Articles de revues : « Multilevel Finite Element Method »

1

Niekamp, R., et E. Stein. « The hierarchically graded multilevel finite element method ». Computational Mechanics 27, n^o 4 (7 avril 2001) : 302–4. http://dx.doi.org/10.1007/s004660100242.

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Han, Xiaole, Yu Li et Hehu Xie. « A Multilevel Correction Method for Steklov Eigenvalue Problem by Nonconforming Finite Element Methods ». Numerical Mathematics : Theory, Methods and Applications 8, n^o 3 (août 2015) : 383–405. http://dx.doi.org/10.4208/nmtma.2015.m1334.

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AbstractIn this paper, a multilevel correction scheme is proposed to solve the Steklov eigenvalue problem by nonconforming finite element methods. With this new scheme, the accuracy of eigenpair approximations can be improved after each correction step which only needs to solve a source problem on finer finite element space and an Steklov eigenvalue problem on the coarsest finite element space. This correction scheme can increase the overall efficiency of solving eigenvalue problems by the nonconforming finite element method. Furthermore, as same as the direct eigenvalue solving by nonconforming finite element methods, this multilevel correction method can also produce the lower-bound approximations of the eigenvalues.

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Zhang, Yamiao, Biwu Huang, Jiazhong Zhang et Zexia Zhang. « A Multilevel Finite Element Variational Multiscale Method for Incompressible Navier-Stokes Equations Based on Two Local Gauss Integrations ». Mathematical Problems in Engineering 2017 (2017) : 1–13. http://dx.doi.org/10.1155/2017/4917054.

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A multilevel finite element variational multiscale method is proposed and applied to the numerical simulation of incompressible Navier-Stokes equations. This method combines the finite element variational multiscale method based on two local Gauss integrations with the multilevel discretization using Newton correction on each step. The main idea of the multilevel finite element variational multiscale method is that the equations are first solved on a single coarse grid by finite element variational multiscale method; then finite element variational multiscale approximations are generated on a succession of refined grids by solving a linearized problem. Moreover, the stability analysis and error estimate of the multilevel finite element variational multiscale method are given. Finally, some numerical examples are presented to support the theoretical analysis and to check the efficiency of the proposed method. The results show that the multilevel finite element variational multiscale method is more efficient than the one-level finite element variational multiscale method, and for an appropriate choice of meshes, the multilevel finite element variational multiscale method is not only time-saving but also highly accurate.

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Hoppe, Ronald H. W., et Barbara Wohlmuth. « Efficient numerical solution of mixed finite element discretizations by adaptive multilevel methods ». Applications of Mathematics 40, n^o 3 (1995) : 227–48. http://dx.doi.org/10.21136/am.1995.134292.

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Huang Junlong, 黄俊龙, et 余景景 Yu Jingjing. « Bioluminescence Tomography Based on Multilevel Adaptive Finite Element Method ». Chinese Journal of Lasers 45, n^o 6 (2018) : 0607003. http://dx.doi.org/10.3788/cjl201845.0607003.

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Axelsson, O., et M. Larin. « An algebraic multilevel iteration method for finite element matrices ». Journal of Computational and Applied Mathematics 89, n^o 1 (mars 1998) : 135–53. http://dx.doi.org/10.1016/s0377-0427(97)00241-0.

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Akimov, Pavel A., Alexandr M. Belostosky, Marina L. Mozgaleva, Mojtaba Aslami et Oleg A. Negrozov. « Correct Multilevel Discrete-Continual Finite Element Method of Structural Analysis ». Advanced Materials Research 1040 (septembre 2014) : 664–69. http://dx.doi.org/10.4028/www.scientific.net/amr.1040.664.

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The distinctive paper is devoted to correct multilevel discrete-continual finite element method (DCFEM) of structural analysis based on precise analytical solutions of resulting multipoint boundary problems for systems of ordinary differential equations with piecewise-constant coefficients. Corresponding semianalytical (discrete-continual) formulations are contemporary mathematical models which currently becoming available for computer realization. Major peculiarities of DCFEM include universality, computer-oriented algorithm involving theory of distributions, computational stability, optimal conditionality of resulting systems and partial Jordan decompositions of matrices of coefficients, eliminating necessity of calculation of root vectors.

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Aslami, Mojtaba, et Pavel A. Akimov. « Wavelet-based finite element method for multilevel local plate analysis ». Thin-Walled Structures 98 (janvier 2016) : 392–402. http://dx.doi.org/10.1016/j.tws.2015.10.011.

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Xie, Hehu, et Tao Zhou. « A multilevel finite element method for Fredholm integral eigenvalue problems ». Journal of Computational Physics 303 (décembre 2015) : 173–84. http://dx.doi.org/10.1016/j.jcp.2015.09.043.

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Lin, Qun, Hehu Xie et Fei Xu. « Multilevel correction adaptive finite element method for semilinear elliptic equation ». Applications of Mathematics 60, n^o 5 (15 septembre 2015) : 527–50. http://dx.doi.org/10.1007/s10492-015-0110-x.

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Talebi, Hossein, Goangseup Zi, Mohammad Silani, Esteban Samaniego et Timon Rabczuk. « A Simple Circular Cell Method for Multilevel Finite Element Analysis ». Journal of Applied Mathematics 2012 (2012) : 1–15. http://dx.doi.org/10.1155/2012/526846.

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A simple multiscale analysis framework for heterogeneous solids based on a computational homogenization technique is presented. The macroscopic strain is linked kinematically to the boundary displacement of a circular or spherical representative volume which contains the microscopic information of the material. The macroscopic stress is obtained from the energy principle between the macroscopic scale and the microscopic scale. This new method is applied to several standard examples to show its accuracy and consistency of the method proposed.

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Jung, Michael, et Ulrich Rüde. « Implicit Extrapolation Methods for Multilevel Finite Element Computations ». SIAM Journal on Scientific Computing 17, n^o 1 (janvier 1996) : 156–79. http://dx.doi.org/10.1137/0917012.

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Chen, Feng Wang and Jinru. « A Local Multilevel Preconditioners for the Adaptive Mortar Finite Element Method ». Journal of Computational Mathematics 31, n^o 5 (juin 2013) : 532–48. http://dx.doi.org/10.4208/jcm.1307-m4290.

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Atlamazoglou, P. E., G. C. Pagiatakis et N. K. Uzunoglu. « A multilevel formulation of the finite-element method for electromagnetic scattering ». IEEE Transactions on Antennas and Propagation 47, n^o 6 (juin 1999) : 1071–79. http://dx.doi.org/10.1109/8.777134.

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Darbandi, Masoud, Soheyl Vakili et Gerry E. Schneider. « Efficient multilevel restriction–prolongation expressions for hybrid finite volume element method ». International Journal of Computational Fluid Dynamics 22, n^o 1-2 (janvier 2008) : 29–38. http://dx.doi.org/10.1080/10618560701737203.

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Hu, Guanghui, Hehu Xie et Fei Xu. « A multilevel correction adaptive finite element method for Kohn–Sham equation ». Journal of Computational Physics 355 (février 2018) : 436–49. http://dx.doi.org/10.1016/j.jcp.2017.11.024.

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Eibert, T. F. « A multilevel fast spectral domain algorithm for electromagnetic analysis of infinite periodic arrays with large unit cells ». Advances in Radio Science 4 (4 septembre 2006) : 41–47. http://dx.doi.org/10.5194/ars-4-41-2006.

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Abstract. A multilevel fast spectral domain algorithm (MLFSDA) is introduced for the efficient evaluation of the matrix vector products due to the boundary integral (BI) operator within a hybrid finite element - BI (FEBI) method for the analysis of infinite periodic arrays. The MLFSDA utilizes the diagonalization property of the spectral domain (SD) BI representation and handles the large numbers of Floquet modes required for large (with respect to wavelength) periodic unit cells by similar hierarchical techniques as applied in the multilevel fast multipole method/algorithm (MLFMM/MLFMA). With the capability of the MLFSDA to handle very large periodic unit cells, it becomes possible to model finite antennas and scatterers with the infinite periodic array model. For a cavity-backed antenna element and for a semi-finite array of 4 cavity-backed antenna elements in the finite direction, the dependence of the input impedances on the unit cell sizes is investigated and it is found that array resonances disappear for reasonably large unit cell dimensions. Finally, a semi-finite array of antipodal Vivaldi antenna elements is considered and simulation results for infinite periodic, finite, and semi-finite array configurations are compared to measured data.

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Akimov, Pavel A., et Marina L. Mozgaleva. « Wavelet-Based Multilevel Discrete-Continual Finite Element Method for Local Plate Analysis ». Applied Mechanics and Materials 351-352 (août 2013) : 13–16. http://dx.doi.org/10.4028/www.scientific.net/amm.351-352.13.

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High-accuracy solution of the problem of plate analysis is normally required in some pre-known domains (regions with the risk of significant stresses that could potentially lead to the destruction of structure, regions which are subject to specific operational requirements). The distinctive paper is devoted to correct wavelet-based multilevel discrete-continual finite element method for local analysis of plates with regular (in particular, constant or piecewise constant) physical and geometrical parameters (properties) in one direction. Initial discrete-continual operational formulation of the considering problem and corresponding operational formulation with the use of wavelet basis are presented. Due to special algorithms of averaging within multigrid approach, reduction of the problem is provided. Resultant multipoint boundary problem of structural mechanics for system of ordinary differential equations with piecewise-constant coefficients is given.

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Xu, Fei, Qiumei Huang, Huiting Yang et Hongkun Ma. « Multilevel correction goal-oriented adaptive finite element method for semilinear elliptic equations ». Applied Numerical Mathematics 172 (février 2022) : 224–41. http://dx.doi.org/10.1016/j.apnum.2021.10.001.

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Hong, Qichen, Hehu Xie et Fei Xu. « A Multilevel Correction Type of Adaptive Finite Element Method for Eigenvalue Problems ». SIAM Journal on Scientific Computing 40, n^o 6 (janvier 2018) : A4208—A4235. http://dx.doi.org/10.1137/17m1138157.

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SHI, ZhongCi, XueJun XU et PeiPei LU. « Local multilevel methods for adaptive discontinuous Galerkin finite element methods ». SCIENTIA SINICA Mathematica 42, n^o 5 (1 mai 2012) : 409–28. http://dx.doi.org/10.1360/012011-1004.

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Tang, Shibing, et Xuejun Xu. « An Optimal Multilevel Method with One Smoothing Step for the Morley Element ». Computational Methods in Applied Mathematics 21, n^o 3 (3 juin 2021) : 609–33. http://dx.doi.org/10.1515/cmam-2020-0061.

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Abstract In this paper, a class of multilevel preconditioning schemes is presented for solving the linear algebraic systems resulting from the application of Morley nonconforming element approximations to the biharmonic Dirichlet problem. Based on an appropriate space splitting of the finite element spaces associated with the refinements and the abstract Schwarz framework, we prove that the proposed multilevel methods with one smoothing step are optimal, i.e., the convergence rate is independent of the mesh sizes and mesh levels. Moreover, the computational complexity is also optimal since the smoothers are performed only once on each level in the algorithm. Numerical experiments are provided to confirm the optimality of the suggested methods.

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Xie, Hehu, et Manting Xie. « A Multigrid Method for Ground State Solution of Bose-Einstein Condensates ». Communications in Computational Physics 19, n^o 3 (mars 2016) : 648–62. http://dx.doi.org/10.4208/cicp.191114.130715a.

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AbstractA multigrid method is proposed to compute the ground state solution of Bose-Einstein condensations by the finite element method based on the multilevel correction for eigenvalue problems and the multigrid method for linear boundary value problems. In this scheme, obtaining the optimal approximation for the ground state solution of Bose-Einstein condensates includes a sequence of solutions of the linear boundary value problems by the multigrid method on the multilevel meshes and some solutions of nonlinear eigenvalue problems some very low dimensional finite element space. The total computational work of this scheme can reach almost the same optimal order as solving the corresponding linear boundary value problem. Therefore, this type of multigrid scheme can improve the overall efficiency for the simulation of Bose-Einstein condensations. Some numerical experiments are provided to validate the efficiency of the proposed method.

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He, Xiaowei, Yanbin Hou, Duofang Chen, Yuchuan Jiang, Man Shen, Junting Liu, Qitan Zhang et Jie Tian. « Sparse Regularization-Based Reconstruction for Bioluminescence Tomography Using a Multilevel Adaptive Finite Element Method ». International Journal of Biomedical Imaging 2011 (2011) : 1–11. http://dx.doi.org/10.1155/2011/203537.

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Bioluminescence tomography (BLT) is a promising tool for studying physiological and pathological processes at cellular and molecular levels. In most clinical or preclinical practices, fine discretization is needed for recovering sources with acceptable resolution when solving BLT with finite element method (FEM). Nevertheless, uniformly fine meshes would cause large dataset and overfine meshes might aggravate the ill-posedness of BLT. Additionally, accurately quantitative information of density and power has not been simultaneously obtained so far. In this paper, we present a novel multilevel sparse reconstruction method based on adaptive FEM framework. In this method, permissible source region gradually reduces with adaptive local mesh refinement. By using sparse reconstruction withl1regularization on multilevel adaptive meshes, simultaneous recovery of density and power as well as accurate source location can be achieved. Experimental results for heterogeneous phantom and mouse atlas model demonstrate its effectiveness and potentiality in the application of quantitative BLT.

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Starke, Gerhard. « Multilevel Boundary Functionals for Least-Squares Mixed Finite Element Methods ». SIAM Journal on Numerical Analysis 36, n^o 4 (janvier 1999) : 1065–77. http://dx.doi.org/10.1137/s0036142997329803.

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Kraus, Johannes, Maria Lymbery et Svetozar Margenov. « Robust multilevel methods for quadratic finite element anisotropic elliptic problems ». Numerical Linear Algebra with Applications 21, n^o 3 (11 mars 2013) : 375–98. http://dx.doi.org/10.1002/nla.1876.

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Akimov, Pavel A., et Marina L. Mozgaleva. « Wavelet-Based Multilevel Discrete-Continual Finite Element Method for Local Deep Beam Analysis ». Applied Mechanics and Materials 405-408 (septembre 2013) : 3165–68. http://dx.doi.org/10.4028/www.scientific.net/amm.405-408.3165.

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High-accuracy solution of the problem of deep beam analysis is normally required in some pre-known domains (regions with the risk of significant stresses that could potentially lead to the destruction of structure, regions which are subject to specific operational requirements). The distinctive paper is devoted to correct wavelet-based multilevel discrete-continual finite element method for local analysis of deep beams with regular (in particular, constant or piecewise constant) physical and geometrical parameters (properties) in one direction. Initial discrete-continual operational formulation of the considering problem and corresponding operational formulation with the use of wavelet basis are presented. Due to special algorithms of averaging within multigrid approach, reduction of the problem is provided. Resultant multipoint boundary problem of structural mechanics for system of ordinary differential equations with piecewise-constant coefficients is given.

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Gong, Wei, Hehu Xie et Ningning Yan. « Adaptive Multilevel Correction Method for Finite Element Approximations of Elliptic Optimal Control Problems ». Journal of Scientific Computing 72, n^o 2 (23 février 2017) : 820–41. http://dx.doi.org/10.1007/s10915-017-0386-y.

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Liu, Hui, Xiaoyu Sun, Yuanjie Xu et Xihua Chu. « A hierarchical multilevel finite element method for mechanical analyses of periodical composite structures ». Composite Structures 131 (novembre 2015) : 115–27. http://dx.doi.org/10.1016/j.compstruct.2015.05.001.

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He, Yinnian, et Kam-Moon Liu. « A multilevel finite element method in space-time for the Navier-Stokes problem ». Numerical Methods for Partial Differential Equations 21, n^o 6 (2005) : 1052–78. http://dx.doi.org/10.1002/num.20077.

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Xu, Xuejun. « Optimality of Local Multilevel Methods for AdaptiveNonconforming P1 Finite Element Methods ». Journal of Computational Mathematics 31, n^o 1 (juin 2013) : 22–46. http://dx.doi.org/10.4208/jcm.1203-m3960.

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Ewing, R. E., et J. Wang. « Analysis of multilevel decomposition iterative methods for mixed finite element methods ». ESAIM : Mathematical Modelling and Numerical Analysis 28, n^o 4 (1994) : 377–98. http://dx.doi.org/10.1051/m2an/1994280403771.

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Baumgarten, Niklas, et Christian Wieners. « The parallel finite element system M++ with integrated multilevel preconditioning and multilevel Monte Carlo methods ». Computers & ; Mathematics with Applications 81 (janvier 2021) : 391–406. http://dx.doi.org/10.1016/j.camwa.2020.03.004.

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Yue, Jianguang. « Micro-Macro Simulation Technique Combined with Multilevel Damage Assessment Methodology for RC Building Structures ». Advances in Materials Science and Engineering 2015 (2015) : 1–13. http://dx.doi.org/10.1155/2015/764517.

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In order to assess the inherent damage mechanism of reinforced concrete (RC) structures, a micro-macro simulation technique combined with multilevel damage assessment methodology is presented. An element-coupling model is developed by combining mixed dimensional finite elements with the aid of multipoint constraint equations, which could be achieved from the energy conservation principle. Thus, the micro-scale damage details could be obtained in a macro-scale setting of the global structure. Furthermore, using different damage indicators, a generalized damage model is combined with the multilevel damage performance to assess the damage evolution. Finally, an in situ lateral loading test of a real RC frame structure was analyzed to verify this proposed damage assessment methodology. The finite element method utilizing the proposed damage model products results in good agreement with those of the tests. It shows that the proposed methodology is a very helpful tool to assess and reveal the inherent damage mechanism of RC structures.

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Bespalov, Alex, Dirk Praetorius et Michele Ruggeri. « Two-Level a Posteriori Error Estimation for Adaptive Multilevel Stochastic Galerkin Finite Element Method ». SIAM/ASA Journal on Uncertainty Quantification 9, n^o 3 (janvier 2021) : 1184–216. http://dx.doi.org/10.1137/20m1342586.

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Ackermann, J., et R. Roitzsch. « A two-dimensional multilevel adaptive finite element method for the time-independent Schrödinger equation ». Chemical Physics Letters 214, n^o 1 (octobre 1993) : 109–17. http://dx.doi.org/10.1016/0009-2614(93)85463-x.

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Dziekonski, Adam, Adam Lamecki et Michal Mrozowski. « GPU Acceleration of Multilevel Solvers for Analysis of Microwave Components With Finite Element Method ». IEEE Microwave and Wireless Components Letters 21, n^o 1 (janvier 2011) : 1–3. http://dx.doi.org/10.1109/lmwc.2010.2089974.

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Khodadadian, Amirreza, Maryam Parvizi, Mostafa Abbaszadeh, Mehdi Dehghan et Clemens Heitzinger. « A multilevel Monte Carlo finite element method for the stochastic Cahn–Hilliard–Cook equation ». Computational Mechanics 64, n^o 4 (25 février 2019) : 937–49. http://dx.doi.org/10.1007/s00466-019-01688-1.

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Akimov, Pavel A., Marina L. Mozgaleva, Mojtaba Aslami et Oleg A. Negrozov. « Local High-Accuracy Plate Analysis Using Wavelet-Based Multilevel Discrete-Continual Finite Element Method ». Key Engineering Materials 685 (février 2016) : 962–66. http://dx.doi.org/10.4028/www.scientific.net/kem.685.962.

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The distinctive paper is devoted to application of wavelet-based discrete-continual finite element method (WDCFEM), to analysis of plates with piecewise constant physical and geometrical parameters in so-called “basic” direction. Initial continual and discrete-continual formulations of the problem are presented. Due to special algorithms of averaging using wavelet basis within multigrid approach, reduction of the problem is provided. Resultant multipoint boundary problem for system of ordinary differential equations is given.

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Layton, W., H. K. Lee et J. Peterson. « Numerical Solution of the Stationary Navier--Stokes Equations Using a Multilevel Finite Element Method ». SIAM Journal on Scientific Computing 20, n^o 1 (janvier 1998) : 1–12. http://dx.doi.org/10.1137/s1064827596306045.

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Aghabarati, Ali, et Jon P. Webb. « Multilevel Methods for $p$-Adaptive Finite Element Analysis of Electromagnetic Scattering ». IEEE Transactions on Antennas and Propagation 61, n^o 11 (novembre 2013) : 5597–606. http://dx.doi.org/10.1109/tap.2013.2277713.

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Kornhuber, Ralf, Christoph Schwab et Maren-Wanda Wolf. « Multilevel Monte Carlo Finite Element Methods for Stochastic Elliptic Variational Inequalities ». SIAM Journal on Numerical Analysis 52, n^o 3 (janvier 2014) : 1243–68. http://dx.doi.org/10.1137/130916126.

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Vassilevski, Panayot S., et Junping Wang. « Multilevel iterative methods for mixed finite element discretizations of elliptic problems ». Numerische Mathematik 63, n^o 1 (décembre 1992) : 503–20. http://dx.doi.org/10.1007/bf01385872.

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Li, Shishun, Xinping Shao et Zhiyong Si. « Local Multilevel Method on Adaptively Refined Meshes for Elliptic Problems with Smooth Complex Coefficients ». Numerical Mathematics : Theory, Methods and Applications 8, n^o 3 (août 2015) : 336–55. http://dx.doi.org/10.4208/nmtma.2015.m1323.

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AbstractIn this paper, a local multilevel algorithm is investigated for solving linear systems arising from adaptive finite element approximations of second order elliptic problems with smooth complex coefficients. It is shown that the abstract theory for local multilevel algorithm can also be applied to elliptic problems whose dominant coefficient is complex valued. Assuming that the coarsest mesh size is sufficiently small, we prove that this algorithm with Gauss-Seidel smoother is convergent and optimal on the adaptively refined meshes generated by the newest vertex bisection algorithm. Numerical experiments are reported to confirm the theoretical analysis.

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Blondeel, Philippe, Pieterjan Robbe, Cédric Van hoorickx, Stijn François, Geert Lombaert et Stefan Vandewalle. « p-Refined Multilevel Quasi-Monte Carlo for Galerkin Finite Element Methods with Applications in Civil Engineering ». Algorithms 13, n^o 5 (28 avril 2020) : 110. http://dx.doi.org/10.3390/a13050110.

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Civil engineering applications are often characterized by a large uncertainty on the material parameters. Discretization of the underlying equations is typically done by means of the Galerkin Finite Element method. The uncertain material parameter can be expressed as a random field represented by, for example, a Karhunen–Loève expansion. Computation of the stochastic responses, i.e., the expected value and variance of a chosen quantity of interest, remains very costly, even when state-of-the-art Multilevel Monte Carlo (MLMC) is used. A significant cost reduction can be achieved by using a recently developed multilevel method: p-refined Multilevel Quasi-Monte Carlo (p-MLQMC). This method is based on the idea of variance reduction by employing a hierarchical discretization of the problem based on a p-refinement scheme. It is combined with a rank-1 Quasi-Monte Carlo (QMC) lattice rule, which yields faster convergence compared to the use of random Monte Carlo points. In this work, we developed algorithms for the p-MLQMC method for two dimensional problems. The p-MLQMC method is first benchmarked on an academic beam problem. Finally, we use our algorithm for the assessment of the stability of slopes, a problem that arises in geotechnical engineering, and typically suffers from large parameter uncertainty. For both considered problems, we observe a very significant reduction in the amount of computational work with respect to MLMC.

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Ghosh, S., et S. Raju. « Localized metal forming simulation by r-s-adapted arbitrary Lagrangian-Eulerian finite element method ». Journal of Strain Analysis for Engineering Design 32, n^o 4 (1 mai 1997) : 237–52. http://dx.doi.org/10.1243/0309324971513373.

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In this paper, an adaptive arbitrary Lagrangian—Eulerian (ALE) large deformation finite element method (FEM) is developed for solving metal forming problems with strain localization. The ALE mesh movement is coupled with r-adaptation of automatic node relocation to minimize mesh distortion during the process of deformation. A strain localization phenomenon is incorporated through constitutive relations for porous ductile materials. Prediction of localized deformation is achieved through a multilevel mesh superimposition method, called s-adaptation. A few metal forming problems are simulated to test the effectiveness of this model.

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Wan, Ting, et Zhaoneng Jiang. « Multilevel compressed block decomposition-based finite-element domain decomposition method for the fast analysis of finite periodic structures ». International Journal of Numerical Modelling : Electronic Networks, Devices and Fields 30, n^o 5 (30 septembre 2016) : e2194. http://dx.doi.org/10.1002/jnm.2194.

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Foresti, S., G. Brussino, S. Hassanzadeh et V. Sonnad. « Multilevel solution method for the p-version of finite elements ». Computer Physics Communications 53, n^o 1-3 (mai 1989) : 349–55. http://dx.doi.org/10.1016/0010-4655(89)90172-0.

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Carreño, A., A. Vidal-Ferrándiz, D. Ginestar et G. Verdú. « Multilevel method to compute the lambda modes of the neutron diffusion equation ». Applied Mathematics and Nonlinear Sciences 2, n^o 1 (24 juin 2017) : 225–36. http://dx.doi.org/10.21042/amns.2017.1.00019.

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AbstractDetermination of the reactor kinetic characteristics is very important for the design and development of a new reactor system. In this sense, the computation of lambda modes associated to a nuclear power reactor has interest since these modes can be used to analyze the reactor criticality and to develop modal methods to analyze transient situations in the reactor. In this paper, the lambda problem has been discretized using a high order finite element method to obtain a generalized algebraic eigenvalue problem. A multilevel method is proposed to solve this generalized eigenvalue problem combining a hierarchy of meshes with a Modified Block Newton method. The Krylov-Schur method is used to compare the efficiency of the multilevel method solving several benchmark problems.

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Wang, Wei-Jie, Xiao-Jie Chen, Han-Yu Li, Hai-Jing Zhou et Wen-Yan Yin. « A Multilevel Method With Novel Correction Strategy for Parallel Finite-Element Analysis of Electromagnetic Problems ». IEEE Transactions on Antennas and Propagation 66, n^o 7 (juillet 2018) : 3787–91. http://dx.doi.org/10.1109/tap.2018.2816680.

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Articles de revues sur le sujet « Multilevel Finite Element Method »

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