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Journal articles on the topic 'Hp-FEM'

Author: Grafiati

Published: 4 June 2021

Last updated: 13 February 2022

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1

SCHÖTZAU, DOMINIK, and CHRISTOPH SCHWAB. "MIXED hp-FEM ON ANISOTROPIC MESHES." Mathematical Models and Methods in Applied Sciences 08, no. 05 (1998): 787–820. http://dx.doi.org/10.1142/s0218202598000366.

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Mixed hp-FEM for incompressible fluid flow on anisotropic meshes are analyzed. A discrete inf–sup condition is proved with a constant independent of the meshwidth and the aspect ratio. For each polynomial degree k≥2 we present velocity-pressure subspace pairs which are stable on quadrilateral mesh-patches independently of the element aspect ratio, implying in particular divergence stability on the so-called Shishkin-meshes. Moreover, the inf–sup constant is shown to depend on the spectral order k like k-1/2 for quadrilateral meshes and like k-3 for meshes containing triangles. New consistency results for spectral elements on anisotropic meshes are also proved.

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2

Guo, Hongbo, Yuqing Hou, Xiaowei He, Jingjing Yu, Jingxing Cheng, and Xin Pu. "Adaptive hp finite element method for fluorescence molecular tomography with simplified spherical harmonics approximation." Journal of Innovative Optical Health Sciences 07, no. 02 (2014): 1350057. http://dx.doi.org/10.1142/s1793545813500570.

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Recently, the simplified spherical harmonics equations (SPN) model has attracted much attention in modeling the light propagation in small tissue geometries at visible and near-infrared wavelengths. In this paper, we report an efficient numerical method for fluorescence molecular tomography (FMT) that combines the advantage of SPN model and adaptive hp finite element method (hp-FEM). For purposes of comparison, hp-FEM and h-FEM are, respectively applied to the reconstruction process with diffusion approximation and SPN model. Simulation experiments on a 3D digital mouse atlas and physical experiments on a phantom are designed to evaluate the reconstruction methods in terms of the location and the reconstructed fluorescent yield. The experimental results demonstrate that hp-FEM with SPN model, yield more accurate results than h-FEM with diffusion approximation model does. The phantom experiments show the potential and feasibility of the proposed approach in FMT applications.

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3

Dauge, Monique, and Christoph Schwab. "hp-FEM for three-dimensional elastic plates." ESAIM: Mathematical Modelling and Numerical Analysis 36, no. 4 (2002): 597–630. http://dx.doi.org/10.1051/m2an:2002027.

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4

Szymczak, Arkadiusz, Anna Paszýnska, Maciej Paszýnski, and David Pardo. "Anisotropic 2D mesh adaptation in hp-adaptive FEM." Procedia Computer Science 4 (2011): 1818–27. http://dx.doi.org/10.1016/j.procs.2011.04.197.

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5

Šolín, Pavel, and Tomáš Vejchodský. "A weak discrete maximum principle for hp-FEM." Journal of Computational and Applied Mathematics 209, no. 1 (2007): 54–65. http://dx.doi.org/10.1016/j.cam.2006.10.028.

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6

Eibner, T., and J. M. Melenk. "Multilevel preconditioning for the boundary concentrated hp-FEM." Computer Methods in Applied Mechanics and Engineering 196, no. 37-40 (2007): 3713–25. http://dx.doi.org/10.1016/j.cma.2006.10.034.

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7

Giani, Stefano, and Pavel Solin. "Solving elliptic eigenproblems with adaptive multimesh hp-FEM." Journal of Computational and Applied Mathematics 394 (October 2021): 113528. http://dx.doi.org/10.1016/j.cam.2021.113528.

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8

Ma, Zhong Hua, De Jun Liu, and Qi Feng. "Adaptive hp-Finite Element Method for Electromagnetic Field Logging Problems." Advanced Materials Research 442 (January 2012): 109–13. http://dx.doi.org/10.4028/www.scientific.net/amr.442.109.

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A novel, highly efficient and accurate adaptive higher-order finite element method (hp-FEM) is proposed for electromagnetic field problems. Presented in this paper are the vector expression of Maxwell's equations, three kinds of boundary conditions, stability weak formulation of Maxwell's equations, and automatic hp-adaptivity strategy. This method can select optimal refinement and calculation strategies based on the practical formation model and error estimation. Numerical experiments show that the new hp-FEM has an exponential convergence rate in terms of relative error in a user-prescribed quantity of interest against the degrees of freedom, which provides more accurate results than those obtained using the adaptive h-FEM. The methodology is freely available online in the form of a general public licensed C++ library Hermes (http://hpfem.org/hermes).

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9

COSTABEL, MARTIN, MONIQUE DAUGE, and CHRISTOPH SCHWAB. "EXPONENTIAL CONVERGENCE OF hp-FEM FOR MAXWELL EQUATIONS WITH WEIGHTED REGULARIZATION IN POLYGONAL DOMAINS." Mathematical Models and Methods in Applied Sciences 15, no. 04 (2005): 575–622. http://dx.doi.org/10.1142/s0218202505000480.

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The time-harmonic Maxwell equations do not have an elliptic nature by themselves. Their regularization by a divergence term is a standard tool to obtain equivalent elliptic problems. Nodal finite element discretizations of Maxwell's equations obtained from such a regularization converge to wrong solutions in any non-convex polygon. Modification of the regularization term consisting in the introduction of a weight restores the convergence of nodal FEM, providing optimal convergence rates for the h version of finite elements. We prove exponential convergence of hp FEM for the weighted regularization of Maxwell's equations in plane polygonal domains provided the hp-FE spaces satisfy a series of axioms. We verify these axioms for several specific families of hp finite element spaces.

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10

Solin, Pavel, and Michal Kuraz. "Solving the nonstationary Richards equation with adaptive hp-FEM." Advances in Water Resources 34, no. 9 (2011): 1062–81. http://dx.doi.org/10.1016/j.advwatres.2011.04.020.

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11

Brandsmeier, Holger, Kersten Schmidt, and Christoph Schwab. "A multiscale hp-FEM for 2D photonic crystal bands." Journal of Computational Physics 230, no. 2 (2011): 349–74. http://dx.doi.org/10.1016/j.jcp.2010.09.018.

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12

Banz, Lothar, and Ernst P. Stephan. "hp-adaptive IPDG/TDG-FEM for parabolic obstacle problems." Computers & Mathematics with Applications 67, no. 4 (2014): 712–31. http://dx.doi.org/10.1016/j.camwa.2013.03.003.

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13

Solin, Pavel, Lukas Korous, and Pavel Kus. "Hermes2D, a C++ library for rapid development of adaptive hp-FEM and hp-DG solvers." Journal of Computational and Applied Mathematics 270 (November 2014): 152–65. http://dx.doi.org/10.1016/j.cam.2014.02.007.

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14

Chernov, Alexey, and Lorenzo Mascotto. "The harmonic virtual element method: stabilization and exponential convergence for the Laplace problem on polygonal domains." IMA Journal of Numerical Analysis 39, no. 4 (2018): 1787–817. http://dx.doi.org/10.1093/imanum/dry038.

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Abstract We introduce the harmonic virtual element method (VEM) (harmonic VEM), a modification of the VEM (Beirão da Veiga et al. (2013) Basic principles of virtual element methods. Math. Models Methods Appl. Sci., 23, 199–214.) for the approximation of the two-dimensional Laplace equation using polygonal meshes. The main difference between the harmonic VEM and the VEM is that in the former method only boundary degrees of freedom are employed. Such degrees of freedom suffice for the construction of a proper energy projector on (piecewise harmonic) polynomial spaces. The harmonic VEM can also be regarded as an ‘$H^1$-conformisation’ of the Trefftz discontinuous Galerkin-finite element method (TDG-FEM) (Hiptmair et al. (2014) Approximation by harmonic polynomials in starshaped domains and exponential convergence of Trefftz hp-DGFEM. ESAIM Math. Model. Numer. Anal., 48, 727–752.). We address the stabilization of the proposed method and develop an hp version of harmonic VEM for the Laplace equation on polygonal domains. As in TDG-FEM, the asymptotic convergence rate of harmonic VEM is exponential and reaches order $\mathscr{O}(\exp (-b\sqrt [2]{N}))$, where $N$ is the number of degrees of freedom. This result overperforms its counterparts in the framework of hp FEM (Schwab, C. (1998)p- and hp-Finite Element Methods: Theory and Applications in Solid and Fluid Mechanics. Clarendon Press Oxford.) and hp VEM (Beirão da Veiga et al. (2018) Exponential convergence of the hp virtual element method with corner singularity. Numer. Math., 138, 581–613.), where the asymptotic rate of convergence is of order $\mathscr{O}(\exp(-b\sqrt [3]{N}))$.

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15

Xenophontos, Serge Nicaise and Christos. "An hp-FEM for Singularly Perturbed Transmission Problems." Journal of Computational Mathematics 35, no. 2 (2017): 152–68. http://dx.doi.org/10.4208/jcm.1607-m2014-0187.

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16

Eibner, T., and J. M. Melenk. "A local error analysis of the boundary-concentrated hp-FEM." IMA Journal of Numerical Analysis 26, no. 4 (2006): 752–78. http://dx.doi.org/10.1093/imanum/drl003.

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17

Wihler, Thomas. "An hp -Adaptive FEM Procedure based on Continuous Sobolev Embeddings." PAMM 11, no. 1 (2011): 11–14. http://dx.doi.org/10.1002/pamm.201110004.

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18

Melenk, J. M., and C. Schwab. "hp FEM for Reaction-Diffusion Equations I: Robust Exponential Convergence." SIAM Journal on Numerical Analysis 35, no. 4 (1998): 1520–57. http://dx.doi.org/10.1137/s0036142997317602.

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19

Pugal, D., P. Solin, K. J. Kim, and A. Aabloo. "hp -FEM electromechanical transduction model of ionic polymer–metal composites." Journal of Computational and Applied Mathematics 260 (April 2014): 135–48. http://dx.doi.org/10.1016/j.cam.2013.09.011.

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20

Beuchler, Sven, and Martin Purrucker. "Schwarz Type Solvers for -FEM Discretizations of Mixed Problems." Computational Methods in Applied Mathematics 12, no. 4 (2012): 369–90. http://dx.doi.org/10.2478/cmam-2012-0030.

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AbstractThis paper investigates the discretization of mixed variational formulation as, e.g., the Stokes problem by means of the hp-version of the finite element method. The system of linear algebraic equations is solved by the preconditioned Bramble-Pasciak conjugate gradient method. The development of an efficient preconditioner requires three ingredients, a preconditioner related to the components of the velocity modes, a preconditioner for the Schur complement related to the components of the pressure modes and a discrezation by a stable finite element pair which satisfies the discrete inf-sup-condition. The last condition is also important in order to obtain a stable discretization scheme. The preconditioner for the velocity modes is adapted from fast $hp$-FEM preconditioners for the potential equation. Moreover, we will prove that the preconditioner for the Schur complement can be chosen as a diagonal matrix if the pressure is discretized by discontinuous finite elements. We will prove that the system of linear algebraic equations can be solved in almost optimal complexity. This yields quasioptimal hp-FEM solvers for the Stokes problems and the linear elasticity problems. The latter are robust with respect to the contraction ratio ν. The efficiency of the presented solver is shown in several numerical examples.

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21

Al‐Odat, M. Q. "Numerical analysis of cutting tool temperature in dry machining processes with embedded heat pipe." Engineering Computations 27, no. 5 (2010): 658–73. http://dx.doi.org/10.1108/02644401011050930.

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PurposeThe purpose of this paper is to conduct a full three‐dimensional numerical analysis to simulate the thermal behavior of high speed steel (HSS) cutting tool, with temperature dependent thermal properties, in dry machining with embedded heat pipe (HP), and investigate the effects of HP installation, variable thermal properties, generated heat flux and cutting speed.Design/methodology/approachThe heat transfer equation used to predict cutting tool temperature is parabolic partial differential equation. Grid points including independent variables are initially formed in solution of partial differential equation by finite element method (FEM). In this paper, one‐dimensional heat transfer equation with variable thermophysical properties is solved by FEM.FindingsIn this paper, the heat transfer equation in cutting tool is solved for variable thermophysical properties and the temperature field and temperature history are obtained. Variable thermophysical properties are considered to display the temperature fields in the cutting tool.Originality/valueA full three‐dimensional numerical analysis is conducted to simulate the thermal behavior of HSS cutting tool, with temperature dependent thermal properties, in dry machining with embedded HP. The heat conduction equation is solved by FEM analysis.

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22

Wang, Mengyu, Kersten Schmidt, Aytac Alparslan, and Christian V. Hafner. "HP-FEM AND PML ANALYSIS OF PLASMONIC PARTICLES IN LAYERED MEDIA." Progress In Electromagnetics Research 142 (2013): 523–44. http://dx.doi.org/10.2528/pier13081407.

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23

Solin, Pavel. "Adaptive hp-FEM with Arbitrary-Level Hanging Nodes for Maxwell's Equations." Advances in Applied Mathematics and Mechanics 2, no. 4 (2010): 518–32. http://dx.doi.org/10.4208/aamm.10-m1012.

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24

Vejchodský, Tomáš, Pavel Šolín, and Martin Zítka. "Modular hp-FEM system HERMES and its application to Maxwell’s equations." Mathematics and Computers in Simulation 76, no. 1-3 (2007): 223–28. http://dx.doi.org/10.1016/j.matcom.2007.02.001.

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25

Šolín, Pavel, Jakub Červený, and Ivo Doležel. "Arbitrary-level hanging nodes and automatic adaptivity in the hp-FEM." Mathematics and Computers in Simulation 77, no. 1 (2008): 117–32. http://dx.doi.org/10.1016/j.matcom.2007.02.011.

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26

Szymczak, Arkadiusz, Anna Paszyńska, Maciej Paszyński, and David Pardo. "Preventing deadlock during anisotropic 2D mesh adaptation in hp-adaptive FEM." Journal of Computational Science 4, no. 3 (2013): 170–79. http://dx.doi.org/10.1016/j.jocs.2011.09.001.

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27

Gerdes, K., A. M. Matache, and C. Schwab. "Analysis of Membrane Locking in hp FEM for a Cylindrical Shell." ZAMM 78, no. 10 (1998): 663–86. http://dx.doi.org/10.1002/(sici)1521-4001(199810)78:10<663::aid-zamm663>3.0.co;2-g.

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28

Eibner, T., and J. M. Melenk. "An adaptive strategy for hp-FEM based on testing for analyticity." Computational Mechanics 39, no. 5 (2006): 575–95. http://dx.doi.org/10.1007/s00466-006-0107-0.

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29

Banz, Lothar, and Andreas Schröder. "Biorthogonal basis functions in hp-adaptive FEM for elliptic obstacle problems." Computers & Mathematics with Applications 70, no. 8 (2015): 1721–42. http://dx.doi.org/10.1016/j.camwa.2015.07.010.

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30

Gatto, P., and J. S. Hesthaven. "Efficient Preconditioning of hp-FEM Matrices by Hierarchical Low-Rank Approximations." Journal of Scientific Computing 72, no. 1 (2017): 49–80. http://dx.doi.org/10.1007/s10915-016-0347-x.

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31

Solin, P., J. Cerveny, L. Dubcova, and D. Andrs. "Monolithic discretization of linear thermoelasticity problems via adaptive multimesh hp-FEM." Journal of Computational and Applied Mathematics 234, no. 7 (2010): 2350–57. http://dx.doi.org/10.1016/j.cam.2009.08.092.

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32

Solin, Pavel, and Lukas Korous. "Space-time adaptive $$hp$$ -FEM for problems with traveling sharp fronts." Computing 95, S1 (2012): 709–22. http://dx.doi.org/10.1007/s00607-012-0243-7.

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33

Beuchler, Sven. "Wavelet solvers for hp-FEM discretizations in 3D using hexahedral elements." Computer Methods in Applied Mechanics and Engineering 198, no. 13-14 (2009): 1138–48. http://dx.doi.org/10.1016/j.cma.2008.06.014.

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34

Wang, Xiuling, and Darrell W. Pepper. "Application of an hp-Adaptive FEM for Solving Thermal Flow Problems." Journal of Thermophysics and Heat Transfer 21, no. 1 (2007): 190–98. http://dx.doi.org/10.2514/1.22414.

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35

Li, Hui, Yi-Bo Jiang, and Jian-Wen Cai. "A study of azimuthal electromagnetic wave LWD based on self-adaptive hp finite element method." Modern Physics Letters B 32, no. 34n36 (2018): 1840073. http://dx.doi.org/10.1142/s0217984918400730.

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Azimuthal electromagnetic wave logging-while-drilling (LWD) technology can detect weak electromagnetic wave signal and realize real-time resistivity imaging. It has great values to reduce drilling cost and increase drilling rate. In this paper, self-adaptive hp finite element method (FEM) has been used to study the azimuthal resistivity LWD responses in different conditions. Numerical simulation results show that amplitude attenuation and phase shift of directional electromagnetic wave signals are closely related to induced magnetic field and azimuthal angle. The peak value and polarity of geological guidance signals can be used to distinguish reservoir interface and achieve real-time geosteering drilling. Numerical simulation results also show the accuracy of the self-adaptive hp FEM and provide physical interpretation of peak value and polarity of the geological guidance signals.

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36

MARAZZINA, DANIELE, OLEG REICHMANN, and CHRISTOPH SCHWAB. "hp-DGFEM FOR KOLMOGOROV–FOKKER–PLANCK EQUATIONS OF MULTIVARIATE LÉVY PROCESSES." Mathematical Models and Methods in Applied Sciences 22, no. 01 (2012): 1150005. http://dx.doi.org/10.1142/s0218202512005897.

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We analyze the discretization of nonlocal degenerate integrodifferential equations arising as so-called forward equations for jump-diffusion processes. Such equations arise in option pricing problems when the stochastic dynamics of the markets is modeled by Lévy driven stochastic volatility models. Well-posedness of the arising equations is addressed. We develop and analyze stable discretization schemes, in particular the discontinuous Galerkin Finite Element Methods (DG-FEM). In the DG-FEM, a new regularization of hypersingular integrals in the Dirichlet form of the pure jump part of infinite variation processes is proposed, allowing in particular a stable DG discretization of hypersingular integral operators. Robustness of the stabilized discretization with respect to various degeneracies in the characteristic triple of the stochastic process is proved. We provide in particular an hp-error analysis of the DG-FEM. Numerical experiments for model equations confirm the theoretical results.

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37

Šolín, Pavel, Tomáš Vejchodský, and Roberto Araiza. "Discrete conservation of nonnegativity for elliptic problems solved by the hp-FEM." Mathematics and Computers in Simulation 76, no. 1-3 (2007): 205–10. http://dx.doi.org/10.1016/j.matcom.2007.01.015.

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38

Li, Hui, De-Jun Liu, Zhong-hua Ma, and Xin-sheng Gao. "Parameter Response Numerical Simulation of Resistivity LWD Instrument Based on Hp-FEM." Procedia Engineering 29 (2012): 2122–26. http://dx.doi.org/10.1016/j.proeng.2012.01.273.

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39

Melenk, J. M. "On condition numbers in hp-FEM with Gauss–Lobatto-based shape functions." Journal of Computational and Applied Mathematics 139, no. 1 (2002): 21–48. http://dx.doi.org/10.1016/s0377-0427(01)00391-0.

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40

Schotzau, D. "Exponential convergence in a Galerkin least squares hp-FEM for Stokes flow." IMA Journal of Numerical Analysis 21, no. 1 (2001): 53–80. http://dx.doi.org/10.1093/imanum/21.1.53.

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41

Bauer, Andrew C., and Abani K. Patra. "Performance of parallel preconditioners for adaptive hp FEM discretization of incompressible flows." Communications in Numerical Methods in Engineering 18, no. 5 (2002): 305–13. http://dx.doi.org/10.1002/cnm.465.

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42

Han, Runqiang, Jimin Liang, Xiaochao Qu, et al. "A source reconstruction algorithm based on adaptive hp-FEM for bioluminescence tomography." Optics Express 17, no. 17 (2009): 14481. http://dx.doi.org/10.1364/oe.17.014481.

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43

Banz, Lothar, Jan Petsche, and Andreas Schröder. "hp-FEM for a stabilized three-field formulation of the biharmonic problem." Computers & Mathematics with Applications 77, no. 9 (2019): 2463–88. http://dx.doi.org/10.1016/j.camwa.2018.12.037.

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44

Jin, D., P. D. Ledger, and A. J. Gil. "An hp-fem framework for the simulation of electrostrictive and magnetostrictive materials." Computers & Structures 133 (March 2014): 131–48. http://dx.doi.org/10.1016/j.compstruc.2013.10.009.

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45

Chleboun, Jan, and Pavel Solin. "On optimal node and polynomial degree distribution in one-dimensional $$hp$$ -FEM." Computing 95, S1 (2012): 75–88. http://dx.doi.org/10.1007/s00607-012-0232-x.

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46

Solin, Pavel, and Stefano Giani. "An iterative adaptive hp-FEM method for non-symmetric elliptic eigenvalue problems." Computing 95, S1 (2012): 183–213. http://dx.doi.org/10.1007/s00607-012-0251-7.

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47

Houston, Paul, Dominik Schötzau, and Thomas P. Wihler. "An hp-adaptive mixed discontinuous Galerkin FEM for nearly incompressible linear elasticity." Computer Methods in Applied Mechanics and Engineering 195, no. 25-28 (2006): 3224–46. http://dx.doi.org/10.1016/j.cma.2005.06.012.

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48

Zhu, Lingxue, and Haijun Wu. "Preasymptotic Error Analysis of CIP-FEM and FEM for Helmholtz Equation with High Wave Number. Part II: $hp$ Version." SIAM Journal on Numerical Analysis 51, no. 3 (2013): 1828–52. http://dx.doi.org/10.1137/120874643.

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49

Strug, Barbara, Anna Paszynśka, Maciej Paszynśki, and Ewa Grabska. "Using a graph grammar system in the finite element method." International Journal of Applied Mathematics and Computer Science 23, no. 4 (2013): 839–53. http://dx.doi.org/10.2478/amcs-2013-0063.

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Abstract The paper presents a system of Composite Graph Grammars (CGGs)modelling adaptive two dimensional hp Finite Element Method (hp-FEM) algorithms with rectangular finite elements. A computational mesh is represented by a composite graph. The operations performed over the mesh are defined by the graph grammar rules. The CGG system contains different graph grammars defining different kinds of rules of mesh transformations. These grammars allow one to generate the initial mesh, assign values to element nodes and perform h- and p-adaptations. The CGG system is illustrated with an example from the domain of geophysics.

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50

Pereira, J. P., C. A. Duarte, D. Guoy, and X. Jiao. "hp-Generalized FEM and crack surface representation for non-planar 3-D cracks." International Journal for Numerical Methods in Engineering 77, no. 5 (2009): 601–33. http://dx.doi.org/10.1002/nme.2419.

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