메뉴 건너뛰기




Volumn 29, Issue 1, 2007, Pages 118-138

An adaptive multilevel method for time-harmonic maxwell equations with singularities

Author keywords

Adaptive finite element method; Maxwell equations; Multigrid method; Singularities of solutions

Indexed keywords

ADAPTIVE ALGORITHMS; ERROR ANALYSIS; HARMONIC ANALYSIS; PROBLEM SOLVING;

EID: 38349029360     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/050636012     Document Type: Article
Times cited : (63)

References (27)
  • 1
    • 0000669478 scopus 로고    scopus 로고
    • Adaptive multilevel methods for edge element discretizations of Maxwell's equations
    • R. BECK, P. DEUFLHARD, R. HIPTMAIR, R. H. W. HOPPE, AND B. WOHLMUTH, Adaptive multilevel methods for edge element discretizations of Maxwell's equations, Surveys Math. Indust., 8 (1999), pp. 271-312.
    • (1999) Surveys Math. Indust , vol.8 , pp. 271-312
    • BECK, R.1    DEUFLHARD, P.2    HIPTMAIR, R.3    HOPPE, R.H.W.4    WOHLMUTH, B.5
  • 2
    • 85160669681 scopus 로고    scopus 로고
    • 2-theory of the Maxwell operator in arbitrary domains, Uspekhi Mat. Nauk, 42 (1987), pp. 61-76 (in Russian); Russian Math. Surveys, 43 (1987), pp. 75-96 (in English).
    • 2-theory of the Maxwell operator in arbitrary domains, Uspekhi Mat. Nauk, 42 (1987), pp. 61-76 (in Russian); Russian Math. Surveys, 43 (1987), pp. 75-96 (in English).
  • 3
    • 0000999737 scopus 로고
    • Principal singularities of the electric component of an electromagnetic field in regions with screens
    • M. SH. BIRMAN AND M. Z. SOLOMYAK, Principal singularities of the electric component of an electromagnetic field in regions with screens, St. Petersburg Math. J., 5 (1994), pp. 125- 139.
    • (1994) St. Petersburg Math. J , vol.5 , pp. 125-139
    • BIRMAN, M.S.1    SOLOMYAK, M.Z.2
  • 4
    • 0019928319 scopus 로고
    • On finite element methods for elliptic equations on domains with corners
    • H. BLUM AND M. DOBROWOLSKI, On finite element methods for elliptic equations on domains with corners, Computing, 28 (1982), pp. 53-63.
    • (1982) Computing , vol.28 , pp. 53-63
    • BLUM, H.1    DOBROWOLSKI, M.2
  • 5
    • 0037246541 scopus 로고    scopus 로고
    • On the efficiency of adaptive finite element methods for elliptic problems with discontinuous coefficients
    • Z. CHEN AND S. DAI, On the efficiency of adaptive finite element methods for elliptic problems with discontinuous coefficients, SIAM J. Sci. Comput. 24 (2002), pp. 443-462.
    • (2002) SIAM J. Sci. Comput , vol.24 , pp. 443-462
    • CHEN, Z.1    DAI, S.2
  • 6
    • 0042410889 scopus 로고    scopus 로고
    • Adaptive Galerkin methods with error control for a dynamical Ginzburg- Landau model in superconductivity
    • Z. CHEN AND S. DAI, Adaptive Galerkin methods with error control for a dynamical Ginzburg- Landau model in superconductivity, SIAM J. Numer. Anal. 38 (2001), pp. 1961-1985.
    • (2001) SIAM J. Numer. Anal , vol.38 , pp. 1961-1985
    • CHEN, Z.1    DAI, S.2
  • 7
    • 0000713960 scopus 로고    scopus 로고
    • Finite element methods with matching and nonmatching meshes for Maxwell equations with discontinuous coefficients
    • Z. CHEN, Q. DU, AND J. ZOU, Finite element methods with matching and nonmatching meshes for Maxwell equations with discontinuous coefficients, SIAM J. Numer. Anal., 37 (2000), pp, 1542-1570.
    • (2000) SIAM J. Numer. Anal , vol.37 , pp. 1542-1570
    • CHEN, Z.1    DU, Q.2    ZOU, J.3
  • 8
    • 32944473748 scopus 로고    scopus 로고
    • 1 a posteriori error analysis for nonlinear convection-diffusion problems
    • 1 a posteriori error analysis for nonlinear convection-diffusion problems, Math. Comp., 75 (2006), pp. 43-71.
    • (2006) Math. Comp , vol.75 , pp. 43-71
    • CHEN, Z.1    JI, G.H.2
  • 9
    • 3142769712 scopus 로고    scopus 로고
    • An adaptive finite element method with perfectly matched absorbing layers for the wave scattering by periodic structures
    • Z. CHEN AND H. WU, An adaptive finite element method with perfectly matched absorbing layers for the wave scattering by periodic structures, SIAM J. Numer. Anal. 41 (2003), pp. 799-826.
    • (2003) SIAM J. Numer. Anal , vol.41 , pp. 799-826
    • CHEN, Z.1    WU, H.2
  • 10
    • 84988168833 scopus 로고
    • A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains
    • M. COSTABEL, A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains, Math. Methods Appl. Sci., 12 (1990), pp. 365-268.
    • (1990) Math. Methods Appl. Sci , vol.12 , pp. 365-268
    • COSTABEL, M.1
  • 11
    • 0034382191 scopus 로고    scopus 로고
    • Singularities of electromagnetic fields in polyhedral domains
    • M. COSTABEL AND M. DAUGE, Singularities of electromagnetic fields in polyhedral domains, Arch. Ration. Mech. Anal., 151 (2000), pp. 221-276.
    • (2000) Arch. Ration. Mech. Anal , vol.151 , pp. 221-276
    • COSTABEL, M.1    DAUGE, M.2
  • 12
    • 27744578399 scopus 로고    scopus 로고
    • Computation of resonance frequencies for Maxwell equations in non-smooth domains
    • M. Ainsworth et al, eds, Springer-Verlag, Berlin
    • M. COSTABEL AND M. DAUGE, Computation of resonance frequencies for Maxwell equations in non-smooth domains, in Topics in Computational Wave Propagation, M. Ainsworth et al., eds., Springer-Verlag, Berlin, 2003, pp. 125-161.
    • (2003) Topics in Computational Wave Propagation , pp. 125-161
    • COSTABEL, M.1    DAUGE, M.2
  • 13
    • 0011982241 scopus 로고    scopus 로고
    • A singular field method for the solution of Maxwell's equations in polyhedral domains
    • A.-S. BONNET-BEN DHIA, C. HAZARD, AND S. LOHRENGEL, A singular field method for the solution of Maxwell's equations in polyhedral domains, SIAM J. Appl. Math., 59 (1999), pp. 2028-2044.
    • (1999) SIAM J. Appl. Math , vol.59 , pp. 2028-2044
    • BONNET-BEN DHIA, A.-S.1    HAZARD, C.2    LOHRENGEL, S.3
  • 15
    • 20144366303 scopus 로고    scopus 로고
    • Analysis of a multigrid algorithm for time harmonic Maxwell equations
    • J. GOPALAKRISHNAN, J. E. PASCIAK, AND L. F. DEMKOWICZ, Analysis of a multigrid algorithm for time harmonic Maxwell equations, SIAM J. Numer. Anal., 42 (2004), pp. 90-108.
    • (2004) SIAM J. Numer. Anal , vol.42 , pp. 90-108
    • GOPALAKRISHNAN, J.1    PASCIAK, J.E.2    DEMKOWICZ, L.F.3
  • 17
    • 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
  • 18
    • 0001721512 scopus 로고
    • Optimal multilevel iterative methods for adaptive grids
    • W. F. MITCHELL, Optimal multilevel iterative methods for adaptive grids, SIAM J. Sci. Statist. Comput., 13 (1992), pp. 146-167.
    • (1992) SIAM J. Sci. Statist. Comput , vol.13 , pp. 146-167
    • MITCHELL, W.F.1
  • 19
    • 0032298867 scopus 로고    scopus 로고
    • A posteriori error indicators for Maxwell's equations
    • P. MONK, A posteriori error indicators for Maxwell's equations, J. Comput. Appl. Math., 100 (1998), pp. 173-190.
    • (1998) J. Comput. Appl. Math , vol.100 , pp. 173-190
    • MONK, P.1
  • 21
    • 0034447334 scopus 로고    scopus 로고
    • Data oscillation and convergence of adaptive FEM
    • P. MORIN, R. H. NOCHETTO, AND K. G. SIEBERT, Data oscillation and convergence of adaptive FEM, SIAM J. Numer. Anal., 38 (2000), pp. 466-488.
    • (2000) SIAM J. Numer. Anal , vol.38 , pp. 466-488
    • MORIN, P.1    NOCHETTO, R.H.2    SIEBERT, K.G.3
  • 23
    • 0036453186 scopus 로고    scopus 로고
    • Overlapping Schwarz methods in H(curl) on polyhedral domains
    • J. E. PASCIAK AND J. ZHAO, Overlapping Schwarz methods in H(curl) on polyhedral domains, J. Numer. Math., 10 (2002), pp. 221-234.
    • (2002) J. Numer. Math , vol.10 , pp. 221-234
    • PASCIAK AND, J.E.1    ZHAO, J.2
  • 25
    • 31644445169 scopus 로고    scopus 로고
    • Design of Adaptive Finite Element Software: The Finite Element Toolbox ALBERTA
    • Springer-Verlag, Berlin, Heidelberg
    • A. SCHMIDT AND K. G. SIEBERT, Design of Adaptive Finite Element Software: The Finite Element Toolbox ALBERTA, Lecture Notes in Computational Science and Engineering 2, Springer-Verlag, Berlin, Heidelberg, 2005.
    • (2005) Lecture Notes in Computational Science and Engineering , vol.2
    • SCHMIDT AND, A.1    SIEBERT, K.G.2
  • 26
    • 84966200902 scopus 로고
    • Finite element interpolation of nonsmooth functions satisfying boundary conditions
    • L. R. SCOTT AND Z. ZHANG, Finite element interpolation of nonsmooth functions satisfying boundary conditions, Math. Comp., 54 (1994), pp. 483-493.
    • (1994) Math. Comp , vol.54 , pp. 483-493
    • SCOTT, L.R.1    ZHANG, Z.2
  • 27
    • 85160633514 scopus 로고    scopus 로고
    • Uniform convergence of multigrid V-cycle on adaptively refined finite element meshes for second order elliptic problems, Science
    • in China
    • H. Wu AND Z. CHEN, Uniform convergence of multigrid V-cycle on adaptively refined finite element meshes for second order elliptic problems, Science in China: Ser. A Mathematics, 49 (2006), pp. 1-28.
    • (2006) Ser. A Mathematics , vol.49 , pp. 1-28
    • Wu, H.1    CHEN, Z.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.