메뉴 건너뛰기




Volumn 57, Issue 3, 2013, Pages 582-603

An efficient high-order time integration method for spectral-element discontinuous galerkin simulations in electromagnetics

Author keywords

Arnoldi process; Exponential time integration; Krylov approximation; Matrix exponential; Spectral element discontinuous Galerkin method

Indexed keywords

ARNOLDI PROCESS; DISCONTINUOUS GALERKIN METHODS; EXPONENTIAL TIME INTEGRATION; KRYLOV APPROXIMATION; MATRIX EXPONENTIALS;

EID: 84889101690     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10915-013-9718-8     Document Type: Article
Times cited : (4)

References (34)
  • 1
    • 0037354371 scopus 로고    scopus 로고
    • Nineteen dubios ways to compute the exponential of a matrix, twenty-five years later
    • 1981253 10.1137/S00361445024180
    • Moler, C.; Loan, C.V.: Nineteen dubios ways to compute the exponential of a matrix, twenty-five years later. SIAM Rev. 45(1), 3-49 (2003)
    • (2003) SIAM Rev. , vol.45 , Issue.1 , pp. 3-49
    • Moler, C.1    Loan, C.V.2
  • 2
    • 77956616413 scopus 로고    scopus 로고
    • Exponential integrators
    • 2652783 10.1017/S0962492910000048
    • Hochbruck, M.; Ostermann, A.: Exponential integrators. Acta Numer. 19, 209-286 (2010)
    • (2010) Acta Numer. , vol.19 , pp. 209-286
    • Hochbruck, M.1    Ostermann, A.2
  • 4
    • 0026818185 scopus 로고
    • Analysis of some Krylov subspace approximation to the matrix exponential operator
    • 1149094 10.1137/0729014
    • Saad, Y.: Analysis of some Krylov subspace approximation to the matrix exponential operator. SIAM J. Numer. Anal. 29, 209-228 (1992)
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 209-228
    • Saad, Y.1
  • 5
    • 0001609443 scopus 로고
    • Krylov subspace methods on supercomputers
    • 1025539 10.1137/0910073
    • Saad, Y.: Krylov subspace methods on supercomputers. SIAM J. Sci. Stat. Comput. 10(6), 1200-1232 (1989)
    • (1989) SIAM J. Sci. Stat. Comput. , vol.10 , Issue.6 , pp. 1200-1232
    • Saad, Y.1
  • 6
    • 0000269389 scopus 로고
    • Efficient solution of parabolic equations by Krylov approximation methods
    • 1177807 10.1137/0913071
    • Gallopoulos, E.; Saad, Y.: Efficient solution of parabolic equations by Krylov approximation methods. SIAM J. Sci. Stat. Comput. 13(5), 1236-1264 (1992)
    • (1992) SIAM J. Sci. Stat. Comput. , vol.13 , Issue.5 , pp. 1236-1264
    • Gallopoulos, E.1    Saad, Y.2
  • 7
    • 28244462004 scopus 로고    scopus 로고
    • A low cost Arnoldi method for large linear initial value problems
    • 2173553 10.1080/00207160410001708814
    • Novati, P.: A low cost Arnoldi method for large linear initial value problems. Int. J. Comput. Math. 81(7), 835-844 (2004)
    • (2004) Int. J. Comput. Math. , vol.81 , Issue.7 , pp. 835-844
    • Novati, P.1
  • 8
    • 0002279610 scopus 로고    scopus 로고
    • Exponential integrators for large systems of differential equations
    • 1618808 10.1137/S1064827595295337
    • Hochbruck, M.; Lubich, C.; Selhofer, H.: Exponential integrators for large systems of differential equations. SIAM J. Sci. Comput. 19(5), 1552-1574 (1996)
    • (1996) SIAM J. Sci. Comput. , vol.19 , Issue.5 , pp. 1552-1574
    • Hochbruck, M.1    Lubich, C.2    Selhofer, H.3
  • 9
    • 0347799731 scopus 로고    scopus 로고
    • On the Krylov subspace approximations to the matrix exponential operator
    • 1472203 10.1137/S0036142995280572
    • Hochbruck, M.; Lubich, C.: On the Krylov subspace approximations to the matrix exponential operator. SIAM J. Numer. Anal. 34(5), 1911-1925 (1997)
    • (1997) SIAM J. Numer. Anal. , vol.34 , Issue.5 , pp. 1911-1925
    • Hochbruck, M.1    Lubich, C.2
  • 10
    • 0036740992 scopus 로고    scopus 로고
    • Nodal hihg-order methods on unstructured grids. I: Time-domain solution of Maxwell's equations
    • 1925981 10.1006/jcph.2002.7118
    • Hesthaven, J.S.; Warburton, T.: Nodal hihg-order methods on unstructured grids. I: time-domain solution of Maxwell's equations. J. Comput. Phys. 181(1), 186-221 (2002)
    • (2002) J. Comput. Phys. , vol.181 , Issue.1 , pp. 186-221
    • Hesthaven, J.S.1    Warburton, T.2
  • 11
    • 51749086287 scopus 로고    scopus 로고
    • Algorithms, Analysis, and Applications, Texts in Applied Mathematics. Springer, Berlin
    • Hesthaven, J.S.; Warburton, T.: Nodal Discontinuous Galerkin Methods, Algorithms, Analysis, and Applications, Texts in Applied Mathematics. Springer, Berlin (2008)
    • (2008) Nodal Discontinuous Galerkin Methods
    • Hesthaven, J.S.1    Warburton, T.2
  • 12
    • 1442306605 scopus 로고    scopus 로고
    • Locally divergence-free discontinuous Galerkin methods
    • 2034859 10.1016/j.jcp.2003.09.007
    • Cockburn, B.; Li, F.; Shu, C.W.: Locally divergence-free discontinuous Galerkin methods. J. Comp. Phys. 194, 588-610 (2004)
    • (2004) J. Comp. Phys. , vol.194 , pp. 588-610
    • Cockburn, B.1    Li, F.2    Shu, C.W.3
  • 13
    • 4344562945 scopus 로고    scopus 로고
    • High-order symplectic integration methods for finite element solutions to time dependent Maxwell equations
    • 2079479 10.1109/TAP.2004.832356
    • Rieben, R.; White, D.; Rodrigue, R.: High-order symplectic integration methods for finite element solutions to time dependent Maxwell equations. IEEE Trans. Antennas Propag. 56(8), 2190-2195 (2004)
    • (2004) IEEE Trans. Antennas Propag. , vol.56 , Issue.8 , pp. 2190-2195
    • Rieben, R.1    White, D.2    Rodrigue, R.3
  • 14
    • 34250256485 scopus 로고
    • Mixed finite elements in R3
    • 10.1007/BF01396415
    • Nédeléc, J.C.: Mixed finite elements in R3. Numer. Math. 159(1), 315-341 (1980)
    • (1980) Numer. Math. , vol.159 , Issue.1 , pp. 315-341
    • Nédeléc, J.C.1
  • 15
    • 33646388286 scopus 로고
    • Fourth-order sympletic integration
    • 1060047 10.1016/0167-2789(90)90019-L
    • Forest, E.; Ruth, R.D.: Fourth-order sympletic integration. Physica D 43, 105-117 (1990)
    • (1990) Physica D , vol.43 , pp. 105-117
    • Forest, E.1    Ruth, R.D.2
  • 16
    • 0003171736 scopus 로고
    • A simplectic integration algorithm for separable Hamiltonian functions
    • 1088632 10.1016/0021-9991(91)90299-Z
    • Candy, J.; Rozmus, W.: A simplectic integration algorithm for separable Hamiltonian functions. J. Comput. Phys. 92, 230-256 (1991)
    • (1991) J. Comput. Phys. , vol.92 , pp. 230-256
    • Candy, J.1    Rozmus, W.2
  • 18
    • 0016567489 scopus 로고
    • On logarithmic norms
    • 408227 10.1137/0712055
    • Strom, T.: On logarithmic norms. SIAM J. Numer. Anal. 12(5), 741-753 (1975)
    • (1975) SIAM J. Numer. Anal. , vol.12 , Issue.5 , pp. 741-753
    • Strom, T.1
  • 22
    • 84889093558 scopus 로고    scopus 로고
    • LAPACK, Linear Algebra PACKage
    • LAPACK, Linear Algebra PACKage, http://www.netlib.org/lapack
  • 23
    • 0042839565 scopus 로고    scopus 로고
    • Propagation of light in metallic nanowire arrays: Finite-difference time domain studies of silver cylinders
    • 10.1103/PhysRevB.68.045415
    • Gray, S.K.; Kupka, T.: Propagation of light in metallic nanowire arrays: Finite-difference time domain studies of silver cylinders. Phys. Rev. B 68, 045415/1-045415/11 (2003)
    • (2003) Phys. Rev. B , vol.68
    • Gray, S.K.1    Kupka, T.2
  • 24
    • 0141457691 scopus 로고    scopus 로고
    • Theoretical study of dielectrically coated metallic nanowires
    • 10.1016/j.cplett.2003.08.038
    • Oliva, J.M.; Gray, S.K.: Theoretical study of dielectrically coated metallic nanowires. Chem. Phys. Lett. 379, 325-331 (2003)
    • (2003) Chem. Phys. Lett. , vol.379 , pp. 325-331
    • Oliva, J.M.1    Gray, S.K.2
  • 25
    • 18244397694 scopus 로고    scopus 로고
    • TE/TM field solver for particle beam simulations without numerical Cherenkov radiation
    • 10.1103/PhysRevSTAB.8.042001
    • Zagorodnov, I.: TE/TM field solver for particle beam simulations without numerical Cherenkov radiation. Phys. Rev. Spec. Top. Accel. Beams 8, 042001 (2005)
    • (2005) Phys. Rev. Spec. Top. Accel. Beams , vol.8 , pp. 042001
    • Zagorodnov, I.1
  • 26
    • 33751529439 scopus 로고    scopus 로고
    • Accurate modeling of charged particle beams in linear accelerators
    • 10.1088/1367-2630/8/11/285
    • Gjonaj, E.; Lau, T.; Schnepp, S.; Wolfheimer, F.; Weiland, T.: Accurate modeling of charged particle beams in linear accelerators. New J. Phys. 8, 285 (2006)
    • (2006) New J. Phys. , vol.8 , pp. 285
    • Gjonaj, E.1    Lau, T.2    Schnepp, S.3    Wolfheimer, F.4    Weiland, T.5
  • 27
    • 32644433692 scopus 로고    scopus 로고
    • Fourier spectral simulations and Gegenbauer reconstructions for electromagnetic waves in the presence of a metal nanoparticle
    • 10.1016/j.jcp.2005.06.025
    • Min, M.S.; Lee, T.W.; Fischer, P.F.; Gray, S.K.: Fourier spectral simulations and Gegenbauer reconstructions for electromagnetic waves in the presence of a metal nanoparticle. J. Comput. Phys. 213(2), 730-747 (2006)
    • (2006) J. Comput. Phys. , vol.213 , Issue.2 , pp. 730-747
    • Min, M.S.1    Lee, T.W.2    Fischer, P.F.3    Gray, S.K.4
  • 28
    • 77957027753 scopus 로고    scopus 로고
    • Large-scale electromagnetic modeling based on high-order methods: Nanoscience applications
    • 10.1088/1742-6596/180/1/012016
    • Min, M.S.; Fischer, P.F.; Montgomery, J.; Gray, S.K.: Large-scale electromagnetic modeling based on high-order methods: nanoscience applications. J. Phys. Conf. Ser. 180, 012016 (2009)
    • (2009) J. Phys. Conf. Ser. , vol.180 , pp. 012016
    • Min, M.S.1    Fischer, P.F.2    Montgomery, J.3    Gray, S.K.4
  • 29
    • 84889096091 scopus 로고    scopus 로고
    • Spectral-element discontinuous Galerkin simulations for bunched beam in accelerating structures
    • Min, M.S.; Fischer, P.F.; Chae, Y.C.: Spectral-element discontinuous Galerkin simulations for bunched beam in accelerating structures. In: Proceedings of PAC07, pp. 3432-3434 (2007)
    • (2007) Proceedings of PAC07 , pp. 3432-3434
    • Min, M.S.1    Fischer, P.F.2    Chae, Y.C.3
  • 30
    • 77958513550 scopus 로고    scopus 로고
    • A spectral-element discontinuous Galerkin lattice-Boltzmann method for incompressible flows
    • 2734290 10.1016/j.jcp.2010.09.024
    • Min, M.S.; Lee, T.: A spectral-element discontinuous Galerkin lattice-Boltzmann method for incompressible flows. J. Comput. Phys. 230, 245-259 (2011)
    • (2011) J. Comput. Phys. , vol.230 , pp. 245-259
    • Min, M.S.1    Lee, T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.