SPECTRAL_METHOD

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Prediction of velocity and pressure of gas-liquid flow using spectrum-based physics-informed neural networks
《Applied Mathematics and Mechanics(English Edition)》2025年第2期341-356,共16页Nanxi DING Hengzhen FENG H.Z.LOU Shenghua FU Chenglong LI Zihao ZHANG Wenlong MA Zhengqian ZHANG 
Supported by the National Natural Science Foundation of China(No.62304022)。
This research introduces a spectrum-based physics-informed neural network(SP-PINN)model to significantly improve the accuracy of calculation of two-phase flow parameters,surpassing existing methods that have limitatio...
关键词：physics-informed neural network(PINN) spectral method two-phase flow parameter prediction 
Improved error estimates for a modified exponential Euler method for the semilinear stochastic heat equation with rough initial data
《Science China Mathematics》2024年第12期2873-2898,共26页Xinping Gui Buyang Li Jilu Wang 
supported by National Natural Science Foundation of China(Grant Nos.12071020,12131005 and U2230402);the Research Grants Council of Hong Kong(Grant No.Poly U15300519);an Internal Grant of The Hong Kong Polytechnic University(Grant No.P0038843,Work Programme:ZVX7)。
A class of stochastic Besov spaces BpL^(2)(Ω;˙H^(α)(O)),1≤p≤∞andα∈[−2,2],is introduced to characterize the regularity of the noise in the semilinear stochastic heat equation du−Δudt=f(u)dt+dW(t),under the fol...
关键词：semilinear stochastic heat equation additive noise space-time white noise exponential Euler method spectral method strong convergence stochastic Besov space real interpolation 
An accurate and efficient space-time Galerkin spectral method for the subdiffusion equation
《Science China Mathematics》2024年第10期2387-2408,共22页Wei Zeng Chuanju Xu 
supported by National Natural Science Foundation of China (Grant No. 11971408)。
In this paper, we design and analyze a space-time spectral method for the subdiffusion equation.Here, we are facing two difficulties. The first is that the solutions of this equation are usually singular near the init...
关键词：subdiffusion equations variable transformation Ψ-Sobolev spaces WELL-POSEDNESS space-time Galerkin spectral method error estimate fast algorithm 
EFFICIENT SPECTRAL METHODS FOR EIGENVALUE PROBLEMS OF THE INTEGRAL FRACTIONAL LAPLACIAN ONABALLOFANYDIMENSION
《Journal of Computational Mathematics》2024年第4期1032-1062,共31页Suna Ma Huiyuan Li Zhimin Zhang Hu Chen Lizhen Chen 
supported by the National Natural Science Foundation of China(Grant No.12101325)and by the NUPTSF(Grant No.NY220162);The second author was supported by the National Natural Science Foundation of China(Grant Nos.12131005,11971016);The third author was supported by the National Natural Science Foundation of China(Grant No.12131005);The fifth author was supported by the National Natural Science Foundation of China(Grant Nos.12131005,U2230402).
An efficient spectral-Galerkin method for eigenvalue problems of the integral fractional Laplacian on a unit ball of any dimension is proposed in this paper.The symmetric positive definite linear system is retained ex...
关键词：Integral fractional Laplacian Spectral method Eigenvalue problem Regularity analysis Error estimate 
Effect of fore/aft-loaded rotor on compressor stability under inlet circumferential distortion
《Chinese Journal of Aeronautics》2024年第5期199-213,共15页Dakun SUN Benhao GU Fangfei NING Dengke XU Xiaofeng SUN 
The research presented here was supported by the National Natural Science Foundation of China(Nos.52306036 and 52325602);the Science Center for Gas Turbine Project,China(Nos.P2022-A-II-002-001 and P2022-C-II-003-001);the Project funded by China Postdoctoral Science Foundation(No.2022M720346);the National Science and Technology Major Projectc,China(Nos.Y2022-II-0003-0006 and Y2022-II-0002-0005);Also,the research is supported by the Key Laboratory of Pre-Research Management Centre,China(No.6142702200101);the Fundamental Research Funds for the Central Universities,China(Nos.YWF-23-Q-1009 and YWF-23-Q-1065).
A modified small perturbation stability prediction model for axial compressors with circumferential inlet distortions is established and applied to investigate the effect of fore/aft-loaded rotor on compressor stabili...
关键词：Axial compressor stability Inlet distortion Blade loading Small perturbation Time-space spectral method 
A Novel Error Analysis of Spectral Method for the Anomalous Subdiffusion Problems with Multi-term Time-fractional Derivative
《Acta Mathematicae Applicatae Sinica》2023年第4期943-961,共19页Bo TANG Yan-ping CHEN Bin XIE Xiu-xiu LIN 
supported by the State Key Program of National Natural Science Foundation of China(Nos.11931003);National Natural Science Foundation of China(Nos.41974133)。
This paper aims to extend a space-time spectral method to address the multi-term time-fractional subdiffusion equations with Caputo derivative. In this method, the Jacobi polynomials are adopted as the basis functions...
关键词：space-time spectral methods multi-term time-fractional WELL-POSEDNESS a posteriori error estimates 
Efficient Finite Difference/Spectral Method for the Time Fractional Ito Equation Using Fast Fourier Transform Technic
《Communications on Applied Mathematics and Computation》2023年第4期1591-1600,共10页Dakang Cen Zhibo Wang Seakweng Vong 
the National Natural Science Foundation of China(No.11701103);the Young Top-notch Talent Program of Guangdong Province of China(No.2017GC010379);the Natural Science Foundation of Guangdong Province of China(No.2022A1515012147);the Project of Science and Technology of Guangzhou of China(No.202102020704);the Opening Project of Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University of China(2021023);the Science and Technology Development Fund,Macao SAR(File No.0005/2019/A);the University of Macao of China(File Nos.MYRG2020-00035-FST,MYRG2018-00047-FST).
A finite difference/spectral scheme is proposed for the time fractional Ito equation.The mass conservation and stability of the numerical solution are deduced by the energy method in the L^(2)norm form.To reduce the c...
关键词：Time fractional Ito equation Finite difference method Spectral method STABILITY 
A Spectral Segmentation Method for Large Meshes
《Communications in Mathematics and Statistics》2023年第3期583-607,共25页Xiaohan Bao Weihua Tong Falai Chen 
supported by the National Natural Science Foundation of China(Nos.61877056,61972368);the Anhui Provincial Natural Science Foundation,PR China(No.1908085QA11).
Mesh segmentation is a fundamental and critical task in mesh processing,and it has been studied extensively in computer graphics and geometric modeling communities.However,current methods are not well suited for segme...
关键词：Mesh segmentation Spectral method Progressive mesh Feature-aware simplification Geodesic curvature flow 
A Priori Error Estimates for Spectral Galerkin Approximations of Integral State-Constrained Fractional Optimal Control Problems
《Advances in Applied Mathematics and Mechanics》2023年第3期568-582,共15页Juan Zhang Jiabin Song Huanzhen Chen 
This work was partly supported by National Natural Science Foundation of China(Grant Nos.:12101283,12271233 and 12171287);Natural Science Foundation of Shandong Province(Grant Nos.:ZR2019YQ05,2019KJI003,and ZR2016JL004).
The fractional optimal control problem leads to significantly increased computational complexity compared to the corresponding classical integer-order optimal control problem,due to the global properties of fractional...
关键词：Fractional optimal control problem state constraint spectral method Jacobi polynomial a priori error estimate 
Modified Legendre Rational Spectral Method for Burgers Equation on the Whole Line
《Journal of Mathematical Study》2022年第4期415-431,共17页Liutao Tian Yujian Jiao 
supported in part by the National Natural Science Foundation of China(Grant Nos.12271365,11771299 and 12171141);Nature Science Fundation of Shanghai(Grant Nos.22ZR1445400 and 20JC1413800).
In this paper,we propose a spectral method for the Burgers equation using the modified Legendre rational functions,and prove its generalized stability and convergence.Numerical results demonstrate the efficiency of th...
关键词：Burgers equation spectral method modified Legendre rational functions problem on the whole line 
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