6951,18 @@ @unpublished{HeinzelreiterEtAl2024
 	year = {2024},
 }
 
+@article{HuangEtAl2024,
+	author = {Huang, Jianguo and Ju, Lili and Xu, Yuejin},
+	doi = {10.1002/num.23116},
+	issn = {1098-2426},
+	journal = {Numerical Methods for Partial Differential Equations},
+	month = {May},
+	publisher = {Wiley},
+	title = {A parareal exponential integrator finite element method for semilinear parabolic equations},
+	url = {http://dx.doi.org/10.1002/num.23116},
+	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 @unpublished{IbrahimEtAl2024,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},
@@ -7079,6 +7091,15 @@ @unpublished{SchnaubeltEtAl2024
 	year = {2024},
 }
 
+@unpublished{SouzaEtAl2024,
+	abstract = {Simulation of the monodomain equation, crucial for modeling the heart's electrical activity, faces scalability limits when traditional numerical methods only parallelize in space. To optimize the use of large multi-processor computers by distributing the computational load more effectively, time parallelization is essential. We introduce a high-order parallel-in-time method addressing the substantial computational challenges posed by the stiff, multiscale, and nonlinear nature of cardiac dynamics. Our method combines the semi-implicit and exponential spectral deferred correction methods, yielding a hybrid method that is extended to parallel-in-time employing the PFASST framework. We thoroughly evaluate the stability, accuracy, and robustness of the proposed parallel-in-time method through extensive numerical experiments, using practical ionic models such as the ten-Tusscher-Panfilov. The results underscore the method's potential to significantly enhance real-time and high-fidelity simulations in biomedical research and clinical applications.},
+	author = {Giacomo Rosilho de Souza and Simone Pezzuto and Rolf Krause},
+	howpublished = {arXiv:2405.19994v1 [math.NA]},
+	title = {High-order parallel-in-time method for the monodomain equation in cardiac electrophysiology},
+	url = {http://arxiv.org/abs/2405.19994v1},
+	year = {2024},
+}
+
 @unpublished{SterckEtAl2024,
 	abstract = {We consider the parallel-in-time solution of scalar nonlinear conservation laws in one spatial dimension. The equations are discretized in space with a conservative finite-volume method using weighted essentially non-oscillatory (WENO) reconstructions, and in time with high-order explicit Runge-Kutta methods. The solution of the global, discretized space-time problem is sought via a nonlinear iteration that uses a novel linearization strategy in cases of non-differentiable equations. Under certain choices of discretization and algorithmic parameters, the nonlinear iteration coincides with Newton's method, although, more generally, it is a preconditioned residual correction scheme. At each nonlinear iteration, the linearized problem takes the form of a certain discretization of a linear conservation law over the space-time domain in question. An approximate parallel-in-time solution of the linearized problem is computed with a single multigrid reduction-in-time (MGRIT) iteration. The MGRIT iteration employs a novel coarse-grid operator that is a modified conservative semi-Lagrangian discretization and generalizes those we have developed previously for non-conservative scalar linear hyperbolic problems. Numerical tests are performed for the inviscid Burgers and Buckley--Leverett equations. For many test problems, the solver converges in just a handful of iterations with convergence rate independent of mesh resolution, including problems with (interacting) shocks and rarefactions.},
 	author = {H. De Sterck and R. D. Falgout and O. A. Krzysik and J. B. Schroder},