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An Extrapolation Cascadic MultigridMethod for Elliptic Problems on Reentrant Domains

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Advances in Applied Mathematics and Mechanics 2017年第6期9卷 1347-1363页

作者： kejia pan Dongdong He Chuanmiao Chen School of Mathematics and Statistics Central South UniversityChangshaHunan 410083China School of Aerospace Engineering and Applied Mechanics Tongji UniversityShanghai 200092China College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing(Ministry of Education of China)Hunan Normal UniversityChangshaHunan 410081China

This paper proposes an extrapolation cascadic multigrid(EXCMG)method to solve elliptic problems in domains with reentrant *** a class ofλ-graded meshes,we derive some new extrapolation formulas to construct a high-order approximation to the finite element solution on the next finer mesh using the numerical solutions on two-level of grids(current and previous grids).Then,this high-order approximation is used as the initial guess to reduce computational cost of the conjugate gradient *** application of this idea results in the EXCMG method proposed in this ***,numerical results for a crack problem and an L-shaped problem are presented to verify the efficiency and effectiveness of the proposed EXCMG method.

关键词： Richardson extrapolation Cascadicmultigrid gradedmesh elliptic problems corner singularity

Asymptotic expansions of finite element solutions to Robin problems in H^3 and their application in extrapolation cascadic multigrid method

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Science China Mathematics 2014年第4期57卷 687-698页

作者： HU HongLing CHEN ChuanMiao pan kejia College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China)Hunan Normal University School of Mathematics and Statistics Central South University Key Laboratory of Metallogenic Prediction of Nonferrous Metals Ministry of EducationSchool of Geosciences and Info-PhysicsCentral South University

For the Poisson equation with Robin boundary conditions,by using a few techniques such as orthogonal expansion(M-type),separation of the main part and the finite element projection,we prove for the first time that the asymptotic error expansions of bilinear finite element have the accuracy of O(h3)for u∈*** on the obtained asymptotic error expansions for linear finite elements,extrapolation cascadic multigrid method(EXCMG)can be used to solve Robin problems ***,by virtue of Richardson not only the accuracy of the approximation is improved,but also a posteriori error estimation is ***,some numerical experiments that confirm the theoretical analysis are presented.

关键词： finite element Richardson extrapolation Robin problem asymptotic expansion cascadic multi-grid method

The rapid densification behavior of powder metallurgy Ti alloys by induction heating sintering

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Journal of Materials Science & Technology 2024年第14期181卷 152-164页

作者： kejia pan Xiaotao Liu Bao Wang Shuai Gao Shixing Wu Ning Li State Key Laboratory of Materials Processing and Die&Mould Technology School of Materials Science and EngineeringHuazhong University of Science and TechnologyWuhan 430074China

Micropores are decisive to mechanical properties and thermal deformation capabilities of powder met-allurgy(P/M)Ti alloys sintered *** a result,achieving express densification is of prime im-portance and has attracted increasing attention *** heating owns the merits of high effi-ciency,short process,and low cost,and thus has huge potential to be used as a sintering approach for the fabrication of P/M Ti ***,the facilitated densification behavior associated with induction heating sintering remains unclear so *** address it,powder metallurgy Ti6Al4V is manufactured via induction heating sintering with which the underlying sintering mechanism is investigated *** is found that induction heating could generate a fully densified compact in a remarkably shortened time,demonstrating its superior sintering efficiency as compared with conventional resistance furnace *** finite element analysis reveals that the maximum current density during induction heating can reach 10^(6)A m^(–2)though the magnetic field strength is solely 0.02 T,leading to a slight tempera-ture difference of approximately 30℃between the interior and exterior of the ***,the rapid heating essentially starts at sharp corners of particles due to the potent current concentration ef-fect,which facilitates the cracking of the particle surface oxide film and thus enhances the direct contact between ***,the electromigration effect caused by induction current promotes the diffusion capability of elements,giving rise to expedited densification,alloying,and chemical *** work provides not only critical insight into the sintering mechanism of induction heating sintering but also significant guidance for low-cost powder metallurgy materials preparation.

关键词： Titanium alloy Powder metallurgy Induction heating sintering Radiation heating sintering Current field Simulation

A global mantle conductivity model derived from 8 years of Swarm satellite magnetic data

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Earth and Planetary Physics 2023年第1期7卷 49-56页

作者： HongBo Yao ZhengYong Ren kejia pan JingTian Tang KeKe Zhang Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring Ministry of Education(Central South University)Changsha 410083China Hunan Key Laboratory of Nonferrous Resources and Geological Hazards Exploration Central South UniversityChangsha 410083China School of Geosciences and Info-Physics Central South UniversityChangsha 410083China School of Mathematics and Statistics Central South UniversityChangsha 410083China State Key Laboratory of Lunar and Planetary Sciences Macao University of Science and TechnologyTaipaMacaoChina

Mantle conductivity imaging is one of the scientific goals of the forthcoming Macao Science Satellite-1(MSS-1).To achieve this goal,we develop a data analysis and inversion scheme for satellite magnetic data to probe global one-dimensional(1D)mantle conductivity *** this scheme,we present a new global mantle conductivity model by analyzing over 8 years of Swarm satellite magnetic ***,after sophisticated data selection procedures and the removal of core and crustal fields,the inducing and induced spherical harmonic coefficients of magnetic potential due to the magnetospheric ring current are ***,satellite Cresponses are estimated from the time series of these ***,the observed responses are inverted for both smooth and threejump conductivity models using a quasi-Newton *** obtained conductivity models are in general agreement with previous global mantle conductivity models.A comparison of our conductivity model with the laboratory conductivity model suggests the mean state of the upper mantle and transition zone is relatively *** scheme can be used to process the forthcoming Macao Science Satellite-1 magnetic data.

关键词： Macao Science Satellite-1 satellite magnetic data mantle conductivity global electromagnetic induction

New Sixth-Order Compact Schemes for Poisson/Helmholtz Equations

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Numerical Mathematics(Theory,Methods and Applications) 2023年第2期16卷 393-409页

作者： kejia pan Kang Fu Jin Li Hongling Hu Zhilin Li School of Mathematics and Statistics HNP-LAMACentral South UniversityChangsha 410083China MOE-LCSM School of Mathematics and StatisticsHunan Normal UniversityChangsha 410081China CRSC&Department of Mathematics North Carolina State UniversityRaleighNC 27695-8205USA

Some new sixth-order compact finite difference schemes for Poisson/Helmholtz equations on rectangular domains in both two-and three-dimensions are developed and *** from a few sixth-order compact finite difference schemes in the literature,the finite difference and weight coefficients of the new methods have analytic simple *** of the new ideas is to use a weighted combination of the source term at staggered grid points which is important for grid points near the boundary and avoids partial derivatives of the source ***,the new compact schemes are exact for 2D and 3D Poisson equations if the solution is a polynomial less than or equal to *** coefficient matrices of the new schemes are M-matrices for Helmholtz equations with wave number K≤0,which guarantee the discrete maximum principle and lead to the convergence of the new sixth-order compact *** examples in both 2D and 3D are presented to verify the effectiveness of the proposed schemes.

关键词： Poisson equation Helmholtz equation sixth-order compact scheme maximum principle staggered grid.

Extrapolation Cascadic Multigrid Method for Cell-Centered FV Discretization of Diffusion Equations with Strongly Discontinuous and Anisotropic Coefficients

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Communications in Computational Physics 2022年第5期31卷 1561-1584页

作者： kejia pan Xiaoxin Wu Yunlong Yu Zhiqiang Sheng Guangwei Yuan School of Mathematics and Statistics HNP-LAMACentral South UniversityChangsha 410083P.R.China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijing 100088P.R.China

Extrapolation cascadic multigrid(EXCMG)method with conjugate gradient smoother is very efficient for solving the elliptic boundary value problems with linearfinite element ***,it is not trivial to generalize the vertex-centred EXCMG method to cell-centeredfinite volume(FV)methods for diffusion equations with strongly discontinuous and anisotropic coefficients,since a non-nested hierarchy of grid nodes are used in the cell-centered *** cell-centered FV schemes,the vertex values(auxiliary unknowns)need to be approximated by cell-centered ones(primary unknowns).One of the novelties is to propose a new gradient transfer(GT)method of interpolating vertex unknowns with cell-centered ones,which is easy to implement and applicable to general diffusion *** main novelty of this paper is to design a multigrid prolongation operator based on the GT method and splitting extrapolation method,and then propose a cell-centered EXCMG method with BiCGStab smoother for solving the large linear system resulting from linear FV discretization of diffusion equations with strongly discontinuous and anisotropic *** experiments are presented to demonstrate the high efficiency of the proposed method.

关键词： Diffusion equation discontinuous coefficients anisotropic coefficients Richardson extrapolation finite volume scheme cell-centered multigrid method

2.5维直流电法正演中Fourier逆变换离散波数的最优化选取

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中南大学学报（自然科学版） 2013年第7期44卷 2819-2826页

作者：潘克家汤井田中南大学有色金属成矿预测教育部重点实验室地球科学与信息物理学院湖南长沙410083 中南大学数学与统计学院湖南长沙410083

从优化模型和计算方法 2方面改进点源2.5维直流电法正演中Fourier逆变换离散波数的最优化选取方法。首先利用均匀半空间点源电位的精确解,基于最小二乘法给出计算离散波数的改进非线性最优化问题;然后,利用差分进化(DE)算法进行求解;最... 详细信息

从优化模型和计算方法 2方面改进点源2.5维直流电法正演中Fourier逆变换离散波数的最优化选取方法。首先利用均匀半空间点源电位的精确解,基于最小二乘法给出计算离散波数的改进非线性最优化问题;然后,利用差分进化(DE)算法进行求解;最后,研究参与计算的电极距数对模拟精度的影响。对具有解析解的典型地电模型,通过与已有文献计算结果进行比较,验证方法的可行性。研究结果表明:增加参与计算的电极距数可有效提高视电阻率曲线近源处的计算精度,并能保证较大电性差异情形下的计算精度;与现有离散波数相比,本文方法得到的波数具有更高的精度和更大的适用范围。

关键词：直流电法有限单元法 Fourier逆变换离散波数差分进化算法

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自动识别油藏边界水侵量微分方程反演算法

石油学报 2008年第5期29卷 747-751页

作者：潘克家谭永基王才经复旦大学数学科学学院上海200433 中国石油大学数学与计算科学学院山东东营257061

针对水驱油数值模拟,提出一种基于微分方程反演的自动历史拟合算法,解决了单相微可压缩流体渗流中油藏边界水侵量自动识别问题。利用生产井的动态观测资料识别油藏边界上的水侵量,在数学上称为边界控制反问题。基于微分方程反演理论,将... 详细信息

针对水驱油数值模拟,提出一种基于微分方程反演的自动历史拟合算法,解决了单相微可压缩流体渗流中油藏边界水侵量自动识别问题。利用生产井的动态观测资料识别油藏边界上的水侵量,在数学上称为边界控制反问题。基于微分方程反演理论,将其转化为一个非线性优化问题,利用共轭梯度法求解。共轭梯度法是通过引入相应的伴随问题和敏感性问题,分别确定每次迭代的搜索方向和搜索步长,解决了时空域中一般反演方法的不稳定性、收敛速度慢和依赖于初值等一系列问题。理论模型和实际资料检验表明,该方法不仅丰富了微分方程反演理论,而且具有生产实用价值。

关键词：水驱油藏数值模拟水侵量自动历史拟合算法微分方程反演共轭梯度法

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单纯形上校正高斯-勒让德求积公式

计算机工程与应用 2012年第35期48卷 7-10,130页

作者：潘克家汤井田中南大学有色金属成矿预测教育部重点实验室地球科学与信息物理学院长沙410083 中南大学数学与统计学院长沙410083 高性能计算与随机信息处理教育部重点实验室长沙410081

基于高斯-勒让德求积公式余项,给出相应的校正积分公式,提高了至少两阶代数精度。通过坐标变换将三角形、四面体区域变成正方形、立方体积分区域,把校正高斯求积公式推广到高维单纯形上多重积分的计算。通过与二维三角形单元和三维四面... 详细信息

基于高斯-勒让德求积公式余项,给出相应的校正积分公式,提高了至少两阶代数精度。通过坐标变换将三角形、四面体区域变成正方形、立方体积分区域,把校正高斯求积公式推广到高维单纯形上多重积分的计算。通过与二维三角形单元和三维四面体单元上的Hammer求积公式比较发现,校正求积公式的精度非常高,能更快收敛到积分真值,在工程实际中具有较大的应用价值。

关键词：单纯形高斯积分有限元代数精度积分余项