Merge pull request #1121 from Parallel-in-Time/bibtex-bibbot-1120-f270ff6

pint.bib updates

Author: pancetta

_bibliography/pint.bib

@@ -8546,6 +8546,20 @@ @article{AraujoEtAl2026
 	year = {2026},
 }
 
+@article{BhattEtAl2026,
+	author = {Bhatt, Rishabh and Debreu, Laurent and Vidard, Arthur},
+	doi = {10.1016/j.jcp.2026.115164},
+	issn = {0021-9991},
+	journal = {Journal of Computational Physics},
+	month = {Nov},
+	pages = {115164},
+	publisher = {Elsevier BV},
+	title = {Time-parallel incremental 4D-Var for two-dimensional rotating shallow water system},
+	url = {http://dx.doi.org/10.1016/j.jcp.2026.115164},
+	volume = {564},
+	year = {2026},
+}
+
 @unpublished{BoltenEtAl2026,
 	abstract = {In this work, the performance of different spectral deferred corrections (SDC) methods applied to initial value problems for differential-algebraic equations (DAEs) of index one is analyzed. The SDC method solves a series of correction equations, and after each iteration, the numerical solution is corrected by adding the obtained approximation of the error. The formulation of the SDC method allows for a parallelization across the method to obtain small-scale parallelism, for which a number of processes equal to the number of collocation nodes can be used. Recently, an analytical approach to finding optimal diagonal coefficients for parallel SDC was proposed. So far, no analysis with the new coefficients for parallel SDC applied to DAEs was done. We demonstrate that parallel SDC methods solve DAE problems with high accuracy faster than the associated sequential SDC schemes, obtaining speedup in a small-scale parallel regime.},
 	author = {Matthias Bolten and Lisa Wimmer},
@@ -8821,6 +8835,15 @@ @article{LinEtAl2026
 	year = {2026},
 }
 
+@unpublished{LinEtAl2026b,
+	abstract = {The parareal algorithm is one of the most widely studied parallel-in-time methods for the numerical approximation of time-dependent problems. For non-diffusive equations, however, standard parareal methods may converge slowly or even become unstable due to the absence of damping, while nonlinear interactions can transfer and amplify phase errors across Fourier modes. In this work, we consider the nonlinear Schrödinger equation (NLS) as a representative non-diffusive model and analyze parareal algorithms with an exact fine propagator, with particular emphasis on the design of suitable coarse propagators. We establish a general convergence framework, valid for solutions with limited regularity, under stability and local truncation error assumptions on the coarse propagator. These assumptions are verified for selected exponential low-regularity integrators designed for one-dimensional quadratic and cubic NLS equations, which achieve optimal approximation orders without derivative loss. To the best of our knowledge, this is the first construction of parareal algorithms for NLS equations that are provably linearly convergent, with a contraction factor proportional to the coarse time-step size even for solutions of limited regularity. Numerical experiments on quadratic, cubic, and quintic NLS equations demonstrate rapid convergence and improved performance over parareal variants using classical coarse propagators, including Lie and Strang splitting methods and first- and third-order exponential Runge--Kutta integrators.},
+	author = {Qingle Lin and Zhi Zhou},
+	howpublished = {arXiv:2607.00384v1 [math.NA]},
+	title = {Exponential Low-Regularity Parareal Algorithms for Nonlinear Schrödinger Equations},
+	url = {https://arxiv.org/abs/2607.00384v1},
+	year = {2026},
+}
+
 @unpublished{LuEtAl2026,
 	abstract = {Parabolic optimal control problems arise in numerous scientific and engineering applications. They typically lead to large-scale coupled forward-backward systems that cannot be treated with classical time-stepping schemes and are computationally expensive to solve. Therefore, parallel methods are essential to reduce the computational time required. In this work, we investigate a time domain decomposition approach, namely the time parallel Schwarz method, applied to parabolic optimal control problems. We analyze the convergence behavior and focus on the weak scalability property of this method as the number of time intervals increases. To characterize the spectral radius of the iteration matrix, we present two analysis techniques: the construction of a tailored matrix norm and the application of block Toeplitz matrix theory. Our analyses yield both nonasymptotic bounds on the spectral radius and an asymptotic characterization of the eigenvalues as the number of time intervals tends to infinity. Numerical experiments further confirm our theoretical findings and demonstrate the weak scalability of the time parallel Schwarz method. This work introduces the first theoretical tool for analyzing the weak scalability of time domain decomposition methods, and our results shed light on the suitability of our algorithm for large-scale simulations on modern high-performance computing architectures.},
 	author = {Liu-Di Lu and Tommaso Vanzan},