메뉴 건너뛰기




Volumn 6, Issue 3, 2007, Pages 711-740

A sparse spectral method for homogenization multiscale problems

Author keywords

Homogenization; Multiscale methods; Sparse Fourier representation; Spectral methods; Sublinear algorithm

Indexed keywords

BOOLEAN FUNCTIONS; FAST FOURIER TRANSFORMS; FOURIER ANALYSIS; MATHEMATICAL TRANSFORMATIONS; SPECTRUM ANALYSIS;

EID: 51149113295     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/060676258     Document Type: Article
Times cited : (20)

References (33)
  • 1
    • 0141682262 scopus 로고    scopus 로고
    • Finite difference heterogeneous multiscale method for homogenization problems
    • A. ABDULLE AND W. E, Finite difference heterogeneous multiscale method for homogenization problems, J. Comput. Phys., 191 (2003), pp. 18-39.
    • (2003) J. Comput. Phys , vol.191 , pp. 18-39
    • ABDULLE, A.1
  • 3
    • 0028483749 scopus 로고
    • Special finite element methods for a class of second order elliptic problems upith rough coefficients
    • I. BABUŠKA, G. CALOZ, AND J. E. OSBORN, Special finite element methods for a class of second order elliptic problems upith rough coefficients, SIAM J. Numer. Anal., 31 (1994), pp. 945-981.
    • (1994) SIAM J. Numer. Anal , vol.31 , pp. 945-981
    • BABUŠKA, I.1    CALOZ, G.2    OSBORN, J.E.3
  • 5
    • 0346985377 scopus 로고    scopus 로고
    • A multiresolution strategy for numerical homogenization of nonlinear ODEs
    • G. BEYLKIN, M. E. BREWSTER, AND A. C. GILBERT, A multiresolution strategy for numerical homogenization of nonlinear ODEs, Appl. Comput. Harmon. Anal., 5 (1998), pp. 450-486.
    • (1998) Appl. Comput. Harmon. Anal , vol.5 , pp. 450-486
    • BEYLKIN, G.1    BREWSTER, M.E.2    GILBERT, A.C.3
  • 6
    • 0001542801 scopus 로고
    • A multiresolution strategy for numerical homogenization
    • G. BEYLKIN AND M. BREWSTER, A multiresolution strategy for numerical homogenization, Appl. Comput. Harmon. Anal., 2 (1995), pp. 327-349.
    • (1995) Appl. Comput. Harmon. Anal , vol.2 , pp. 327-349
    • BEYLKIN, G.1    BREWSTER, M.2
  • 8
    • 4243606192 scopus 로고    scopus 로고
    • R. CAR AND M. PARRINELLO, Unified approach for molecular dynamics and density-functional theory, Phys. Rev. Lett., 55 (1985), pp. 2471-2474.
    • R. CAR AND M. PARRINELLO, Unified approach for molecular dynamics and density-functional theory, Phys. Rev. Lett., 55 (1985), pp. 2471-2474.
  • 9
    • 29244442306 scopus 로고    scopus 로고
    • S. CHEN, W. E, AND C.-W. SHU, The heterogeneous multiscale method based on the discontinuous Galerkin method for hyperbolic and parabolic problems, Multiscale Model. Simul., 3 (2005), pp. 871-894.
    • S. CHEN, W. E, AND C.-W. SHU, The heterogeneous multiscale method based on the discontinuous Galerkin method for hyperbolic and parabolic problems, Multiscale Model. Simul., 3 (2005), pp. 871-894.
  • 11
    • 51149118921 scopus 로고    scopus 로고
    • W. E AND B. ENGQUIST, Multiscale modeling and computation, Notices Amer. Math. Soc., 50 (2003), pp. 1062-1070.
    • W. E AND B. ENGQUIST, Multiscale modeling and computation, Notices Amer. Math. Soc., 50 (2003), pp. 1062-1070.
  • 12
    • 51149085451 scopus 로고    scopus 로고
    • W. E AND B. ENGQUIST, The heterogeneous multiscale methods, Commun. Math. Sci., 1 (2003), pp. 87-133.
    • W. E AND B. ENGQUIST, The heterogeneous multiscale methods, Commun. Math. Sci., 1 (2003), pp. 87-133.
  • 13
    • 0037367420 scopus 로고    scopus 로고
    • Heterogeneous multiscale method: A general methodology for multiscale modeling
    • W. E, B. ENGQUIST, AND Z. HUANG, Heterogeneous multiscale method: A general methodology for multiscale modeling, Phys. Rev. B, 67 (2003), 092101.
    • (2003) Phys. Rev. B , vol.67 , pp. 092101
    • ENGQUIST, W.E.B.1    HUANG, Z.2
  • 14
    • 0141711679 scopus 로고    scopus 로고
    • Wavelet-based numerical homogenization with applications
    • Notes Comput. Sci. Eng. 20, T. J. Barth, T. F. Chan, and R. Haimes, eds, Springer-Verlag, Berlin
    • B. ENGQUIST AND O. RUNBORG, Wavelet-based numerical homogenization with applications, in Multiscale and Multiresolution Methods: Theory and Applications, Lect. Notes Comput. Sci. Eng. 20, T. J. Barth, T. F. Chan, and R. Haimes, eds., Springer-Verlag, Berlin, 2001, pp. 97-148.
    • (2001) Multiscale and Multiresolution Methods: Theory and Applications, Lect , pp. 97-148
    • ENGQUIST, B.1    RUNBORG, O.2
  • 15
    • 20744449792 scopus 로고    scopus 로고
    • The design and implementation of FFTW3
    • M. FRIGO AND S. JOHNSON, The design and implementation of FFTW3, Proc. IEEE, 93 (2005), pp. 216-231.
    • (2005) Proc. IEEE , vol.93 , pp. 216-231
    • FRIGO, M.1    JOHNSON, S.2
  • 17
    • 30844452004 scopus 로고    scopus 로고
    • A. C. GILBERT, S. MUTHUKRISHNAN, AND M. STRAUSS, Improved time bounds for near-optimal sparse Fourier representation, in Wavelets XI, Proc. SPIE 5914, M. Papadakis, A. F. Laine, and M. A. Unser, eds., SPIE, Bellingham, WA, 2005, pp. 398-412.
    • A. C. GILBERT, S. MUTHUKRISHNAN, AND M. STRAUSS, Improved time bounds for near-optimal sparse Fourier representation, in Wavelets XI, Proc. SPIE 5914, M. Papadakis, A. F. Laine, and M. A. Unser, eds., SPIE, Bellingham, WA, 2005, pp. 398-412.
  • 19
    • 85190396500 scopus 로고    scopus 로고
    • T. Y. HOU AND X.-H. WU, A multiscale finite element method for elliptic problems in composite materials and porous media, J. Comput. Phys., 134 (1997), pp. 169-189.
    • T. Y. HOU AND X.-H. WU, A multiscale finite element method for elliptic problems in composite materials and porous media, J. Comput. Phys., 134 (1997), pp. 169-189.
  • 20
    • 0039982148 scopus 로고    scopus 로고
    • Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients
    • T. Y. Hou, X.-H. WU, AND Z. CAI, Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients, Math. Comp., 68 (1999), pp. 913-943.
    • (1999) Math. Comp , vol.68 , pp. 913-943
    • Hou, T.Y.1    WU, X.-H.2    CAI, Z.3
  • 23
    • 85128858890 scopus 로고    scopus 로고
    • Equation-free, coarse-grained multiscale computation: Enabling microscopic simulators to perform system-level analysis
    • I. G. KEVREKIDIS, C. W. GEAR, J. M. HYMAN, P. G. KEVREKIDIS, O. RUNBORG, AND C. THEODOROPOULOS, Equation-free, coarse-grained multiscale computation: Enabling microscopic simulators to perform system-level analysis, Commun. Math. Sci., 1 (2003), pp. 715-762.
    • (2003) Commun. Math. Sci , vol.1 , pp. 715-762
    • KEVREKIDIS, I.G.1    GEAR, C.W.2    HYMAN, J.M.3    KEVREKIDIS, P.G.4    RUNBORG, O.5    THEODOROPOULOS, C.6
  • 25
    • 0034190245 scopus 로고    scopus 로고
    • Homogenization via p-FEM for problems with microstructure
    • A.-M. MATACHE AND C. SCHWAB, Homogenization via p-FEM for problems with microstructure, Appl. Numer. Math., 33 (2000), pp. 43-59.
    • (2000) Appl. Numer. Math , vol.33 , pp. 43-59
    • MATACHE, A.-M.1    SCHWAB, C.2
  • 26
    • 54149091405 scopus 로고    scopus 로고
    • P. MING AND P. ZHANG, Analysis of the heterogeneous multiscale method for parabolic homogenization problems, Math. Comp., 76 (2007), pp. 153-177.
    • P. MING AND P. ZHANG, Analysis of the heterogeneous multiscale method for parabolic homogenization problems, Math. Comp., 76 (2007), pp. 153-177.
  • 27
  • 28
    • 0030158774 scopus 로고    scopus 로고
    • Quasicontinuum analysis of defects in crystals
    • E. B. TADMOR, M. ORTIZ, AND R. PHILLIPS, Quasicontinuum analysis of defects in crystals, Phil. Mag. A, 73 (1996), pp. 1529-1563.
    • (1996) Phil. Mag. A , vol.73 , pp. 1529-1563
    • TADMOR, E.B.1    ORTIZ, M.2    PHILLIPS, R.3
  • 29
    • 0034730149 scopus 로고    scopus 로고
    • Coarse stability and bifurcation analysis using time-steppers: A reaction-diffusion example
    • C. THEODOROPOULOS, Y.-H. QIAN, AND I. G. KEVREKIDIS, "Coarse" stability and bifurcation analysis using time-steppers: A reaction-diffusion example, Proc. Natl. Acad. Sci. USA, 97 (2000), pp. 9840-9843.
    • (2000) Proc. Natl. Acad. Sci. USA , vol.97 , pp. 9840-9843
    • THEODOROPOULOS, C.1    QIAN, Y.-H.2    KEVREKIDIS, I.G.3
  • 31
    • 51149122888 scopus 로고    scopus 로고
    • R. VOIGT, D. GOTTLIEB, AND M. HUSSAINI, EDS., Spectral Methods for Partial Differential Equations, SIAM, Philadelphia, 1984.
    • R. VOIGT, D. GOTTLIEB, AND M. HUSSAINI, EDS., Spectral Methods for Partial Differential Equations, SIAM, Philadelphia, 1984.
  • 32
    • 26944493362 scopus 로고    scopus 로고
    • Theoretical and experimental analysis of a randomized algorithm for sparse Fourier transform analysis
    • J. ZOU, A.C. GILBERT, M. STRAUSS, AND I. DAUBECHIES, Theoretical and experimental analysis of a randomized algorithm for sparse Fourier transform analysis, J. Comput. Phys., 211 (2006), pp. 572-595.
    • (2006) J. Comput. Phys , vol.211 , pp. 572-595
    • ZOU, J.1    GILBERT, A.C.2    STRAUSS, M.3    DAUBECHIES, I.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.