메뉴 건너뛰기




Volumn 211, Issue 2, 2006, Pages 659-699

A class of difference schemes with flexible local approximation

Author keywords

Flexible approximation; Generalized finite difference method; Multiparticle problems; Photonic crystals; Plasmon particles; Scattering; The Poisson Boltzmann equation; The Schr dinger equation; Wave propagation

Indexed keywords

BOUNDARY LAYERS; ELECTROSTATICS; FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; HARMONIC ANALYSIS; POLYNOMIALS; VARIATIONAL TECHNIQUES;

EID: 26944471129     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2005.06.011     Document Type: Article
Times cited : (63)

References (125)
  • 1
    • 26944453460 scopus 로고
    • On approximation of functions by harmonic polynomials
    • V.V. Andrievskii On approximation of functions by harmonic polynomials Math. USSR-Izvestiya 51 1 1987 1-13
    • (1987) Math. USSR-Izvestiya , vol.51 , Issue.1 , pp. 1-13
    • Andrievskii, V.V.1
  • 2
    • 0036410391 scopus 로고    scopus 로고
    • Unified analysis of discontinuous Galerkin methods for elliptic problems
    • D.N. Arnold F. Brezzi B. Cockburn L.D. Marini Unified analysis of discontinuous Galerkin methods for elliptic problems SIAM J. Numer. Anal. 39 5 2002 1749-1779
    • (2002) SIAM J. Numer. Anal. , vol.39 , Issue.5 , pp. 1749-1779
    • Arnold, D.N.1    Brezzi, F.2    Cockburn, B.3    Marini, L.D.4
  • 3
    • 0042964833 scopus 로고    scopus 로고
    • The meshless local Petrov-Galerkin (MLPG) method: A simple and less-costly alternative to the finite element and boundary element methods
    • S.N. Atluri S.P. Shen The meshless local Petrov-Galerkin (MLPG) method: a simple and less-costly alternative to the finite element and boundary element methods CMES - Comput. Model. Eng. Sci. 3 1 2002 11-51
    • (2002) CMES - Comput. Model. Eng. Sci. , vol.3 , Issue.1 , pp. 11-51
    • Atluri, S.N.1    Shen, S.P.2
  • 4
    • 0032136132 scopus 로고    scopus 로고
    • A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics
    • S.N. Atluri T. Zhu A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics Comput. Mech. 22 1998 117-127
    • (1998) Comput. Mech. , vol.22 , pp. 117-127
    • Atluri, S.N.1    Zhu, T.2
  • 5
    • 0028483749 scopus 로고
    • Special finite-element methods for a class of 2nd-order elliptic problems with rough coefficients
    • I. Babuška G. Caloz J.E. Osborn Special finite-element methods for a class of 2nd-order elliptic problems with rough coefficients SIAM J. Numer. Anal. 31 4 1994 945-981
    • (1994) SIAM J. Numer. Anal. , vol.31 , Issue.4 , pp. 945-981
    • Babuška, I.1    Caloz, G.2    Osborn, J.E.3
  • 7
    • 1542681822 scopus 로고    scopus 로고
    • Survey of meshless and generalized finite element methods: A unified approach
    • Ivo Babuška Uday Banerjee John E. Osborn Survey of meshless and generalized finite element methods: A unified approach Acta Numer. 12 2003 1-125
    • (2003) Acta Numer. , vol.12 , pp. 1-125
    • Babuška, I.1    Banerjee, U.2    Osborn, J.E.3
  • 8
    • 0028734274 scopus 로고
    • The p and h-p versions of the finite element method, basic principles and properties
    • Ivo Babuška Manil Suri The p and h-p versions of the finite element method, basic principles and properties SIAM Rev. 36 1994 578-632
    • (1994) SIAM Rev. , vol.36 , pp. 578-632
    • Babuška, I.1    Suri, M.2
  • 9
    • 0035964342 scopus 로고    scopus 로고
    • Electrostatics of nanosystems: Application to microtubules and the ribosome
    • N.A. Baker D. Sept J. Simpson M.J. Holst J.A. McCammon Electrostatics of nanosystems: Application to microtubules and the ribosome PNAS 98 18 2001 10037-10041
    • (2001) PNAS , vol.98 , Issue.18 , pp. 10037-10041
    • Baker, N.A.1    Sept, D.2    Simpson, J.3    Holst, M.J.4    McCammon, J.A.5
  • 13
    • 84972515287 scopus 로고
    • Approximation of harmonic functions of three variables by harmonic polynomials
    • Stefan Bergman Approximation of harmonic functions of three variables by harmonic polynomials Duke Math. J. 33 2 1966 379-387
    • (1966) Duke Math. J. , vol.33 , Issue.2 , pp. 379-387
    • Bergman, S.1
  • 14
    • 0003602386 scopus 로고    scopus 로고
    • Computational Electromagnetism: Variational Formulations, Complementarity, Edge Elements
    • San Diego: Academic Press
    • Alain Bossavit Computational Electromagnetism: Variational Formulations, Complementarity, Edge Elements 1998 Academic Press San Diego
    • (1998)
    • Bossavit, A.1
  • 15
    • 0037166224 scopus 로고    scopus 로고
    • The discontinuous Petrov-Galerkin method for elliptic problems
    • C.L. Bottasso S. Micheletti R. Sacco The discontinuous Petrov-Galerkin method for elliptic problems Comput. Meth. Appl. Mech. Eng. 191 31 2002 3391-3409
    • (2002) Comput. Meth. Appl. Mech. Eng. , vol.191 , Issue.31 , pp. 3391-3409
    • Bottasso, C.L.1    Micheletti, S.2    Sacco, R.3
  • 18
    • 0032515215 scopus 로고    scopus 로고
    • Further considerations on residual free bubbles for advective-diffusive equations
    • F. Brezzi L.P. Franca A. Russo Further considerations on residual free bubbles for advective-diffusive equations Comput. Meth. Appl. Mech. Eng. 166 1998 25-33
    • (1998) Comput. Meth. Appl. Mech. Eng. , vol.166 , pp. 25-33
    • Brezzi, F.1    Franca, L.P.2    Russo, A.3
  • 19
    • 0000054413 scopus 로고    scopus 로고
    • Real-space multigrid-based approach to large-scale electronic structure calculations
    • E.L. Briggs D.J. Sullivan J. Bernholc Real-space multigrid-based approach to large-scale electronic structure calculations Phys. Rev. B 54 20 1996 14362-14375
    • (1996) Phys. Rev. B , vol.54 , Issue.20 , pp. 14362-14375
    • Briggs, E.L.1    Sullivan, D.J.2    Bernholc, J.3
  • 20
    • 0034548629 scopus 로고    scopus 로고
    • An a priori error analysis of the local discontinuous Galerkin method for elliptic problems
    • P. Castillo B. Cockburn I. Perugia D. Schöotzau An a priori error analysis of the local discontinuous Galerkin method for elliptic problems SIAM J. Numer. Anal. 38 5 2000 1676-1706
    • (2000) SIAM J. Numer. Anal. , vol.38 , Issue.5 , pp. 1676-1706
    • Castillo, P.1    Cockburn, B.2    Perugia, I.3    Schöotzau, D.4
  • 21
    • 4244066847 scopus 로고
    • Finite-difference scheme to solve Schrödinger equations
    • Rongqing Chen Zhizhan Xu Lan Sun Finite-difference scheme to solve Schrödinger equations Phys. Rev. E 47 5 1993 3799-3802
    • (1993) Phys. Rev. E , vol.47 , Issue.5 , pp. 3799-3802
    • Chen, R.1    Xu, Z.2    Sun, L.3
  • 24
    • 0036493596 scopus 로고    scopus 로고
    • Magnetic field simulation using conformal FIT formulations
    • M. Clemens T. Weiland Magnetic field simulation using conformal FIT formulations IEEE Trans. Magn. 38 2 2002 389-392
    • (2002) IEEE Trans. Magn. , vol.38 , Issue.2 , pp. 389-392
    • Clemens, M.1    Weiland, T.2
  • 26
    • 0001362649 scopus 로고    scopus 로고
    • High accuracy solution of Maxwell's equations using nonstandard finite differences
    • James B. Cole High accuracy solution of Maxwell's equations using nonstandard finite differences Comput. Phys. 11 3 1997 287-292
    • (1997) Comput. Phys. , vol.11 , Issue.3 , pp. 287-292
    • Cole, J.B.1
  • 27
    • 2442610677 scopus 로고    scopus 로고
    • High-accuracy FDTD solution of the absorbing wave equation, and conducting Maxwell's equations based on a nonstandard finite-difference model
    • J.B. Cole High-accuracy FDTD solution of the absorbing wave equation, and conducting Maxwell's equations based on a nonstandard finite-difference model IEEE Trans. Antennas Propagation 52 3 2004 725-729
    • (2004) IEEE Trans. Antennas Propagation , vol.52 , Issue.3 , pp. 725-729
    • Cole, J.B.1
  • 29
    • 0030383252 scopus 로고    scopus 로고
    • Treatment of material discontinuity in the element-free Galerkin method
    • L. Cordes B. Moran Treatment of material discontinuity in the element-free Galerkin method Comput. Meth. Appl. Mech. Eng. 139 1996 75-89
    • (1996) Comput. Meth. Appl. Mech. Eng. , vol.139 , pp. 75-89
    • Cordes, L.1    Moran, B.2
  • 30
    • 0001439211 scopus 로고    scopus 로고
    • Numerical solution of the Poisson-Boltzmann equation using tetrahedral finite-element meshes
    • C.M. Cortis R.A. Friesner Numerical solution of the Poisson-Boltzmann equation using tetrahedral finite-element meshes J. Comput. Chem. 18 13 1997 1591-1608
    • (1997) J. Comput. Chem. , vol.18 , Issue.13 , pp. 1591-1608
    • Cortis, C.M.1    Friesner, R.A.2
  • 31
    • 0015762231 scopus 로고
    • Conforming and nonconforming finite element methods for solving the stationary Stokes equation
    • MR 49:8401
    • M. Crouzeix P.A. Raviart Conforming and nonconforming finite element methods for solving the stationary Stokes equation RAIRO Anal. Numer. 7 R-3 1973 33-76 MR 49:8401
    • (1973) RAIRO Anal. Numer. , vol.7 , Issue.R-3 , pp. 33-76
    • Crouzeix, M.1    Raviart, P.A.2
  • 32
    • 0034917053 scopus 로고    scopus 로고
    • Towards an efficient meshless computational technique: The method of finite spheres
    • Suvranua De Klaus-Jürgena Bathe Towards an efficient meshless computational technique: The method of finite spheres Eng. Comput. 18 1-2 2001 170-192
    • (2001) Eng. Comput. , vol.18 , Issue.1-2 , pp. 170-192
    • De, S.1    Bathe, K.-J.2
  • 33
    • 0033640077 scopus 로고    scopus 로고
    • Fraction of condensed counterions around a charged rod: Comparison of Poisson-Boltzmann theory and computer simulations
    • Markus Deserno Christian Holm Sylvio May Fraction of condensed counterions around a charged rod: Comparison of Poisson-Boltzmann theory and computer simulations Macromolecules 33 2000 199-205
    • (2000) Macromolecules , vol.33 , pp. 199-205
    • Deserno, M.1    Holm, C.2    May, S.3
  • 34
    • 0033359772 scopus 로고    scopus 로고
    • A conformal finite-difference time-domain technique for modeling cylindrical dielectric resonators
    • S. Dey R. Mittra A conformal finite-difference time-domain technique for modeling cylindrical dielectric resonators IEEE Trans. MTT 47 9 1999 1737-1739
    • (1999) IEEE Trans. MTT , vol.47 , Issue.9 , pp. 1737-1739
    • Dey, S.1    Mittra, R.2
  • 35
    • 0000898778 scopus 로고    scopus 로고
    • Efficient pseudospectral flow simulations in moderately complex geometries
    • C.D. Dimitropoulos Brian J. Edwards Kyung-Sun Chae Antony N. Beris Efficient pseudospectral flow simulations in moderately complex geometries J. Comput. Phys. 144 1998 517-549
    • (1998) J. Comput. Phys. , vol.144 , pp. 517-549
    • Dimitropoulos, C.D.1    Edwards, B.J.2    Chae, K.-S.3    Beris, A.N.4
  • 38
    • 17544389134 scopus 로고    scopus 로고
    • Generalized finite element methods for three-dimensional structural mechanics problems
    • C.A. Duarte I. Babuška J.T. Oden Generalized finite element methods for three-dimensional structural mechanics problems Comput. Struct. 77 2 2000 215-232
    • (2000) Comput. Struct. , vol.77 , Issue.2 , pp. 215-232
    • Duarte, C.A.1    Babuška, I.2    Oden, J.T.3
  • 40
    • 0000568642 scopus 로고
    • On the use of singular functions with finite elements approximations
    • G.J. Fix S. Gulati G.I. Wakoff On the use of singular functions with finite elements approximations J. Comput. Phys. 13 1973 209-228
    • (1973) J. Comput. Phys. , vol.13 , pp. 209-228
    • Fix, G.J.1    Gulati, S.2    Wakoff, G.I.3
  • 41
    • 0035976385 scopus 로고    scopus 로고
    • Molecular mechanics and dynamics of biomolecules using a solvent continuum model
    • F. Fogolari G. Esposito P. Viglino H. Molinari Molecular mechanics and dynamics of biomolecules using a solvent continuum model J. Comput. Chem. 22 15 2001 1830-1842
    • (2001) J. Comput. Chem. , vol.22 , Issue.15 , pp. 1830-1842
    • Fogolari, F.1    Esposito, G.2    Viglino, P.3    Molinari, H.4
  • 42
    • 85190569119 scopus 로고    scopus 로고
    • private communication
    • Gary Friedman, private communication, 2002-2005.
    • (2002)
    • Friedman, G.1
  • 43
    • 1942486247 scopus 로고    scopus 로고
    • Time-domain beam propagation method for nonlinear optical propagation analysis and its application to photonic crystal circuits
    • T. Fujisawa M. Koshiba Time-domain beam propagation method for nonlinear optical propagation analysis and its application to photonic crystal circuits J. Lightwave Technol. 22 2 2004 684-691
    • (2004) J. Lightwave Technol. , vol.22 , Issue.2 , pp. 684-691
    • Fujisawa, T.1    Koshiba, M.2
  • 44
    • 0001163179 scopus 로고
    • Molecular dynamics simulations for charged colloidal dispersions
    • M. Fushiki Molecular dynamics simulations for charged colloidal dispersions J. Chem. Phys. 97 2 1992 6700-6713
    • (1992) J. Chem. Phys. , vol.97 , Issue.2 , pp. 6700-6713
    • Fushiki, M.1
  • 45
    • 0029357365 scopus 로고
    • Finite element solution of open region electrostatic problems incorporating the measured equation of invariance
    • G.K. Gothard S.M. Rao T.K. Sarkar M. Salazar Palma Finite element solution of open region electrostatic problems incorporating the measured equation of invariance IEEE Microwave Guided Wave Lett. 5 8 1995 252-254
    • (1995) IEEE Microwave Guided Wave Lett. , vol.5 , Issue.8 , pp. 252-254
    • Gothard, G.K.1    Rao, S.M.2    Sarkar, T.K.3    Salazar Palma, M.4
  • 46
    • 0035971738 scopus 로고    scopus 로고
    • A smooth permittivity function for Poisson-Boltzmann solvation methods
    • and references therein
    • J.A. Grant B.T. Pickup A. Nicholls A smooth permittivity function for Poisson-Boltzmann solvation methods J. Comput. Chem. 22 6 2001 608-640 and references therein
    • (2001) J. Comput. Chem. , vol.22 , Issue.6 , pp. 608-640
    • Grant, J.A.1    Pickup, B.T.2    Nicholls, A.3
  • 47
    • 0034969881 scopus 로고    scopus 로고
    • A particle-partition of unity method for the solution of elliptic, parabolic and hyperbolic PDE
    • M. Griebel M.A. Schweitzer A particle-partition of unity method for the solution of elliptic, parabolic and hyperbolic PDE SIAM J. Sci. Comp. 22 3 2000 853-890
    • (2000) SIAM J. Sci. Comp. , vol.22 , Issue.3 , pp. 853-890
    • Griebel, M.1    Schweitzer, M.A.2
  • 48
    • 0036985976 scopus 로고    scopus 로고
    • A particle-partition of unity method-part II: Efficient cover construction and reliable integration
    • M. Griebel M.A. Schweitzer A particle-partition of unity method-part II: efficient cover construction and reliable integration SIAM J. Sci. Comp. 23 5 2002 1655-1682
    • (2002) SIAM J. Sci. Comp. , vol.23 , Issue.5 , pp. 1655-1682
    • Griebel, M.1    Schweitzer, M.A.2
  • 49
    • 0037249135 scopus 로고    scopus 로고
    • A particle-partition of unity method-part III: A multilevel solver
    • M. Griebel M.A. Schweitzer A particle-partition of unity method-part III: A multilevel solver SIAM J. Sci. Comp. 24 2 2002 377-409
    • (2002) SIAM J. Sci. Comp. , vol.24 , Issue.2 , pp. 377-409
    • Griebel, M.1    Schweitzer, M.A.2
  • 50
    • 0036630994 scopus 로고    scopus 로고
    • High-accuracy finite-difference equations for dielectric waveguide analysis I: Uniform regions and dielectric interfaces
    • G. Ronald Hadley High-accuracy finite-difference equations for dielectric waveguide analysis I: Uniform regions and dielectric interfaces J. Lightwave Technol. 20 7 2002 1210-1218
    • (2002) J. Lightwave Technol. , vol.20 , Issue.7 , pp. 1210-1218
    • Ronald, H.G.1
  • 51
    • 0036630789 scopus 로고    scopus 로고
    • High-accuracy finite-difference equations for dielectric waveguide analysis II: Dielectric corners
    • G. Ronald Hadley High-accuracy finite-difference equations for dielectric waveguide analysis II: Dielectric corners J. Lightwave Technol. 20 7 2002 1219-1231
    • (2002) J. Lightwave Technol. , vol.20 , Issue.7 , pp. 1219-1231
    • Ronald, H.G.1
  • 52
    • 4444298200 scopus 로고    scopus 로고
    • Local approximation matching for open boundary problems
    • D. Halverson G. Friedman I. Tsukerman Local approximation matching for open boundary problems IEEE Trans. Magn. 40 4 2004 2152-2154
    • (2004) IEEE Trans. Magn. , vol.40 , Issue.4 , pp. 2152-2154
    • Halverson, D.1    Friedman, G.2    Tsukerman, I.3
  • 53
    • 28144432041 scopus 로고
    • Fourth order accurate finite difference methods for time-harmonic wave propagation
    • I. Harari E. Turkel Fourth order accurate finite difference methods for time-harmonic wave propagation J. Comput. Phys. 119 1995 252-270
    • (1995) J. Comput. Phys. , vol.119 , pp. 252-270
    • Harari, I.1    Turkel, E.2
  • 55
    • 0032204074 scopus 로고    scopus 로고
    • Electrostatic solution for three-dimensional arbitrarily shaped conducting bodies using finite element and measured equation of invariance
    • J.H. Henderson S.M. Rao Electrostatic solution for three-dimensional arbitrarily shaped conducting bodies using finite element and measured equation of invariance IEEE Trans. Antennas Propagation 46 11 1998 1660-1664
    • (1998) IEEE Trans. Antennas Propagation , vol.46 , Issue.11 , pp. 1660-1664
    • Henderson, J.H.1    Rao, S.M.2
  • 57
    • 0035788953 scopus 로고    scopus 로고
    • Discrete Hodge operators
    • R. Hiptmair Discrete Hodge operators Numer. Math. 90 2001 265-289
    • (2001) Numer. Math. , vol.90 , pp. 265-289
    • Hiptmair, R.1
  • 58
    • 0029016182 scopus 로고
    • Classical electrostatics in biology and chemistry
    • B. Honig A. Nicholls Classical electrostatics in biology and chemistry Science 268 5214 1995 1144-1149
    • (1995) Science , vol.268 , Issue.5214 , pp. 1144-1149
    • Honig, B.1    Nicholls, A.2
  • 59
    • 0029405472 scopus 로고
    • Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid-scale models, bubbles and the origins of stabilized methods
    • T.J.R. Hughes Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid-scale models, bubbles and the origins of stabilized methods Comput. Meth. Appl. Mech. Eng. 127 1995 387-401
    • (1995) Comput. Meth. Appl. Mech. Eng. , vol.127 , pp. 387-401
    • Hughes, T.J.R.1
  • 60
    • 0001530314 scopus 로고
    • On the convergence of finite-difference approximations to one-dimensional singular boundary-value problems
    • Pierre Jamet On the convergence of finite-difference approximations to one-dimensional singular boundary-value problems Numer. Math. 14 1970 355-378
    • (1970) Numer. Math. , vol.14 , pp. 355-378
    • Jamet, P.1
  • 61
    • 0002450222 scopus 로고
    • Basis for development of large finite elements locally satisfying all field equations
    • J. Jirousek Basis for development of large finite elements locally satisfying all field equations Comp. Meth. Appl. Mech. Eng. 14 1978 65-92
    • (1978) Comp. Meth. Appl. Mech. Eng. , vol.14 , pp. 65-92
    • Jirousek, J.1
  • 63
    • 0031120224 scopus 로고    scopus 로고
    • Survey of Trefftz-type element formulations
    • J. Jirousek A.P. Zielinski Survey of Trefftz-type element formulations Comput. Struct. 63 1997 225-242
    • (1997) Comput. Struct. , vol.63 , pp. 225-242
    • Jirousek, J.1    Zielinski, A.P.2
  • 64
    • 34547217759 scopus 로고
    • Optical constants of the noble metals
    • P.B. Johnson R.W. Christy Optical constants of the noble metals Phys. Rev. B 6 12-15 1972 4370-4379
    • (1972) Phys. Rev. B , vol.6 , Issue.12-15 , pp. 4370-4379
    • Johnson, P.B.1    Christy, R.W.2
  • 65
    • 0007528471 scopus 로고    scopus 로고
    • Retardation-induced plasmon resonances in coupled nanoparticles
    • Jörg P. Kottmann Olivier J.F. Martin Retardation-induced plasmon resonances in coupled nanoparticles Opt. Lett. 26 2001 1096-1098
    • (2001) Opt. Lett. , vol.26 , pp. 1096-1098
    • Kottmann, J.P.1    Martin, O.J.F.2
  • 66
    • 0032048164 scopus 로고    scopus 로고
    • EFG approximation with discontinuous derivatives
    • Y. Krongauz T. Belytschko EFG approximation with discontinuous derivatives Int. J. Numer. Meth. Eng. 41 1998 1215-1233
    • (1998) Int. J. Numer. Meth. Eng. , vol.41 , pp. 1215-1233
    • Krongauz, Y.1    Belytschko, T.2
  • 67
    • 0037844977 scopus 로고    scopus 로고
    • A new finite difference method for a class of singular two-point boundary value problems
    • Manoj Kumar A new finite difference method for a class of singular two-point boundary value problems Appl. Math. Comput. 143 2-3 2003 551-557
    • (2003) Appl. Math. Comput. , vol.143 , Issue.2-3 , pp. 551-557
    • Kumar, M.1
  • 68
    • 20244372371 scopus 로고    scopus 로고
    • A new finite difference method for the Helmholtz equation using symbolic computation
    • L.A. Lambe R. Luczak J.W. Nehrbass A new finite difference method for the Helmholtz equation using symbolic computation Int. J. Comput. Eng. Sci. 4 1 2003 121-144
    • (2003) Int. J. Comput. Eng. Sci. , vol.4 , Issue.1 , pp. 121-144
    • Lambe, L.A.1    Luczak, R.2    Nehrbass, J.W.3
  • 71
    • 84966246071 scopus 로고
    • A high-order difference method for differential equations
    • R.E. Lynch J.R. Rice A high-order difference method for differential equations Math. Comput. 34 1980 333-372
    • (1980) Math. Comput. , vol.34 , pp. 333-372
    • Lynch, R.E.1    Rice, J.R.2
  • 72
    • 0031570250 scopus 로고    scopus 로고
    • An analysis of finite volume, finite element, and finite difference methods using some concepts from algebraic topology
    • C. Mattiussi An analysis of finite volume, finite element, and finite difference methods using some concepts from algebraic topology J. Comput. Phys. 133 2 1997 289-309
    • (1997) J. Comput. Phys. , vol.133 , Issue.2 , pp. 289-309
    • Mattiussi, C.1
  • 73
    • 0029308428 scopus 로고
    • A novel finite element for treating inhomogeneous solids
    • S.A. Meguid Z.H. Zhu A novel finite element for treating inhomogeneous solids Int. J. Numer. Meth. Eng. 38 1995 1579-1592
    • (1995) Int. J. Numer. Meth. Eng. , vol.38 , pp. 1579-1592
    • Meguid, S.A.1    Zhu, Z.H.2
  • 75
    • 22844455033 scopus 로고    scopus 로고
    • Operator adapted spectral element methods I: Harmonic and generalized harmonic polynomials
    • J.M. Melenk Operator adapted spectral element methods I: Harmonic and generalized harmonic polynomials Numer. Math. 84 1999 35-69
    • (1999) Numer. Math. , vol.84 , pp. 35-69
    • Melenk, J.M.1
  • 76
    • 0030380578 scopus 로고    scopus 로고
    • The partition of unity finite element method: Basic theory and applications
    • J.M. Melenk I. Babuška The partition of unity finite element method: Basic theory and applications Comput. Meth. Appl. Mech. Eng. 139 1996 289-314
    • (1996) Comput. Meth. Appl. Mech. Eng. , vol.139 , pp. 289-314
    • Melenk, J.M.1    Babuška, I.2
  • 82
    • 0008157573 scopus 로고    scopus 로고
    • A finite difference scheme for elliptic equations with rough coefficients using a Cartesian grid nonconforming to interfaces
    • S. Moskow V. Druskin T. Habashy P. Lee S. Davydycheva A finite difference scheme for elliptic equations with rough coefficients using a Cartesian grid nonconforming to interfaces SIAM J. Numer. Anal. 36 2 1999 442-464
    • (1999) SIAM J. Numer. Anal. , vol.36 , Issue.2 , pp. 442-464
    • Moskow, S.1    Druskin, V.2    Habashy, T.3    Lee, P.4    Davydycheva, S.5
  • 83
    • 0034190406 scopus 로고    scopus 로고
    • A short survey on preconditioning techniques in spectral calculations
    • E.H. Mund A short survey on preconditioning techniques in spectral calculations Appl. Numer. Math. 33 2000 61-70
    • (2000) Appl. Numer. Math. , vol.33 , pp. 61-70
    • Mund, E.H.1
  • 84
    • 0012550019 scopus 로고    scopus 로고
    • Advances in Finite Difference Methods for Electromagnetic Modeling
    • Ph.D. Thesis, Ohio State University
    • J.W. Nehrbass, Advances in Finite Difference Methods for Electromagnetic Modeling. Ph.D. Thesis, Ohio State University, 1996.
    • (1996)
    • Nehrbass, J.W.1
  • 85
    • 0032209437 scopus 로고    scopus 로고
    • A discontinuous hp finite element method for diffusion problems
    • J.T. Oden I. Babuška C.E. Baumann A discontinuous hp finite element method for diffusion problems J. Comput. Phys. 146 1998 491-519
    • (1998) J. Comput. Phys. , vol.146 , pp. 491-519
    • Oden, J.T.1    Babuška, I.2    Baumann, C.E.3
  • 86
    • 85013126603 scopus 로고
    • Spectral methods for problems in complex geometries
    • S.A. Orszag Spectral methods for problems in complex geometries J. Comput. Phys. 37 1 1980 70-92
    • (1980) J. Comput. Phys. , vol.37 , Issue.1 , pp. 70-92
    • Orszag, S.A.1
  • 87
    • 3042777494 scopus 로고    scopus 로고
    • Spectral element methods on triangles and quadrilaterals: Comparisons and applications
    • R. Pasquetti F. Rapetti Spectral element methods on triangles and quadrilaterals: Comparisons and applications J. Comput. Phys. 198 2004 349-362
    • (2004) J. Comput. Phys. , vol.198 , pp. 349-362
    • Pasquetti, R.1    Rapetti, F.2
  • 90
    • 0037844439 scopus 로고    scopus 로고
    • Generalized finite element method for magnetized nanoparticles
    • A. Plaks I. Tsukerman G. Friedman B. Yellen Generalized finite element method for magnetized nanoparticles IEEE Trans. Magn. 39 3 2003 1436-1439
    • (2003) IEEE Trans. Magn. , vol.39 , Issue.3 , pp. 1436-1439
    • Plaks, A.1    Tsukerman, I.2    Friedman, G.3    Yellen, B.4
  • 91
    • 0036493746 scopus 로고    scopus 로고
    • Method of overlapping patches for electromagnetic computation
    • L. Proekt I. Tsukerman Method of overlapping patches for electromagnetic computation IEEE Trans. Magn. 38 2 2002 741-744
    • (2002) IEEE Trans. Magn. , vol.38 , Issue.2 , pp. 741-744
    • Proekt, L.1    Tsukerman, I.2
  • 92
    • 0011607066 scopus 로고
    • Upstream weighted differencing schemes and their application to elliptic problems involving fluid flow
    • G.D. Raithby K.E. Torrance Upstream weighted differencing schemes and their application to elliptic problems involving fluid flow J. Comput. Fluids 2 1974 191-206
    • (1974) J. Comput. Fluids , vol.2 , pp. 191-206
    • Raithby, G.D.1    Torrance, K.E.2
  • 93
    • 0003260834 scopus 로고
    • On a collocation method for singular two-point boundary value problems
    • G.W. Reddien L.L. Schumaker On a collocation method for singular two-point boundary value problems Numer. Math. 25 1976 427-432
    • (1976) Numer. Math. , vol.25 , pp. 427-432
    • Reddien, G.W.1    Schumaker, L.L.2
  • 94
    • 0035913537 scopus 로고    scopus 로고
    • Extending the applicability of the nonlinear Poisson-Boltzmann equation: Multiple dielectric constants and multivalent ions
    • W. Rocchia E. Alexov B. Honig Extending the applicability of the nonlinear Poisson-Boltzmann equation: Multiple dielectric constants and multivalent ions J. Phys. Chem. B 105 28 2001 6507-6514
    • (2001) J. Phys. Chem. B , vol.105 , Issue.28 , pp. 6507-6514
    • Rocchia, W.1    Alexov, E.2    Honig, B.3
  • 98
    • 0037529067 scopus 로고    scopus 로고
    • Electrostatics and dynamics of proteins
    • T. Simonson Electrostatics and dynamics of proteins Rep. Prog. Phys. 66 5 2003 737-787
    • (2003) Rep. Prog. Phys. , vol.66 , Issue.5 , pp. 737-787
    • Simonson, T.1
  • 99
    • 0032155919 scopus 로고    scopus 로고
    • High order finite difference methods for the Helmholtz equation
    • I. Singer E. Turkel High order finite difference methods for the Helmholtz equation Comput. Meth. Appl. Mech. Eng. 163 1998 343-358
    • (1998) Comput. Meth. Appl. Mech. Eng. , vol.163 , pp. 343-358
    • Singer, I.1    Turkel, E.2
  • 101
    • 0034229715 scopus 로고    scopus 로고
    • Development of two-dimensional elements with a central circular hole
    • A.K. Soh Z.F. Long Development of two-dimensional elements with a central circular hole Comput. Meth. Appl. Mech. Eng. 188 2000 431-440
    • (2000) Comput. Meth. Appl. Mech. Eng. , vol.188 , pp. 431-440
    • Soh, A.K.1    Long, Z.F.2
  • 102
    • 0015368687 scopus 로고
    • A novel finite-difference formulation for differential expressions involving both first and second derivatives
    • D.B. Spalding A novel finite-difference formulation for differential expressions involving both first and second derivatives Int. J. Numer. Meth. Eng. 4 1972 551-559
    • (1972) Int. J. Numer. Meth. Eng. , vol.4 , pp. 551-559
    • Spalding, D.B.1
  • 105
  • 107
    • 0036493670 scopus 로고    scopus 로고
    • Finite formulation of electromagnetic field
    • E. Tonti Finite formulation of electromagnetic field IEEE Trans. Magn. 38 2 2002 333-336
    • (2002) IEEE Trans. Magn. , vol.38 , Issue.2 , pp. 333-336
    • Tonti, E.1
  • 108
    • 4444328799 scopus 로고    scopus 로고
    • Efficient computation of long-range electromagnetic interactions without Fourier Transforms
    • Igor Tsukerman Efficient computation of long-range electromagnetic interactions without Fourier Transforms IEEE Trans. Magn. 40 4 2004 2158-2160
    • (2004) IEEE Trans. Magn. , vol.40 , Issue.4 , pp. 2158-2160
    • Tsukerman, I.1
  • 109
    • 2342458444 scopus 로고    scopus 로고
    • Flexible local approximation method for electro- and magnetostatics
    • Igor Tsukerman Flexible local approximation method for electro- and magnetostatics IEEE Trans. Magn. 40 2 2004 941-944
    • (2004) IEEE Trans. Magn. , vol.40 , Issue.2 , pp. 941-944
    • Tsukerman, I.1
  • 111
    • 23844526194 scopus 로고    scopus 로고
    • Electromagnetic applications of a new finite-difference calculus
    • I. Tsukerman Electromagnetic applications of a new finite-difference calculus IEEE Trans. Magn. 41 7 2005 2206-2225
    • (2005) IEEE Trans. Magn. , vol.41 , Issue.7 , pp. 2206-2225
    • Tsukerman, I.1
  • 112
    • 84945911523 scopus 로고
    • Multiple scattering of radiation by an arbitrary configuration of parallel cylinders
    • Victor Twersky Multiple scattering of radiation by an arbitrary configuration of parallel cylinders J. Acoust. Soc. Am. 24 1952 42-46
    • (1952) J. Acoust. Soc. Am. , vol.24 , pp. 42-46
    • Twersky, V.1
  • 115
    • 0036724711 scopus 로고    scopus 로고
    • A FV-TD electromagnetic solver using adaptive cartesian grids
    • Z.J. Wang A.J. Przekwas Yen Liu A FV-TD electromagnetic solver using adaptive cartesian grids Comput. Phys. Commun. 148 2002 17-29
    • (2002) Comput. Phys. Commun. , vol.148 , pp. 17-29
    • Wang, Z.J.1    Przekwas, A.J.2    Liu, Y.3
  • 116
    • 85190568962 scopus 로고    scopus 로고
    • private communication
    • T. Washio, private communication, 2002-2003.
    • (2002)
    • Washio, T.1
  • 117
    • 85190570546 scopus 로고    scopus 로고
    • private communication
    • J. Webb, private communication, 2004-2005.
    • (2004)
    • Webb, J.1
  • 118
    • 0009853243 scopus 로고    scopus 로고
    • The explicit-jump immersed interface method: Finite difference methods for PDEs with piecewise smooth solutions
    • A. Wiegmann K.P. Bube The explicit-jump immersed interface method: finite difference methods for PDEs with piecewise smooth solutions SIAM J. Numer. Anal. 37 3 2000 827-862
    • (2000) SIAM J. Numer. Anal. , vol.37 , Issue.3 , pp. 827-862
    • Wiegmann, A.1    Bube, K.P.2
  • 119
    • 84894021661 scopus 로고
    • Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media
    • K.S. Yee Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media IEEE Trans. Antennas Propagation AP-14 3 1966 302-307
    • (1966) IEEE Trans. Antennas Propagation , vol.AP-14 , Issue.3 , pp. 302-307
    • Yee, K.S.1
  • 120
    • 0031096315 scopus 로고    scopus 로고
    • The finite-difference time-domain (FDTD) and the finite-volume time-domain (FVTD) methods in solving maxwell's equations
    • K.S. Yee J.S. Chen The finite-difference time-domain (FDTD) and the finite-volume time-domain (FVTD) methods in solving maxwell's equations IEEE Trans. Antennas Propagation 45 3 1997 354-363
    • (1997) IEEE Trans. Antennas Propagation , vol.45 , Issue.3 , pp. 354-363
    • Yee, K.S.1    Chen, J.S.2
  • 121
    • 1142268974 scopus 로고    scopus 로고
    • Programmable assembly of heterogeneous colloidal particle arrays
    • B. Yellen G. Friedman Programmable assembly of heterogeneous colloidal particle arrays Adv. Mater. 16 2 2004 111-115
    • (2004) Adv. Mater. , vol.16 , Issue.2 , pp. 111-115
    • Yellen, B.1    Friedman, G.2
  • 122
    • 4444369820 scopus 로고    scopus 로고
    • Programmable self-aligning ferrofluid masks for lithographic applications
    • B.B. Yellen G. Friedman K.A. Barbee Programmable self-aligning ferrofluid masks for lithographic applications IEEE Trans Magn. 40 4 2004 2994-2996
    • (2004) IEEE Trans. Magn. , vol.40 , Issue.4 , pp. 2994-2996
    • Yellen, B.B.1    Friedman, G.2    Barbee, K.A.3
  • 123
    • 34250126304 scopus 로고
    • On the multilevel splitting of finite-element spaces
    • H. Yserentant On the multilevel splitting of finite-element spaces Numer. Math. 49 4 1986 379-412
    • (1986) Numer. Math. , vol.49 , Issue.4 , pp. 379-412
    • Yserentant, H.1
  • 124
    • 0035172542 scopus 로고    scopus 로고
    • A conformal finite difference time domain technique for modeling curved dielectric surfaces
    • W. Yu R. Mittra A conformal finite difference time domain technique for modeling curved dielectric surfaces IEEE Microwave Wireless Comp. Lett. 11 2001 25-27
    • (2001) IEEE Microwave Wireless Comp. Lett. , vol.11 , pp. 25-27
    • Yu, W.1    Mittra, R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.