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abstract = {Solving multiscale diffusion problems is often computationally expensive due to the spatial and temporal discretization challenges arising from high-contrast coefficients. To address this issue, a partially explicit temporal splitting scheme is proposed. By appropriately constructing multiscale spaces, the spatial multiscale property is effectively managed, and it has been demonstrated that the temporal step size is independent of the contrast. To enhance simulation speed, we propose a parallel algorithm for the multiscale flow problem that leverages the partially explicit temporal splitting scheme. The idea is first to evolve the partially explicit system using a coarse time step size, then correct the solution on each coarse time interval with a fine propagator, for which we consider both the sequential solver and all-at-once solver. This procedure is then performed iteratively till convergence. We analyze the stability and convergence of the proposed algorithm. The numerical experiments demonstrate that the proposed algorithm achieves high numerical accuracy for high-contrast problems and converges in a relatively small number of iterations. The number of iterations stays stable as the number of coarse intervals increases, thus significantly improving computational efficiency through parallel processing.},
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author = {Zhengya Yang and Yating Wang and Wing Tat Leung},
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howpublished = {arXiv:2411.09244v1 [math.NA]},
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title = {Parallel in time partially explicit splitting scheme for high contrast multiscale problems},
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url = {http://arxiv.org/abs/2411.09244v1},
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year = {2024},
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}
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@article{YodaEtAl2024,
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author = {Yoda, Ryo and Bolten, Matthias and Nakajima, Kengo and Fujii, Akihiro},
abstract = {While recent advances in deep learning have shown promising efficiency gains in solving time-dependent partial differential equations (PDEs), matching the accuracy of conventional numerical solvers still remains a challenge. One strategy to improve the accuracy of deep learning-based solutions for time-dependent PDEs is to use the learned solution as the coarse propagator in the Parareal method and a traditional numerical method as the fine solver. However, successful integration of deep learning into the Parareal method requires consistency between the coarse and fine solvers, particularly for PDEs exhibiting rapid changes such as sharp transitions. To ensure such consistency, we propose to use the convolutional neural networks (CNNs) to learn the fully discrete time-stepping operator defined by the traditional numerical scheme used as the fine solver. We demonstrate the effectiveness of the proposed method in solving the classical and mass-conservative Allen-Cahn (AC) equations. Through iterative updates in the Parareal algorithm, our approach achieves a significant computational speedup compared to traditional fine solvers while converging to high-accuracy solutions. Our results highlight that the proposed Parareal algorithm effectively accelerates simulations, particularly when implemented on multiple GPUs, and converges to the desired accuracy in only a few iterations. Another advantage of our method is that the CNNs model is trained on trajectories-based on random initial conditions, such that the trained model can be used to solve the AC equations with various initial conditions without re-training. This work demonstrates the potential of integrating neural network methods into the parallel-in-time frameworks for efficient and accurate simulations of time-dependent PDEs.},
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author = {Yuwei Geng and Junqi Yin and Eric C. Cyr and Guannan Zhang and Lili Ju},
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howpublished = {arXiv:2510.07672v1 [math.NA]},
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title = {Parallel-in-Time Solution of Allen-Cahn Equations by Integrating Operator Learning into the Parareal Method},
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url = {http://arxiv.org/abs/2510.07672v1},
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year = {2025},
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}
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@unpublished{GriebelEtAl2025,
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abstract = {In this article, we present a parallel discretization and solution method for parabolic problems with a higher number of space dimensions. It consists of a parallel-in-time approach using the multigrid reduction-in-time algorithm MGRIT with its implementation in the library XBraid, the sparse grid combination method for discretizing the resulting elliptic problems in space, and a domain decomposition method for each of the subproblems in the combination method based on the space-filling curve approach. As a result, we obtain an extremely fast and embarrassingly parallel solver with excellent speedup and scale-up qualities, which is perfectly suited for parabolic problems with up to six space dimensions. We describe our new parallel approach and show its superior parallelization properties for the heat equation, the chemical master equation and some exemplary stochastic differential equations.},
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author = {Michael Griebel and Marc Alexander Schweitzer and Lukas Troska},
Before pushing you changes, create a `test.sh` file in this folder with this content :
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```sh
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#!/bin/bash
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BODY=""# -> put there the content of the issue
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python $SCRIPT_NAME -b "${BODY}"
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```
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- from github, copy-paste the issue body using the "..." icon and `Copy Markdown`
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- replace $SCRIPT_NAME by the script you want to test, like `issue_to_bibtex.py`, `arxiv_to_publications_correct.py`, ...
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Then, check that the modification of the `_bibliography/pint.bib` file is correct.
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You can commit the changes on the `pint.bib` file (done now, no need to do it again), or reset those and trigger the scripts on Github using the label manipulation on the issue (check if the whole pipeline works well).
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