081202-计算机软件与理论

并行算法与并行软件

1996-09--2001-07   上海大学   博士

-- 研究生

-- 博士

   

2011-06~现在, 中国科学院软件研究所, 研究员
2004-09~2010-05,中国科学院软件研究所, 副研究员
2003-08~2004-08,中国科学院软件研究所, 助理研究员
2001-08~2003-07,中国科学院软件研究所, 博士后

2019-08-31-2023-08-30,中国数学会, 理事

数值计算法
数值计算方法
快速傅里叶变换的理论算法与软件

   

[1] 孙乔, 李会元, 陈峰. 一种面向自主可控异构众核集群的高性能基因比对方法和系统. CN: CN116525008A, 2023-08-01.
[2] 赵玉文, 刘芳芳, 马文静, 李会元, 彭远驰. 基于浮点数压缩技术的大规模FFT实现方法及装置. CN: CN116502028A, 2023-07-28.
[3] 黎雷生, 马文静, 赵海涛, 孙家昶, 李会元. 一种适合复杂异构系统的HPL矩阵更新优化方法. CN: CN111913748A, 2020-11-10.

   

[1] Journal of Parallel and Distributed Computing. 2024,   通讯作者  
[2] Zijian Cao, Qiao Sun, Wenhao Yang, Changcheng Song, Zhe Wang, huiyuan@iscas.ac.cn. A novel HPL-AI approach for FP16-only accelerator and its instantiation on Kunpeng+Ascend AI-specific platform. Journal of Parallel and Distributed Computing[J]. 2024, 第 6 作者  通讯作者  190: 104884, 
[3] Li, Lin, Wang, LiLian, Li, Huiyuan. An Efficient Spectral Trust-Region Deflation Method for Multiple Solutions. JOURNAL OF SCIENTIFIC COMPUTING[J]. 2023, 95(1): http://dx.doi.org/10.1007/s10915-023-02154-0.
[4] Zhao Yuwen, Liu Fangfang, Ma Wenjing, Li Huiyuan, Peng Yuanchi, Wang Cui. MFFT: A GPU Accelerated Highly Efficient Mixed-Precision Large-Scale FFT Framework. ACM Transactions on Architecture and Code Optimization[J]. 2023, null(null): 
[5] Qiao Sun, Wenjing Ma, Huiyuan Li, Jiachang Sun. Evolving the HPL benchmark towards multi-GPGPU clusters. CCF Transactions on High Performance Computing[J]. 2023, 5: 84-96, 
[6] Li, Huiyuan, Liu, Ruiqing, Wang, LiLian. Efficient Hermite Spectral-Galerkin Methods for Nonlocal Diffusion Equations in Unbounded Domains. NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS[J]. 2022, 15(4): 1009-1040, http://sciencechina.cn/gw.jsp?action=detail.jsp&internal_id=7406363&detailType=1.
[7] Lueling Jia, Huiyuan Li, Zhimin Zhang. Sparse spectral-Galerkin method on an arbitrary tetrahedron using generalized Koornwinder polynomials. Journal of Scientific Computing[J]. 2022, 91(22): 
[8] Tiangong Zhang, Huiyuan Li, Zhongqing Wang. Efficientspace-time Jacobi rational spectral methods for second order time-dependent problems on unbounded domains. Applied Numerical Mathematics[J]. 2022, 176: 159-181, 
[9] 袁涛, 牛树梓, 李会元. 动态层次Transformer序列推荐算法. 中文信息学报[J]. 2022, 36(1): 117-126, http://lib.cqvip.com/Qikan/Article/Detail?id=7106890993.
[10] Jianwei Zhou, Huiyuan Li, Zhimin Zhang. A posteriori Error estimates of spectral approximations for second order partial dif- ferential equations in spherical geometries. Journal of Scientific Computing[J]. 2022, 90(56): 
[11] Lixiu Wang, huiyuan@iscas.ac.cn, Zhimin Zhang. H (curl2 )-conforming spectral element method for quad-curl problems. omput. Methods Appl. Math.[J]. 2021, 第 2 作者  通讯作者  
[12] Zhao, Hui, Li, Huiyuan, Zhao, Haitao, Li, Leisheng, Li, Jian. The Influence of Pipe Bending Curvature on H-2-O-2 Gaseous Detonation Wave Front. APPLIED SCIENCES-BASEL[J]. 2021, 11(9): http://dx.doi.org/10.3390/app11093951.
[13] 袁涛, Huiyuan Li, 牛树梓. Topological Interpretable Multi-scale Sequential Recommendation. Database Systems for Advanced Applications - 26th International Conference, DASFAA 2021. 2021, 
[14] Wang, Lixiu, Shan, Weikun, Li, Huiyuan, Zhang, Zhimin. H(curl(2))-conforming quadrilateral spectral element method for quad-curl problems. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES[J]. 2021, 31(10): 1951-1986, 
[15] 孙家昶, 李会元. 国产复杂异构高性能数值软件的研制与测试专题前言. 软件学报[J]. 2021, 32(8): 2287-2288, http://lib.cqvip.com/Qikan/Article/Detail?id=7105477909.
[16] Hao, Zhaopeng, Li, Huiyuan, Zhang, Zhimin, Zhang, Zhongqiang. SHARP ERROR ESTIMATES OF A SPECTRAL GALERKIN METHOD FOR A DIFFUSION-REACTION EQUATION WITH INTEGRAL FRACTIONAL LAPLACIAN ON A DISK. MATHEMATICS OF COMPUTATION[J]. 2021, 90(331): 2107-2135, http://dx.doi.org/10.1090/mcom/3645.
[17] 袁涛, 牛树梓, 李会元. 动态层次Transformer序列推荐算法. 中文信息学报[J]. 2021, 
[18] Pan, Jiajia, Li, Huiyuan. A penalized weak Galerkin spectral element method for second order elliptic equations. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS[J]. 2021, 386: http://dx.doi.org/10.1016/j.cam.2020.113228.
[19] Guo, Yichen, Jia, Lueling, Chen, Huajie, Li, Huiyuan, Zhang, Zhimin. A Mortar Spectral Element Method for Full-Potential Electronic Structure Calculations. COMMUNICATIONS IN COMPUTATIONAL PHYSICS[J]. 2021, 29(5): 1541-1569, https://www.webofscience.com/wos/woscc/full-record/WOS:000633053700009.
[20] 黎雷生, 杨文浩, 马文静, 张娅, 赵慧, 赵海涛, 李会元, 孙家昶. 复杂异构计算系统HPL优化研究. 软件学报[J]. 2021, 
[21] 黎雷生, 杨文浩, 马文静, 张娅, 赵慧, 赵海涛, 李会元, 孙家昶. 复杂异构计算系统HPL的优化. 软件学报[J]. 2021, 32(8): 2307-2318, 
[22] 袁涛, 牛树梓, 李会元. 一种基于CW-RNN的多时间尺度序列建模推荐算法. 中文信息学报[J]. 2020, 97-105, http://lib.cqvip.com/Qikan/Article/Detail?id=00002G4N4J507JP0MPDO3JP16JR.
[23] Lueling Jia, Huiyuan Li, Zhimin Zhang. Numerical analysis on the mortar spectral element methods for Schrödinger eigenvalue problem with an inverse square potential. APPLIED NUMERICAL MATHEMATICS. 2020, 158: 54-84, http://dx.doi.org/10.1016/j.apnum.2020.06.015.
[24] Pan, Jiajia, Li, Huiyuan. A new collocation method using near-minimal Chebyshev quadrature nodes on a square. APPLIED NUMERICAL MATHEMATICS[J]. 2020, 154: 104-128, http://dx.doi.org/10.1016/j.apnum.2020.03.017.
[25] 赵海涛, 孙家昶, 黎雷生, 杨文浩, 赵慧, 李会元. 适合一类复杂异构超算系统的HPL并行计算模型研究. 数据与计算发展前沿[J]. 2020, 2(1): 85-92, http://www.jfdc.cnic.cn/CN/10.11871/jfdc.issn.2096-742X.2020.01.007.
[26] Jia, Lueling, Li, Huiyuan, Zhang, Zhimin. Numerical analysis on the mortar spectral element methods for Schrodinger eigenvalue problem with an inverse square potential. APPLIED NUMERICAL MATHEMATICS[J]. 2020, 158: 54-84, http://dx.doi.org/10.1016/j.apnum.2020.06.015.
[27] An, Jing, Li, Huiyuan, Zhang, Zhimin. Spectral-Galerkin approximation and optimal error estimate for biharmonic eigenvalue problems in circular/spherical/elliptical domains. NUMERICAL ALGORITHMS[J]. 2020, 84(2): 427-455, http://dx.doi.org/10.1007/s11075-019-00760-4.
[28] Zhang, Jing, Li, Huiyuan, Wang, LiLian, Zhang, Zhimin. Ball prolate spheroidal wave functions in arbitrary dimensions. APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS[J]. 2020, 48(2): 539-569, http://dx.doi.org/10.1016/j.acha.2018.08.001.
[29] Huiyuan Li, Weikun Shan, Zhimin Zhang. C1-Conforming Quadrilateral Spectral Element Method for Fourth-Order Equations. 应用数学与计算数学学报(英文)[J]. 2019, 1(3): 403-434, http://lib.cqvip.com/Qikan/Article/Detail?id=7002991301.
[30] 金钟, 陆忠华, 李会元, 迟学斌, 孙家昶. 高性能计算之源起——科学计算的应用现状及发展思考. 中国科学院院刊[J]. 2019, 625-639, http://lib.cqvip.com/Qikan/Article/Detail?id=75898988504849574854484854.
[31] Liu, Yuan, Yu, Xuhong, Wang, Zhongqing, Li, Huiyuan. Hermite-Sobolev orthogonal functions and spectral methods for second- and fourth-order problems on unbounded domains. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS[J]. 2019, 96(5): 950-970, http://dx.doi.org/10.1080/00207160.2018.1474208.
[32] Liu, Wenjie, Wang, LiLian, Li, Huiyuan. OPTIMAL ERROR ESTIMATES FOR CHEBYSHEV APPROXIMATIONS OF FUNCTIONS WITH LIMITED REGULARITY IN FRACTIONAL SOBOLEV-TYPE SPACES. MATHEMATICS OF COMPUTATION[J]. 2019, 88(320): 2857-2895, 
[33] Xuhong Yu, Zhongqing Wang, Huiyuan Li. Jacobi-Sobolev Orthogonal Polynomialsand Spectral Methods for Elliptic Boundary Value Problems. 应用数学与计算数学学报(英文)[J]. 2019, 1(2): 283-308, http://lib.cqvip.com/Qikan/Article/Detail?id=7002437975.
[34] Zhang, Chao, Yao, Hanfeng, Li, Huiyuan. New space-time spectral and structured spectral element methods for high order problems. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS[J]. 2019, 351: 153-166, http://dx.doi.org/10.1016/j.cam.2018.08.038.
[35] Ma, Suna, Li, Huiyuan, Zhang, Zhimin. NOVEL SPECTRAL METHODS FOR SCHRODINGER EQUATIONS WITH AN INVERSE SQUARE POTENTIAL ON THE WHOLE SPACE. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B[J]. 2019, 24(4): 1589-1615, http://dx.doi.org/10.3934/dcdsb.2018221.
[36] Li, Jingliang, Ma, Heping, Li, Huiyuan. A triangular spectral element method for elliptic and Stokes problems. APPLIED MATHEMATICS AND COMPUTATION[J]. 2018, 321: 195-208, http://dx.doi.org/10.1016/j.amc.2017.10.025.
[37] Ma, Suna, Li, Huiyuan, Zhang, Zhimin. Efficient Spectral Methods for Some Singular Eigenvalue Problems. JOURNAL OF SCIENTIFIC COMPUTING[J]. 2018, 77(1): 657-688, http://dx.doi.org/10.1007/s10915-018-0721-y.
[38] Li, JingMin, Wang, ZehongQing, Li, HuiYuan. FULLY DIAGONALIZED CHEBYSHEV SPECTRAL METHODS FOR SECOND AND FOURTH ORDER ELLIPTIC BOUNDARY VALUE PROBLEMS. INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING[J]. 2018, 15(1-2): 243-259, http://apps.webofknowledge.com/CitedFullRecord.do?product=UA&colName=WOS&SID=5CCFccWmJJRAuMzNPjj&search_mode=CitedFullRecord&isickref=WOS:000428719500014.
[39] Ai, Qing, Li, Huiyuan, Wang, Zhongqing. Diagonalized Legendre spectral methods using Sobolev orthogonal polynomials for elliptic boundary value problems. APPLIED NUMERICAL MATHEMATICS[J]. 2018, 127: 196-210, http://dx.doi.org/10.1016/j.apnum.2018.01.003.
[40] Huiyuan Li. Efficient spectral and spectral element methods for eigenvlaue problems of Schrodinger equations with an inverse square potential. SIAM Journal on Scientific Computing. 2017, 
[41] Liu, Fujun, Li, Huiyuan, Wang, Zhongqing. Spectral methods using generalized Laguerre functions for second and fourth order problems. NUMERICAL ALGORITHMS[J]. 2017, 75(4): 1005-1040, http://dx.doi.org/10.1007/s11075-016-0228-2.
[42] Zhao, Jia, Li, Huiyuan, Wang, Qi, Yang, Xiaofeng. Decoupled Energy Stable Schemes for a Phase Field Model of Three-Phase Incompressible Viscous Fluid Flow. JOURNAL OF SCIENTIFIC COMPUTING[J]. 2017, 70(3): 1367-1389, https://www.webofscience.com/wos/woscc/full-record/WOS:000394326400017.
[43] Li, Huiyuan, Zhang, Zhimin. EFFICIENT SPECTRAL AND SPECTRAL ELEMENT METHODS FOR EIGENVALUE PROBLEMS OF SCHRODINGER EQUATIONS WITH AN INVERSE SQUARE POTENTIAL. SIAM JOURNAL ON SCIENTIFIC COMPUTING[J]. 2017, 39(1): A114-A140, http://dx.doi.org/10.1137/16M1069596.
[44] Zhang Jing, Wang LiLian, Li Huiyuan, Zhang Zhimin. Optimal Spectral Schemes Based on Generalized Prolate Spheroidal Wave Functions of Order $$-1$$ - 1. JOURNAL OF SCIENTIFIC COMPUTING[J]. 2017, 
[45] Shan, Weikun, Li, Huiyuan. THE TRIANGULAR SPECTRAL ELEMENT METHOD FOR STOKES EIGENVALUES. MATHEMATICS OF COMPUTATION[J]. 2017, 86(308): 2579-2611, https://www.webofscience.com/wos/woscc/full-record/WOS:000404567600002.
[46] Zhang, Jing, Wang, LiLian, Li, Huiyuan, Zhang, Zhimin. Optimal Spectral Schemes Based on Generalized Prolate Spheroidal Wave Functions of Order-1. JOURNAL OF SCIENTIFIC COMPUTING[J]. 2017, 70(2): 451-477, http://dx.doi.org/10.1007/s10915-016-0253-2.
[47] Zhang, Chao, Gu, Dongqin, Wang, Zhongqing, Li, Huiyuan. Efficient Space-Time Spectral Methods for Second-Order Problems on Unbounded Domains. JOURNAL OF SCIENTIFIC COMPUTING[J]. 2017, 72(2): 679-699, https://www.webofscience.com/wos/woscc/full-record/WOS:000406014800010.
[48] Liu, FuJun, Wang, ZhongQing, Li, HuiYuan. A fully diagonalized spectral method using generalized Laguerre functions on the half line. ADVANCES IN COMPUTATIONAL MATHEMATICS[J]. 2017, 43(6): 1227-1259, http://dx.doi.org/10.1007/s10444-017-9522-3.
[49] Huiyuan Li. Efficient spacet-time spectral methods for second-order problems on unbounded domains. Journal of Scientific Computing. 2017, 
[50] 单炜琨, 李会元. 双调和算子特征值问题的混合三角谱元方法. 计算数学[J]. 2017, 39(1): 81-97, https://d.wanfangdata.com.cn/periodical/jssx201701008.
[51] Huiyuan Li. Fully diagonalized Chebyshev spectral methods for second and fourth order elliptic boundary value problem. International Journal of Numerical Analysis and Modeling. 2017, 
[52] 单炜琨, 李会元. 任意三角形Laplace特征值问题谱方法的数值对比研究. 数值计算与计算机应用[J]. 2015, 36(2): 113-131, http://sciencechina.cn/gw.jsp?action=detail.jsp&internal_id=5452032&detailType=1.
[53] Li Huiyuan. Hexagonal Fourier-Galerkin Methods for the Two-Dimensional Homogeneous Isotropic Decaying Turbulence. JOURNAL OF MATHEMATICAL STUDY[J]. 2014, 47(1): 21-46, 
[54] Li, Huiyuan, Xu, Yuan. SPECTRAL APPROXIMATION ON THE UNIT BALL. SIAM JOURNAL ON NUMERICAL ANALYSIS[J]. 2014, 52(6): 2647-2675, https://www.webofscience.com/wos/woscc/full-record/WOS:000346842100003.
[55] Li, Huiyuan, Ma, Heping, Sun, Weiwei. LEGENDRE SPECTRAL GALERKIN METHOD FOR ELECTROMAGNETIC SCATTERING FROM LARGE CAVITIES. SIAM JOURNAL ON NUMERICAL ANALYSIS[J]. 2013, 51(1): 353-376, http://www.corc.org.cn/handle/1471x/2286510.
[56] Yang, Xiaofeng, Forest, M Gregory, Li, Huiyuan, Liu, Chun, Shen, Jie, Wang, Qi, Chen, Falai. Modeling and simulations of drop pinch-off from liquid crystal filaments and the leaky liquid crystal faucet immersed in viscous fluids. JOURNAL OF COMPUTATIONAL PHYSICS[J]. 2013, 236: 1-14, http://dx.doi.org/10.1016/j.jcp.2012.10.042.
[57] 李会元, 乔海军. 六边形Fourier谱方法. 应用数学与计算数学学报[J]. 2013, 147-162, http://lib.cqvip.com/Qikan/Article/Detail?id=45155439.
[58] Samson, Michael Daniel, Li, Huiyuan, Wang, LiLian. A new triangular spectral element method I: implementation and analysis on a triangle. NUMERICAL ALGORITHMS[J]. 2013, 64(3): 519-547, http://dx.doi.org/10.1007/s11075-012-9677-4.
[59] Li, Huiyuan, Sun, Jiachang, Xu, Yuan. Discrete Fourier Analysis and Chebyshev Polynomials with G(2) Group. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS[J]. 2012, 8: https://doaj.org/article/183e934d863b4b33a73a2d2e92666354.
[60] 李会元. 六边形区域 Fourier 谱方法. 应用数学与计算数学学报. 2012, 
[61] 陈家杰, 李会元, 张先轶. 六边形区域快速傅里叶变换的CUDA—MPI算法及其实现. 数值计算与计算机应用[J]. 2012, 33(1): 59-72, http://lib.cqvip.com/Qikan/Article/Detail?id=40981820.
[62] Li Youyun, Wang LiLian, Li Huiyuan, Ma Heping. A new spectral method on triangles. LECTURE NOTES IN COMPUTATIONAL SCIENCE AND ENGINEERING. 2011, 237-246, http://www.corc.org.cn/handle/1471x/2306186.
[63] Li Youyun, Wang LiLian, Li Huiyuan, Ma Heping. A new spectral method on triangles. LECTURE NOTES IN COMPUTATIONAL SCIENCE AND ENGINEERING. 2011, 237-246, http://www.corc.org.cn/handle/1471x/2306186.
[64] 纪园园, 李会元. 非线性守恒律高阶谱粘性法的收敛性. 应用数学与计算数学学报[J]. 2011, 25(2): 224-234, http://lib.cqvip.com/Qikan/Article/Detail?id=40374858.
[65] Li, Huiyuan, Sun, Jiachang, Xu, Yuan. Discrete Fourier analysis with lattices on planar domains. NUMERICAL ALGORITHMS[J]. 2010, 55(2-3): 279-300, http://dx.doi.org/10.1007/s11075-010-9388-7.
[66] Huiyuan Li. Discrete Fourier analysis on fundamental domain of Ad lattice and on simplex in d-variables. Journal of Fourier Analysis and its Applications. 2010, 
[67] 余元, 张云泉, 李会元. 一类非张量积区域快速傅立叶变换算法在匡产并行机上的可扩展性测试. 数值计算与计算机应用[J]. 2010, 123-130, http://lib.cqvip.com/Qikan/Article/Detail?id=34240138.
[68] Li, Huiyuan, Wang, LiLian. A SPECTRAL METHOD ON TETRAHEDRA USING RATIONAL BASIS FUNCTIONS. INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING[J]. 2010, 7(2): 330-355, https://www.webofscience.com/wos/woscc/full-record/WOS:000279261800008.
[69] Li, Huiyuan, Xu, Yuan. Discrete Fourier Analysis on Fundamental Domain and Simplex of A (d) Lattice in d-Variables. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS[J]. 2010, 16(3): 383-433, http://dx.doi.org/10.1007/s00041-009-9106-9.
[70] 余元, 张云泉, 李会元. 一类非张量积区域快速傅立叶变换算法在国产并行机上的可扩展性测试. 数值计算与计算机应用[J]. 2010, 31(2): 123-130, 
[71] 李会元. 一类非张量积区域快速傅里叶变换算法在国产并行机上的可扩展测试. 数值数学与计算机应用. 2010, 
[72] Li, Huiyuan, Shen, Jie. OPTIMAL ERROR ESTIMATES IN JACOBI-WEIGHTED SOBOLEV SPACES FOR POLYNOMIAL APPROXIMATIONS ON THE TRIANGLE. MATHEMATICS OF COMPUTATION[J]. 2010, 79(271): 1621-1646, https://www.webofscience.com/wos/woscc/full-record/WOS:000279776900014.
[73] Li, Huiyuan, Sun, Jiachang, Xu, Yuan. Discrete fourier analysis with lattices on planar domains. 2nd Dolomites Workshop on Constructive Approximation and Applications (DWCAA09). 2010, 279-300, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000281792800010&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=3a85505900f77cc629623c3f2907beab.
[74] Huiyuan Li. Chebyshev-Legendre spectral method for solving the two-dimensional vorticity equations with homogeneous Dirichelte conditions. Numerical Methods for Partial Differential Equations. 2009, 
[75] Li, Huiyuan, Sun, Jiachang, Xu, Yuan. Cubature Formula and Interpolation on the Cubic Domain. NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS[J]. 2009, 2(2): 119-152, http://apps.webofknowledge.com/CitedFullRecord.do?product=UA&colName=WOS&SID=5CCFccWmJJRAuMzNPjj&search_mode=CitedFullRecord&isickref=WOS:000274152900001.
[76] Li, Huiyuan, Xu, Yuan. DISCRETE FOURIER ANALYSIS ON A DODECAHEDRON AND A TETRAHEDRON. MATHEMATICS OF COMPUTATION[J]. 2009, 78(266): 999-1029, http://apps.webofknowledge.com/CitedFullRecord.do?product=UA&colName=WOS&SID=5CCFccWmJJRAuMzNPjj&search_mode=CitedFullRecord&isickref=WOS:000263026800015.
[77] 李明亮, 李会元, 孙家昶. 平行六边形区域非均匀节点快速傅立叶变换. 数值计算与计算机应用[J]. 2009, 58-69, http://lib.cqvip.com/Qikan/Article/Detail?id=29793087.
[78] Wu, Hua, Ma, Heping, Li, Huiyuan. Chebyshev-Legendre Spectral Method for Solving the Two-dimensional Vorticity Equations with Homogeneous Dirichlet Conditions. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS[J]. 2009, 25(3): 740-755, https://www.webofscience.com/wos/woscc/full-record/WOS:000265250000013.
[79] Huiyuan Li, Jiachang Sun, Yuan Xu. Cubature Formula and Interpolation on the Cubic Domain. 高等学校计算数学学报：英文版[J]. 2009, 2(2): 119-152, http://lib.cqvip.com/Qikan/Article/Detail?id=30856071.
[80] 李会元. 平行六边形区域非均匀节点快速傅里叶变换. 数值数学与计算机应用. 2009, 
[81] Shen, Jie, Wang, LiLian, Li, Huiyuan. A TRIANGULAR SPECTRAL ELEMENT METHOD USING FULLY TENSORIAL RATIONAL BASIS FUNCTIONS. SIAM JOURNAL ON NUMERICAL ANALYSIS[J]. 2009, 47(3): 1619-1650, https://www.webofscience.com/wos/woscc/full-record/WOS:000267745900002.
[82] Li, Huiyuan, Sun, Jiachang, Xu, Yuan. Discrete Fourier analysis, cubature, and interpolation on a hexagon and a triangle. SIAM JOURNAL ON NUMERICAL ANALYSIS[J]. 2008, 46(4): 1653-1681, http://dx.doi.org/10.1137/060671851.
[83] 马和平, 李会元. Super spectral viscosity method for nonlinear conservation laws. 上海大学学报：英文版[J]. 2006, 10(1): 9-14, http://lib.cqvip.com/Qikan/Article/Detail?id=21180672.
[84] Jingliang Li, Heping Ma, Huiyuan Li. A Triangular Spectral Element Method A Triangular Spectral Element Method for Elliptic and Stokes Problems. APPLIED MATHEMATICS AND COMPUTATION. http://dx.doi.org/10.1016/j.amc.2017.10.025.

   

（ 1 ） 高性能谱/谱元方法研究及其在多相复杂流体中的应用 , 负责人, 国家任务, 2015-01--2018-12
（ 2 ） 强非线性偏微分方程基于梯度重构的新型算法, 参与, 国家任务, 2015-01--2018-12
（ 3 ） 一类奇异与分数阶方程的新型谱方法, 负责人, 国家任务, 2019-01--2022-12
（ 4 ） 大规模数值模拟应用移植优化与平台集成, 负责人, 国家任务, 2019-01--2022-12
（ 5 ） 发展方程的tau-Chebyshev时空谱元方法, 参与, 国家任务, 2019-01--2022-12
（ 6 ） ARM硬件基础数学库-基础向量数学与统计学库优化合作项目, 负责人, 企业委托, 2021-01--2021-12
（ 7 ） HPC Benchmark 及加速库大颗粒项目, 负责人, 企业委托, 2020-09--2023-09
（ 8 ） 大规模数值模拟应用移植优化与平台集成, 负责人, 国家任务, 2021-12--2024-11
（ 9 ） 偏微分方程特征值问题的特征适应型算法与理论, 参与, 国家任务, 2022-01--2026-12

（1）A New Triangular Spectral Element Method   李会元、王立联等   2010-11-26
（2） A Legendre Spectral Method for the Electromagnetic Scattering from a   海峡两岸2010年计算数学学术研讨会    李会元、Weiwei Sun   2010-08-03
（3）Lattice DFT and multivariate cubature and interpolation   李会元、徐源   2009-07-06
（4）A direct spectral method on the ball and its optimal error estimate   李会元   2009-06-25

已指导学生

陈家杰  硕士研究生  081202-计算机软件与理论  

乔海军  硕士研究生  081202-计算机软件与理论  

任晓波  硕士研究生  081202-计算机软件与理论  

单炜琨  博士研究生  081202-计算机软件与理论  

袁涛  博士研究生  081202-计算机软件与理论  

潘佳佳  博士研究生  081202-计算机软件与理论  

李敏  博士研究生  081202-计算机软件与理论  

现指导学生

岳星言  博士研究生  081202-计算机软件与理论  

赵玉文  博士研究生  081202-计算机软件与理论  

薄震强  硕士研究生  085212-软件工程  

曹子健  博士研究生  081200-计算机科学与技术  

彭远驰  硕士研究生  085400-电子信息  

杨文浩  博士研究生  081200-计算机科学与技术  

苏子童  硕士研究生  085400-电子信息  

张宠  博士研究生  081200-计算机科学与技术  

王忠良  硕士研究生  081200-计算机科学与技术