메뉴 건너뛰기




Volumn 33, Issue 4, 2011, Pages 2095-2114

Adaptive multilevel methods with local smoothing for H1-and Hcurl-conforming high order finite element methods

Author keywords

Adaptive mesh refinement; Finite element method; Hanging nodes; Maxwell equations; Multigrid methods

Indexed keywords

MAXWELL EQUATIONS;

EID: 80052730942     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/090778523     Document Type: Article
Times cited : (69)

References (45)
  • 1
    • 0034386185 scopus 로고    scopus 로고
    • Multigrid in H (div) and H (curl)
    • D. N. ARNOLD, R. S. FALK, AND R. WINTHER, Multigrid in H (div) and H (curl), Numer. Math., 85(2000), pp. 197-217.
    • (2000) Numer. Math. , vol.85 , pp. 197-217
    • Arnold, D.N.1    Falk, R.S.2    Winther, R.3
  • 2
    • 34548277425 scopus 로고    scopus 로고
    • Deal. II-A general-purpose object-oriented finite element library
    • W. BANGERTH, R. HARTMANN, AND G. KANSCHAT, deal. II-A general-purpose object-oriented finite element library, ACM Trans. Math. Software, 33(2007), 24.
    • (2007) ACM Trans. Math. Software , vol.33 , pp. 24
    • Bangerth, W.1    Hartmann, R.2    Kanschat, G.3
  • 4
    • 67649261504 scopus 로고    scopus 로고
    • Data structures and requirements for hp finite element software
    • W. BANGERTH AND O. KAYSER-HEROLD, Data structures and requirements for hp finite element software, ACM Trans. Math. Software, 36(2009), 4.
    • (2009) ACM Trans. Math. Software , vol.36 , pp. 4
    • Bangerth, W.1    Kayser-Herold, O.2
  • 7
    • 0012065009 scopus 로고    scopus 로고
    • Load balancing for adaptive multigrid methods
    • PII S1064827596297562
    • P. BASTIAN, Load balancing for adaptive multigrid methods, SIAM J. Sci. Comput., 19(1998), pp. 1303-1321. (Pubitemid 128616143)
    • (1998) SIAM Journal of Scientific Computing , vol.19 , Issue.4 , pp. 1303-1321
    • Bastian, P.1
  • 8
    • 33750825596 scopus 로고    scopus 로고
    • Multigrid methods on adaptively refined grids
    • DOI 10.1109/MCSE.2006.116, 1717314
    • P. BASTIAN AND C. WIENERS, Multigrid methods on adaptively refined grids, Comput. Sci. Eng., 8(2006), pp. 44-54. (Pubitemid 44711776)
    • (2006) Computing in Science and Engineering , vol.8 , Issue.6 , pp. 44-54
    • Bastian, P.1    Wieners, C.2
  • 9
    • 0034421041 scopus 로고    scopus 로고
    • Residual based a posteriori error estimators for eddy current computation
    • R. BECK, R. HIPTMAIR, R. H. W. HOPPE, AND B. WOHLMUTH, Residual based a posteriori error estimators for eddy current computation, M2AN Math. Model. Numer. Anal., 34(2000), pp. 159-182.
    • (2000) M2AN Math. Model. Numer. Anal. , vol.34 , pp. 159-182
    • Beck, R.1    Hiptmair, R.2    Hoppe, R.H.W.3    Wohlmuth, B.4
  • 10
    • 0442298658 scopus 로고    scopus 로고
    • Multigrid techniques for finite elements on locally refined meshes
    • R. BECKER AND M. BRAACK, Multigrid techniques for finite elements on locally refined meshes, Numer. Linear Algebra Appl., 7(2000), pp. 363-379.
    • (2000) Numer. Linear Algebra Appl. , vol.7 , pp. 363-379
    • Becker, R.1    Braack, M.2
  • 12
    • 80052755428 scopus 로고    scopus 로고
    • A local adaptive refinement method with multigrid preconditioning illustrated by multiphase flows simulations
    • available online at
    • F. BOYER, C. LAPUERTA, S. MINJEAUD, AND B. PIAR, A Local Adaptive Refinement Method with Multigrid Preconditioning Illustrated by Multiphase Flows Simulations, Technical report, 2008; available online at http://hal.archives- ouvertes.fr/hal-00307186.
    • (2008) Technical Report
    • Boyer, F.1    Lapuerta, C.2    Minjeaud, S.3    Piar, B.4
  • 13
    • 0003320310 scopus 로고
    • Multigrid methods
    • Longman Scientific & Technical, Harlow, UK
    • J. H. BRAMBLE, Multigrid Methods, Pitman Res. Notes Math. Ser. 294, Longman Scientific & Technical, Harlow, UK, 1993.
    • (1993) Pitman Res. Notes Math. Ser. , vol.294
    • Bramble, J.H.1
  • 14
    • 84966234195 scopus 로고
    • Parallel multilevel preconditioners
    • J. H. BRAMBLE, J. E. PASCIAK, AND J. XU, Parallel multilevel preconditioners, Math. Comp., 55(1990), pp. 1-22.
    • (1990) Math. Comp. , vol.55 , pp. 1-22
    • Bramble, J.H.1    Pasciak, J.E.2    Xu, J.3
  • 15
    • 84966233568 scopus 로고
    • Multi-level adaptive solutions to boundary-value problems
    • A. BRANDT, Multi-level adaptive solutions to boundary-value problems, Math. Comp., 31(1977), pp. 333-390.
    • (1977) Math. Comp. , vol.31 , pp. 333-390
    • Brandt, A.1
  • 17
    • 54249162100 scopus 로고    scopus 로고
    • Quasi-optimal convergence rate for an adaptive finite element method
    • J. M. CASCON, C. KREUZER, R. H. NOCHETTO, AND K. G. SIEBERT, Quasi-optimal convergence rate for an adaptive finite element method, SIAM J. Numer. Anal., 46(2008), pp. 2524-2550.
    • (2008) SIAM J. Numer. Anal. , vol.46 , pp. 2524-2550
    • Cascon, J.M.1    Kreuzer, C.2    Nochetto, R.H.3    Siebert, K.G.4
  • 19
    • 23044520442 scopus 로고    scopus 로고
    • Multiscale decompositions on bounded domains
    • A. COHEN, W. DAHMEN, AND R. DEVORE, Multiscale decompositions on bounded domains, Trans. Amer. Math. Soc., 352(2000), pp. 3651-3685.
    • (2000) Trans. Amer. Math. Soc. , vol.352 , pp. 3651-3685
    • Cohen, A.1    Dahmen, W.2    DeVore, R.3
  • 20
    • 0035606214 scopus 로고    scopus 로고
    • Adaptive wavelet methods for elliptic operator equations: Convergence rates
    • A. COHEN, W. DAHMEN, AND R. DEVORE, Adaptive wavelet methods for elliptic operator equations: Convergence rates, Math. Comp., 70(2001), pp. 27-75. (Pubitemid 33574336)
    • (2001) Mathematics of Computation , vol.70 , Issue.233 , pp. 27-75
    • Cohen, A.1    Dahmen, W.2    Devore, R.3
  • 21
    • 1542639888 scopus 로고    scopus 로고
    • A convergent adaptive algorithm for Poisson's equation
    • W. DÖRFLER, A convergent adaptive algorithm for Poisson's equation, SIAM J. Numer. Anal., 33(1996), pp. 1106-1124. (Pubitemid 126423840)
    • (1996) SIAM Journal on Numerical Analysis , vol.33 , Issue.3 , pp. 1106-1124
    • Dorfler, W.1
  • 22
    • 21844511143 scopus 로고
    • On the abstract theory of additive and multiplicative Schwarz algorithms
    • M. GRIEBEL AND P. OSWALD, On the abstract theory of additive and multiplicative Schwarz algorithms, Numer. Math., 70(1995), pp. 163-180.
    • (1995) Numer. Math. , vol.70 , pp. 163-180
    • Griebel, M.1    Oswald, P.2
  • 24
    • 0000626839 scopus 로고    scopus 로고
    • Multigrid method for Maxwell's equations
    • R. HIPTMAIR, Multigrid method for Maxwell's equations, SIAM J. Numer. Anal., 36(1998), pp. 204-225.
    • (1998) SIAM J. Numer. Anal. , vol.36 , pp. 204-225
    • Hiptmair, R.1
  • 25
    • 70249144702 scopus 로고    scopus 로고
    • Local multigrid in H (curl)
    • R. HIPTMAIR AND W. ZHENG, Local multigrid in H (curl), J. Comput. Math., 27(2009), pp. 573-603.
    • (2009) J. Comput. Math. , vol.27 , pp. 573-603
    • Hiptmair, R.1    Zheng, W.2
  • 26
    • 0036044675 scopus 로고    scopus 로고
    • Non-nested multi-level solvers for finite element discretisations of mixed problems
    • V. JOHN, P. KNOBLOCH, G. MATTHIES, AND L. TOBISKA, Non-nested multi-level solvers for finite element discretisations of mixed problems, Computing, 68(2002), pp. 313-341.
    • (2002) Computing , vol.68 , pp. 313-341
    • John, V.1    Knobloch, P.2    Matthies, G.3    Tobiska, L.4
  • 28
    • 16244415211 scopus 로고    scopus 로고
    • An adaptive multigrid tool for elliptic and parabolic systems
    • DOI 10.1002/fld.845, 8th ICFD Conference on Numerical Methods for Fluid Dynamics: Part 2
    • A. C. JONES AND P. K. JIMACK, An adaptive multigrid tool for elliptic and parabolic systems, Internat. J. Numer. Methods Fluids, 47(2005), pp. 1123-1128. (Pubitemid 40464877)
    • (2005) International Journal for Numerical Methods in Fluids , vol.47 , Issue.10-11 , pp. 1123-1128
    • Jones, A.C.1    Jimack, P.K.2
  • 30
    • 4944249121 scopus 로고    scopus 로고
    • Multi-level methods for discontinuous Galerkin FEM on locally refined meshes
    • G. KANSCHAT, Multi-level methods for discontinuous Galerkin FEM on locally refined meshes, Comput. & Structures, 82(2004), pp. 2437-2445.
    • (2004) Comput. & Structures , vol.82 , pp. 2437-2445
    • Kanschat, G.1
  • 31
    • 0003318740 scopus 로고
    • Multilevel adaptive methods for partial differential equations
    • SIAM, Philadelphia
    • S. F. MCCORMICK, Multilevel Adaptive Methods for Partial Differential Equations, Frontiers Appl. Math. 6, SIAM, Philadelphia, 1989.
    • (1989) Frontiers Appl. Math. , vol.6
    • McCormick, S.F.1
  • 32
    • 38049130877 scopus 로고    scopus 로고
    • Parallel adaptive multilevel methods with full domain partitions
    • W. F. MITCHELL, Parallel adaptive multilevel methods with full domain partitions, Appl. Numer. Anal. Comput. Math., 1(2004), pp. 36-48.
    • (2004) Appl. Numer. Anal. Comput. Math. , vol.1 , pp. 36-48
    • Mitchell, W.F.1
  • 33
    • 34250256485 scopus 로고
    • Mixed finite elements in R
    • J.-C. NÉDÉLEC, Mixed finite elements in R, Numer. Math., 35(1980), pp. 315-341.
    • (1980) Numer. Math. , vol.35 , pp. 315-341
    • Nédélec, J.-C.1
  • 34
    • 0021488801 scopus 로고
    • Design and data structure of fully adaptive, multigrid, finite-element software
    • M.-C. RIVARA, Design and data structure of fully adaptive, multigrid, finite-element software, ACM Trans. Math. Software, 10(1984), pp. 242-264.
    • (1984) ACM Trans. Math. Software , vol.10 , pp. 242-264
    • Rivara, M.-C.1
  • 35
    • 0003331891 scopus 로고
    • Mathematical and computational techniques for multilevel adaptive methods
    • SIAM, Philadelphia
    • U. RÜDE, Mathematical and Computational Techniques for Multilevel Adaptive Methods, Frontiers Appl. Math. 13, SIAM, Philadelphia, 1993.
    • (1993) Frontiers Appl. Math. , vol.13
    • Rüde, U.1
  • 37
    • 77953819086 scopus 로고    scopus 로고
    • A parallel geometric multigrid method for finite elements on octree meshes
    • R. S. SAMPATH AND G. BIROS, A parallel geometric multigrid method for finite elements on octree meshes, SIAM J. Sci. Comput., 32(2010), pp. 1361-1392.
    • (2010) SIAM J. Sci. Comput. , vol.32 , pp. 1361-1392
    • Sampath, R.S.1    Biros, G.2
  • 38
    • 27144549033 scopus 로고    scopus 로고
    • Design of adaptive finite element software. The finite element toolbox ALBERTA
    • Springer-Verlag, Berlin
    • A. SCHMIDT AND K. SIEBERT, Design of Adaptive Finite Element Software. The Finite Element Toolbox ALBERTA, Lect. Notes Comput. Sci. Eng. 42, Springer-Verlag, Berlin, 2005.
    • (2005) Lect. Notes Comput. Sci. Eng. , vol.42
    • Schmidt, A.1    Siebert, K.2
  • 39
    • 37849008769 scopus 로고    scopus 로고
    • Additive Schwarz preconditioning for p-version triangular and tetrahedral finite elements
    • J. SCHÖBERL, J. M. MELENK, C. PECHSTEIN, AND S. ZAGLMAYR, Additive Schwarz preconditioning for p-version triangular and tetrahedral finite elements, IMA J. Numer. Anal., 28(2008), pp. 1-24.
    • (2008) IMA J. Numer. Anal. , vol.28 , pp. 1-24
    • Schöberl, J.1    Melenk, J.M.2    Pechstein, C.3    Zaglmayr, S.4
  • 40
    • 38749111846 scopus 로고    scopus 로고
    • Arbitrary-level hanging nodes and automatic adaptivity in the hp-FEM
    • DOI 10.1016/j.matcom.2007.02.011, PII S0378475407001504
    • P. SOLÍN, J. CERVENÝ, AND I. DOLEŽEL, Arbitrary-level hanging nodes and automatic adaptivity in the hp-FEM, Math. Comput. Simulation, 77(2008), pp. 117-132. (Pubitemid 351181369)
    • (2008) Mathematics and Computers in Simulation , vol.77 , Issue.1 , pp. 117-132
    • Solin, P.1    Cerveny, J.2    Dolezel, I.3
  • 42
    • 0003943048 scopus 로고    scopus 로고
    • 2nd ed., Springer Ser. Comput. Math, Springer-Verlag, Berlin
    • R. S. VARGA, Matrix Iterative Analysis, 2nd ed., Springer Ser. Comput. Math. 27, Springer-Verlag, Berlin, 2000.
    • (2000) Matrix Iterative Analysis , vol.27
    • Varga, R.S.1
  • 44
    • 0000570696 scopus 로고
    • Iterative methods by space decomposition and subspace correction
    • J. XU, Iterative methods by space decomposition and subspace correction, SIAM Rev., 34(1992), pp. 581-613.
    • (1992) SIAM Rev. , vol.34 , pp. 581-613
    • Xu, J.1
  • 45
    • 34250126304 scopus 로고
    • On the multi-level splitting of finite element spaces
    • H. YSERENTANT, On the multi-level splitting of finite element spaces, Numer. Math., 49(1986), pp. 379-412.
    • (1986) Numer. Math. , vol.49 , pp. 379-412
    • Yserentant, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.