메뉴 건너뛰기




Volumn 198, Issue 1, 2007, Pages 1-18

Eigenfrequencies of fractal drums

Author keywords

Conformal transplantation; Eigenvalues; Fractals; Spectral methods

Indexed keywords

COMPUTATIONAL METHODS; FRACTALS; ITERATIVE METHODS; LINEAR SYSTEMS; NUMERICAL ANALYSIS; PROBLEM SOLVING;

EID: 33748422705     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2005.11.015     Document Type: Article
Times cited : (15)

References (37)
  • 1
    • 33748426262 scopus 로고    scopus 로고
    • L. Banjai, Computation of Conformal Maps by Fast Multipole Method Accelerated Schwarz-Christoffel Transformation, Ph.D. Thesis, Oxford University, England, 2003.
  • 2
    • 2942604708 scopus 로고    scopus 로고
    • A multipole method for Schwarz-Christoffel mapping of polygons with thousands of sides
    • Banjai L., and Trefethen L.N. A multipole method for Schwarz-Christoffel mapping of polygons with thousands of sides. SIAM J. Sci. Comput. 25 3 (2003) 1042-1065
    • (2003) SIAM J. Sci. Comput. , vol.25 , Issue.3 , pp. 1042-1065
    • Banjai, L.1    Trefethen, L.N.2
  • 3
    • 24644462685 scopus 로고    scopus 로고
    • T. Betcke, L.N. Trefethen, Reviving the method of particular solutions. SIAM Rev. 47 (2005) 469-491.
  • 5
    • 0038348074 scopus 로고    scopus 로고
    • Eigenvalues of the Laplacian on regular polygons and polygons resulting from their dissection
    • Cureton L.M., and Kuttler J.R. Eigenvalues of the Laplacian on regular polygons and polygons resulting from their dissection. J. Sound Vibration 220 1 (1999) 83-98
    • (1999) J. Sound Vibration , vol.220 , Issue.1 , pp. 83-98
    • Cureton, L.M.1    Kuttler, J.R.2
  • 6
    • 0003288852 scopus 로고
    • Spectral Theory and Differential Operators
    • Cambridge University Press, Cambridge
    • Davies E.B. Spectral Theory and Differential Operators. Cambridge Studies in Advanced Mathematics vol. 42 (1995), Cambridge University Press, Cambridge
    • (1995) Cambridge Studies in Advanced Mathematics , vol.42
    • Davies, E.B.1
  • 7
    • 0031100472 scopus 로고    scopus 로고
    • Eigenmodes of isospectral drums
    • Driscoll T.A. Eigenmodes of isospectral drums. SIAM Rev. 39 1 (1997) 1-17
    • (1997) SIAM Rev. , vol.39 , Issue.1 , pp. 1-17
    • Driscoll, T.A.1
  • 9
    • 84968502841 scopus 로고
    • The evaluation and estimation of the coefficients in the Chebyshev series expansion of a function
    • Elliott D. The evaluation and estimation of the coefficients in the Chebyshev series expansion of a function. Math. Comput. 18 (1964) 274-284
    • (1964) Math. Comput. , vol.18 , pp. 274-284
    • Elliott, D.1
  • 10
    • 0039347092 scopus 로고
    • Meridian Creative Group, Erie, PA
    • Ferguson C. Helaman Ferguson (1994), Meridian Creative Group, Erie, PA
    • (1994) Helaman Ferguson
    • Ferguson, C.1
  • 11
    • 0000520891 scopus 로고
    • A pseudospectral approach for polar and spherical geometries
    • Fornberg B. A pseudospectral approach for polar and spherical geometries. SIAM J. Sci. Comput. 16 5 (1995) 1071-1081
    • (1995) SIAM J. Sci. Comput. , vol.16 , Issue.5 , pp. 1071-1081
    • Fornberg, B.1
  • 13
    • 0003003063 scopus 로고
    • Approximations and bounds for eigenvalues of elliptic operators
    • Fox L., Henrici P., and Moler C. Approximations and bounds for eigenvalues of elliptic operators. SIAM J. Numer. Anal. 4 (1967) 89-102
    • (1967) SIAM J. Numer. Anal. , vol.4 , pp. 89-102
    • Fox, L.1    Henrici, P.2    Moler, C.3
  • 17
    • 33748425957 scopus 로고    scopus 로고
    • L.H. Howell, Computation of Conformal Maps by Modified Schwarz-Christoffel Transformations. Ph.D. Thesis, Massachusetts Institute of Technology, 1990.
  • 18
    • 0021404192 scopus 로고
    • Eigenvalues of the Laplacian in two dimensions
    • Kuttler J.R., and Sigillito V.G. Eigenvalues of the Laplacian in two dimensions. SIAM Rev. 26 2 (1984) 163-193
    • (1984) SIAM Rev. , vol.26 , Issue.2 , pp. 163-193
    • Kuttler, J.R.1    Sigillito, V.G.2
  • 19
    • 21344474764 scopus 로고
    • Fractals and vibrations: can you hear the shape of a fractal drum?
    • (Symposium in Honor of Benoit Mandelbrot (Curaçao, 1995))
    • Lapidus M.L. Fractals and vibrations: can you hear the shape of a fractal drum?. Fractals 3 4 (1995) 725-736 (Symposium in Honor of Benoit Mandelbrot (Curaçao, 1995))
    • (1995) Fractals , vol.3 , Issue.4 , pp. 725-736
    • Lapidus, M.L.1
  • 21
    • 21844527132 scopus 로고
    • Eigenfunctions of the Koch snowflake domain
    • Lapidus M.L., and Pang M.M.H. Eigenfunctions of the Koch snowflake domain. Comm. Math. Phys. 172 2 (1995) 359-376
    • (1995) Comm. Math. Phys. , vol.172 , Issue.2 , pp. 359-376
    • Lapidus, M.L.1    Pang, M.M.H.2
  • 22
    • 0030502142 scopus 로고    scopus 로고
    • Deflation techniques for an implicitly restarted Arnoldi iteration
    • Lehoucq R.B., and Sorensen D.C. Deflation techniques for an implicitly restarted Arnoldi iteration. SIAM J. Matrix Anal. Appl. 17 4 (1996) 789-821
    • (1996) SIAM J. Matrix Anal. Appl. , vol.17 , Issue.4 , pp. 789-821
    • Lehoucq, R.B.1    Sorensen, D.C.2
  • 26
    • 0009031763 scopus 로고
    • Chebyshev polynomial approximations for the L-membrane eigenvalue problem
    • Mason J.C. Chebyshev polynomial approximations for the L-membrane eigenvalue problem. SIAM J. Appl. Math. 15 (1967) 172-186
    • (1967) SIAM J. Appl. Math. , vol.15 , pp. 172-186
    • Mason, J.C.1
  • 27
    • 33748434978 scopus 로고    scopus 로고
    • J.M. Neuberger, N. Sieben, J.W. Swift, Computing eigenfunctions on the Koch Snowflake: A new grid and symmetry, J. Comput. Appl. Math., 2005, to appear.
  • 28
    • 10644280743 scopus 로고    scopus 로고
    • Computing eigenmodes of elliptic operators using radial basis functions
    • Platte R.B., and Driscoll T.A. Computing eigenmodes of elliptic operators using radial basis functions. Comput. Math. Appl. 48 3-4 (2004) 561-576
    • (2004) Comput. Math. Appl. , vol.48 , Issue.3-4 , pp. 561-576
    • Platte, R.B.1    Driscoll, T.A.2
  • 29
    • 33748416807 scopus 로고    scopus 로고
    • S.C. Reddy, J.A.C. Weideman, The accuracy of the Chebyshev differencing method for analytic functions, SIAM J. Numer. Anal., to appear.
  • 33
    • 0003433067 scopus 로고    scopus 로고
    • The Clarendon Press, Oxford University Press, New York
    • Schwab C. p- and hp-Finite Element Methods (1998), The Clarendon Press, Oxford University Press, New York
    • (1998) p- and hp-Finite Element Methods
    • Schwab, C.1
  • 35
    • 0022661834 scopus 로고
    • The exponential accuracy of Fourier and Chebyshev differencing methods
    • Tadmor E. The exponential accuracy of Fourier and Chebyshev differencing methods. SIAM J. Numer. Anal. 23 1 (1986) 1-10
    • (1986) SIAM J. Numer. Anal. , vol.23 , Issue.1 , pp. 1-10
    • Tadmor, E.1
  • 37
    • 4243632346 scopus 로고
    • Diffusion-limited aggregation a kinetic critical phenomenon
    • Witten T.A., and Sander L.M. Diffusion-limited aggregation a kinetic critical phenomenon. Phys. Rev. Lett. 47 (1981) 1400-1403
    • (1981) Phys. Rev. Lett. , vol.47 , pp. 1400-1403
    • Witten, T.A.1    Sander, L.M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.