吴树林，教授、博士研究生导师，入选国家高层次青年人才计划。1984年10月出生于河南省固始县，2010年5月毕业于华中科技大学，获计算数学专业博士学位，研究方向为发展方程快速算法设计、分析与应用。

主要从事发展方程Parallel-in-Time (PinT) 算法研究。研究贡献包括：提出了同步粗网格矫正策略，显著提升了经典PinT算法的加速效果；基于循环矩阵预处理及Fourier谱分解，提出了求解波动问题的新型PinT算法ParaDiag。 ParaDiag具有网格尺寸无关的快速稳健收敛速度，克服了传统PinT算法求解波动问题面临的本质困难。2020年5月，ParaDiag算法获得PinT科学委员会授权，在该领域官方网站推广宣传 (http://parallel-in-time.org/methods/paradiag)。

两次获得PinT年会大会报告邀请（PinT-2018, 法国CNRS研究中心，邀请人：欧洲科学院院士Yvon Maday； PinT-2022, 法国马赛，邀请人：法国国际数学研究中心主任Pascal Hubert教授)。研究成果得到多位知名学者引用和正面评价。

2023年10月，应邀为《Acta Numerica》(数值年鉴)撰写PinT方向综述性论文。

2024年7月，应邀在国家天元数学东北中心讲授暑期学校课程：Parallel-in-Time (PinT) numerical computation (https://mp.weixin.qq.com/s/w3m6U84YM4zUBeb0wrX-sw)。

代表性论文 (*为通讯作者)

[--] Martin Gander, Shu-Lin Wu*, Tao, Zhou. Time parallelization for hyperbolic and parabolic problems. Acta Numerica, to appear in Vol 4, 2025

[37] Lu Xu and Shu-Lin Wu*. Stability of time-marching MPS–MFS for wave equations. Journal of Scientific Computing, to appear (10.1007/s10915-024-02704-0)

[36] Shu-Lin Wu and Tao Zhou. Convergence analysis of parareal algorithm with non-uniform fine time grid. SIAM Journal on Numerical Analysis, Vol. 62, No. 5, 2024

[35] Shu-Lin Wu, Zhiyong Wang and Tao Zhou. PinT Preconditioner for forward-backward evolutionary equations. SIAM Journal on Matrix Analysis and Applications, Vol. 44, No. 4, pp. 1771-1798, 2023.

[34] Xiaoqiang Yue, Zhiyong Wang and Shu-Lin Wu*. Convergence analysis of a mixed precision parareal algorithm. SIAM Journal on Scientific Computing,  Vol. 45, No. 5, pp. A2483-A2510, 2023.

[33] Jun Liu and Shu-Lin Wu*. Parallel-in-time preconditioner for the Sinc-Nystrom method. SIAM Journal on Scientific Computing, Vol. 44, No. 4, pp. A1510-A1540, 2022

[32] Shu-Lin Wu, Tao Zhou and Zhi Zhou*. A uniform spectral analysis for preconditioned all-at-once system from first-order and second-order evolutionary problems. SIAM Journal on Matrix Analysis and Applications, Vol. 43, No. 3, pp. 1331-1353, 2022

[31] Jun Liu, Xiansheng Wang, Shu-Lin Wu* and Tao Zhou. A well-conditioned direct PinT algorithm for first- and second-order evolutionary equations. Advances in Computational Mathematics, Vol. 48 (16), pp. 1-29, 2022

[30] Shu-Lin Wu and Tao Zhou*. Parallel implementation for the two-stage SDIRK methods via diagonalization. Journal of Computational Physics, Vol. 428, Article Number: 110076, 2021

[29] Jun Liu and Shu-Lin Wu*. A fast block α-circulant preconditoner for all-at-once systems from wave equations. SIAM Journal on Matrix Analysis and Applications, Vol. 41(4), pp. 1912-1943, 2020

[28] Shu-Lin Wu*, Tao Zhou, Xiaojun Chen. A Gauss-Seidel type method for dynamic nonlinear complementarity problems. SIAM Journal on Control and Optimization, Vol.58-6, pp. 3389-3412, 2020

[27] Martin Gander and Shu-Lin Wu*. A diagonalization-based parareal algorithm for dissipative and wave propagation problems. SIAM Journal on Numerical Analysis, Vol. 58, pp. 2981–3009, 2020

[26] Shu-Lin Wu and Jun Liu*. A parallel-in-time block-circulant preconditioner for optimal control of wave equations. SIAM Journal on Scientific Computing, Vol.42, pp. A1510-A1540, 2020

[25] Xian-Ming Gu and Shu-Lin Wu*. A parallel-in-time iterative algorithm for Volterra partial integro-differential problems with weakly singular kernel. Journal of Computational Physics, Vol. 417, pp. 109576, 2020

[24] Shu-Lin Wu and Tao Zhou*. Diagonalization-based parallel-in-time algorithms for parabolic PDE-constrained optimization problems. ESAIM Control Optimisation and Calculus of Variations, Vol. 26, pp. 88, 2020

[23] Shu-Lin Wu* and Tao Zhou. Acceleration of the two-level MGRIT algorithm via the diagonalization technique. SIAM Journal on Scientific Computing, Vol. 41(5), pp. A3421-A3448, 2019

[22] Martin Gander and Shu-Lin Wu*. Convergence analysis of a periodic-like waveform relaxation method for initial-value problems via the diagonalization technique. Numerische Mathematik，Vol. 143(2), pp. 489-527, 2019

[21] Shu-Lin Wu* and Chengming Huang. Asymptotic results of Schwarz waveform relaxation algorithm for time fractional Cable equations. Communications in Computational Physics, Vol. 25, pp. 390-415, 2019

[20] Shu-Lin Wu*. Towards parallel coarse grid correction for the parareal algorithm. SIAM Journal on Scientific Computing, Vol.40, pp. A1446–A1472, 2018

[19] Shu-Lin Wu*, Hui Zhang and Tao Zhou. Solving time-periodic fractional diffusion equations via diagonalization technique and multi-grid. Numerical Linear Algebra with Applications,Vol.25, e2178, 2018

[18] Shu-Lin Wu and Tao Zhou. Parareal algorithms with local time-integrators for time fractional differential equations. Journal of Computational Physics, Vol. 358, pp. 135-149, 2018

[17] Shu-Lin Wu* and Yingxiang Xu. Convergence analysis of Schwarz waveform relaxation with convolution transmission conditions. SIAM Journal on Scientific Computing, Vol. 39, pp. A890-A921, 2017

[16] Shu-Lin Wu* and Xiaojun Chen. A parallel iterative algorithm for differential linear complementarity problems. SIAM Journal on Scientific Computing, Vol.39, pp. A3040-A306, 2017

[15] Shu-Lin Wu* and Tao Zhou. Fast parareal iterations for fractional diffusion equations. Journal of Computational Physics, Vol. 329, pp. 210–226, 2017

[14] Shu-Lin Wu. Optimized overlapping Schwarz waveform relaxation for a class of time-fractional diffusion problems. Journal of Scientific Computing, Vol.72 (2), pp. 842–862, 2017

[13] Shu-Lin Wu* and Mohammad Al-Khaleel. Optimized waveform relaxation methods for RC circuits: discrete case. ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 51, pp. 209–223, 2017

[12] Shu-Lin Wu* and M. D. Al-Khaleel. Parameter optimization in waveform relaxation for fractional-order RC circuits. IEEE Transactions on Circuits and Systems I: Regular Papers, Vol. 64 (7), pp. 1781-1790, 2017

[11] Shu-Lin Wu. A second-order parareal algorithm for fractional PDEs. Journal of Computational Physics, Vol.307, pp. 280-290, 2016

[10] Shu-Lin Wu. Convergence analysis of Parareal-Euler algorithm for ODEs systems with complex eigenvalues. Journal of Scientific Computing, Vol. 67, pp. 644-668, 2016

[9] Shu-Lin Wu* and Tao Zhou. Convergence analysis of three parareal solvers. SIAM Journal on Scientific Computing, Vol.37, pp. A970–A992, 2015

[8] Shu-Lin Wu. Convergence analysis of some second-order Parareal algorithms. IMA Journal of Numerical Analysis, Vol.35, pp. 1315-1341, 2015

[7] Shu-Lin Wu* and Mohammad D. Al-Khaleel. Semi-discrete Schwarz waveform relaxation algorithms for reaction diffusion equations. BIT Numerical Mathematics, Vol. 54, pp. 831-866, 2014

[6] Shu-Lin Wu* and Ting-Zhu Huang. Schwarz waveform relaxation for a neutral functional partial differential equation model of lossless coupled transmission lines. SIAM Journal on Scientific Computing, Vol. 35, pp. A1161–A1191, 2013

[5] Shu-Lin Wu* and Ting-Zhu Huang. Quasi-optimized overlapping Schwarz waveform relaxation algorithm for PDEs with time-delay. Communications in Computational Physics, Vol.14, pp. 780-800, 2013

[4] 吴树林. Robin型离散Schwarz波形松弛算法的收敛性分析. 中国科学A—数学，Vol. 43, pp. 1-24, 2013

[3] Shu-Lin Wu*, Chengming Huang and Ting-Zhu Huang. Convergence analysis of the overlapping Schwarz methods for reaction diffusion with time-delay. IMA Journal of Numerical Analysis, Vol. 32, pp. 632-671, 2012

[2] Shu-Lin Wu* and Kelin Li. Exponential stability of static neural networks with time delay and impulses. IET Control Theory & Applications, Vol.5, pp. 943-951, 2011

[1] Shu-Lin Wu, Baochang Shi* and Chengming Huang. Parareal-Richardson algorithm for solving nonlinear ODEs and PDEs. Communications in Computational Physics, Vol. 6, pp. 883-902, 2009

湖北省优秀博士论文                                       2011

中国科协”青年人才托举工程“                       2016

四川省杰出青年基金                                       2016

国家数学天元东北中心”优秀青年学者“       2021

吉林省”青年拔尖人才“                                   2021

国家高层次青年人才                                      2023

研究工作得到以下基金资助（主持）

1.几类时间依赖微分方程 Parareal 算法收敛性研究（No. 12171080，2022.01-2025.12), 国家自然科学基金-面上项目

2.大规模延迟微分方程组卷积Schwarz波形松弛算法收敛性研究（No.11771313, 2018.01-2021.12),国家自然科学基金-面上项目

3.几类延迟常微分方程的 Schwarz 型波形松弛算法研究（No. 11301362, 2014.01-2016.12)，国家自然科学基金-青年基金

4.Robin 型离散 Schwarz 波形松弛算法的收敛性分析 (No. 11226312，2013.01-2013.12), 国家自然科学基金-数学天元基金

5.两类延迟微分方程的parareal算法收敛性分析（No. 2015M580777, 2015.09-2017.08)，中国博士后科学基金-面上项目(一等)

6.一类初值问题Parareal算法收敛性分析（No.2016T90841, 2016.09-2018.08), 中国博士后科学基金-特别资助

7.非局部演化大规模电路系统快速计算方法研究（No.2018JY0469, 20180.07-2021.07)，四川省科技厅面上项目

8.波传导方程新型时间并行算法研究（No.JC010284408, 2022.01-2024.12), 吉林省自然科学基金-自由探索类基础研究项目

(1) 波动方程时间并行计算方法
Parareal和MGRIT是一类时间层面的多格子算法，是当前时间并行计算研究领域最流行的算法，非常适用于发展方程的快速计算。Parareal、MGRIT及其相关算法对强耗散问题（如热传导问题）数值计算有显著加速效果。对弱耗散问题，如对流占优扩散方程，算法的收敛速度随耗散性的减弱持续变差。对纯波传导方程，如声波方程和Schrodinger方程，Parareal和MGRIT均不收敛。Diagonalization-in-time是课题组独立提出的一类全新时间并行计算方法（算法名称为ParaDiag)。基于国家天河-1号超算平台的大规模计算结果表明，该算法对耗散问题和纯波传导问题均有十分可观的加速效果，且加速比明显高于Parareal和MGRIT。近年来，我们针对几类具有代表性的波传导问题，获得了此类算法完整的谱分析和收敛速度估计，并得到了此类算法收敛性和Runge-Kutta方法稳定性之间的本质联系。

(2) 发展方程(Schwarz) Waveform Relaxation算法
此项研究关注的重点是设计卷积型-SOR迭代和卷积型传输条件，使得Waveform Relaxation算法具有常数收敛因子。我们主要感兴趣不同离散卷积公式对算法常数收敛因子的影响，以及在实际计算中如何快速实现离散卷积。

(3) 基于Laplace Inversion 技术的时间并行算法
这是一类天然并行的时间并行算法，且不受时间节点分布的影响。不足之处是此类算法只适用于纯线性耗散问题。我们致力于拓展此类时间并行算法在非线性问题中的应用。

(4) 带弱奇异核的Volterra 积分-微分方程快速算法
Volterra积分-微分方程是典型的非局部演化发展方程，实际计算需要大量存储空间和不断增加的计算时间。我们致力于探索不同卷积求积公式（特别是Lubich‘s fast convoltion quadratures)在该领域的可能应用，特别关于卷积求积公式和Parareal、Diagonalization-in-time等时间并行算法的结合。

(5) 动态互补问题（DLCP/DNCP）、时间依赖PDE约束优化问题时间并行算法
最优控制问题和互补问题是密切相关的两类问题，在一定数学背景下相互等价。时间依赖PDE约束最优控制问题数值计算通常需要求解一个大规模鞍点代数系统，DLCP/DNCP数值计算需要解决互补变量不光滑问题。我们致力于开发这两类密切相关问题的时间并行算法，并尝试所获结果在转换开关电路系统、期权定价、Signorini渗流问题、波方程优化控制等领域的可能应用。