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adaptive finite element method Based on Optimal Error Estimtes for Linear Elliptic Problems on Concave Corner Domains (continuation)

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Journal of Mathematical Research and Exposition 2004年第2期24卷 273-279页

作者：汤雁郑璇天津大学理学院天津300072 天津城建学院天津300381

This paper is the third part in a series of papers on adaptive finite elementmethods based on optimal error estimates for linear elliptic problems on the concavecorner domains. In this paper, a result is obtained. The algorithms for error controlboth in the energy norm and in the maximum norm presented in part 1 and part 2 ofthis series arc based on this result.

关键词： adaptive finite element method concave corner domain elliptic problems

Phase-field modeling of dendritic growth under forced flow based on adaptive finite element method

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Transactions of Nonferrous Metals Society of China 2015年第1期25卷 241-248页

作者：朱昶胜雷鹏肖荣振冯力兰州理工大学计算机与通信学院兰州730050 兰州理工大学有色金属先进加工与再利用国家重点实验室兰州730050

A mathematical model combined projection algorithm with phase-field method was applied. The adaptive finite element method was adopted to solve the model based on the non-uniform grid, and the behavior of dendritic growth was simulated from undercooled nickel melt under the forced flow. The simulation results show that the asymmetry behavior of the dendritic growth is caused by the forced flow. When the flow velocity is less than the critical value, the asymmetry of dendrite is little influenced by the forced flow. Once the flow velocity reaches or exceeds the critical value, the controlling factor of dendrite growth gradually changes from thermal diffusion to convection. With the increase of the flow velocity, the deflection angle towards upstream direction of the primary dendrite stem becomes larger. The effect of the dendrite growth on the flow field of the melt is apparent. With the increase of the dendrite size, the vortex is present in the downstream regions, and the vortex region is gradually enlarged. Dendrite tips appear to remelt. In addition, the adaptive finite element method can reduce CPU running time by one order of magnitude compared with uniform grid method, and the speed-up ratio is proportional to the size of computational domain.

关键词： dendritic growth phase-field model forced flow adaptive finite element method

adaptive finite element method BASED ON OPTIMAL ERROR ESTIMATES FOR LINEAR ELLIPTIC PROBLEMS ON CONCAVE CORNER DOMAINS

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Transactions of Tianjin University 2001年第1期7卷 64-67页

作者：汤雁天津大学理学院天津300072

An adaptive finite element procedure designed for specific computational goals is presented,using mesh refinement strategies based on optimal or nearly optimal a priori error estimates for the finite element method and using estimators of the local regularity of the unknown exact solution derived from computed approximate *** proposed procedure is analyzed in detail for a non-trivial class of corner problems and shown to be efficient in the sense that the method can generate the correct type of refinements and lead to the desired control under consideration.

关键词： adaptive finite element method priori error estimate optimal mesh design

adaptive finite element method Based on Optimal Error Estimates for Linear Elliptic Problems on Nonconvex Polygonal Domains

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Transactions of Tianjin University 2002年第4期8卷 299-302页

作者：汤雁郑璇天津大学理学院天津300072 天津城建学院天津300381

The subject of this work is to propose adaptive finite element methods based on an optimal maximum norm error control *** estimators of the local regularity of the unknown exact solution derived from computed approximate solutions,the proposed procedures are analyzed in detail for a non-trivial class of corner problems and shown to be efficient in the sense that they generate the correct type of refinement and lead to the desired control under consideration.

关键词： adaptive finite element method error control a priori error estimate

An adaptive finite element method Based on Optimal Error Estimates for Linear Elliptic Problems

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Transactions of Tianjin University 2004年第3期10卷 225-228页

作者：汤雁 School of Sciences Tianjin University Tianjin 300072 China

The subject of the work is to propose a series of papers about adaptive finite element methods based on optimal error control estimate. This paper is the third part in a series of papers on adaptive finite element methods based on optimal error estimates for linear elliptic problems on the concave corner domains. In the preceding two papers (part 1:adaptive finite element method based on optimal error estimate for linear elliptic problems on concave corner domain; part 2:adaptive finite element method based on optimal error estimate for linear elliptic problems on nonconvex polygonal domains), we presented adaptive finite element methods based on the energy norm and the maximum norm. In this paper, an important result is presented and analyzed. The algorithm for error control in the energy norm and maximum norm in part 1 and part 2 in this series of papers is based on this result.

关键词： adaptive finite element method concave corner domain elliptic problems

A LOCAL MULTILEVEL PRECONDITIONER FOR THE adaptive MORTAR finite element method＊

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Journal of Computational Mathematics 2013年第5期31卷 532-548页

作者： Feng Wang Jinru Chen Jiangsu Key Laboratory for NSLSCS School of Mathematical Sciences Nanjing Normal University Nanjing 210023 China

In this paper, we propose a local multilevel preconditioner for the mortar finite element approximations of the elliptic problems. With some mesh assumptions on the interface, we prove that the condition number of the preconditioned systems is independent of the large jump of the coefficients but depends on the mesh levels around the cross points. Some numericM experiments are presented to confirm our theoreticM results.

关键词： Mortar adaptive finite element method Local multilevel method AdditiveSchwarz method.

An Improved adaptive finite element method for the Simulation of Electromagnetic Field in PPFDs

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An Improved Adaptive Finite Element Method for the Simulatio...

Numerical Solution of Acoustic Scattering by an adaptive DtN finite element method

The Fifth Asia-Pacific Conference on Environmental Electromagnetics

作者： Zhanghong Tang Qun Wang and Hongxia Guo College of Materials Science and Engineering Beijing University of Technology Beijing 100124 China Meiwu Shi Maohui Li The Quartermaster Equipment Research Institute of the General Logistics Department of the PLA Beijing 100082 China

＜正＞Basing on the posteriori error estimation and Superconvergent Patch Recovery（SPR） technology,Elena Zhelezina proposed a fast adaptive mesh refinement strategy which can generate the refined mesh for the required accuracy with only one step of ***,the strategy generates too many elements in PPFDs which is unpractical to simulate the PCBs and IC packages with complicated multiple layers,where the electromagnetic field in PPFDs is calculated,since too many elements lead to the FEM sparse matrices can’t be solved on current machines because of inefficient *** this paper,a new formula to estimate the global error is introduced,and then, a new strategy to calculate every element’s refinement degree is *** show that the improved method generates less than half of elements comparing to Elena Zhelezina’s method, but still requires only one step *** mesh refinement strategy was successfully applied to calculate the electromagnetic field in PPFDs for simulating the PCBs and IC packages with high accuracy.

关键词： Parallel Plate Field Domain adaptive finite element method Superconvergent Patch Recovery Refinement Degree PCBs and IC packages

来源： cnki会议评论

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Communications in Computational Physics 2013年第5期13卷 1227-1244页

作者： Xue Jiang Peijun Li Weiying Zheng LSEC Institute of Computational MathematicsAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing100190China Department of Mathematics Purdue UniversityWest LafayetteIndiana47907USA LSEC Institute of Computational MathematicsAcademy of Mathematics and System SciencesChinese Academy of SciencesBeijing100190China

Consider the acoustic wave scattering by an impenetrable obstacle in two dimensions,where the wave propagation is governed by the Helmholtz *** scattering problem is modeled as a boundary value problem over a bounded *** on the Dirichlet-to-Neumann(DtN)operator,a transparent boundary condition is introduced on an artificial circular boundary enclosing the *** adaptive finite element based on a posterior error estimate is presented to solve the boundary value problem with a nonlocal DtN boundary *** experiments are included to compare with the perfectly matched layer(PML)method to illustrate the competitive behavior of the proposed adaptive method.

关键词： Helmholtz equation DtN boundary condition adaptive finite element method a posteriori error estimate

An adaptive finite element PML method for the Acoustic Scattering Problems in Layered Media

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Communications in Computational Physics 2019年第1期25卷 266-288页

作者： Xue Jiang Yu Qi Jianhua Yuan School of Science Beijing University of Posts and TelecommunicationsBeijing 100876China

The paper concerns the numerical solution for the acoustic scattering problems in a two-layer *** perfectly matched layer(PML)technique is adopted to truncate the unbounded physical domain into a bounded computational *** a posteriori error estimate based adaptive finite element method is developed to solve the scattering *** experiments are included to demonstrate the efficiency of the proposed method.

关键词： Acoustic scattering problems layered media perfectly matched layer adaptive finite element method