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Volumn 29, Issue 12, 2005, Pages 1077-1085

Improved numerical solver for Kansa's method based on affine space decomposition

Author keywords

Collocation; Partial differential equation; Radial basis function

Indexed keywords

BOUNDARY ELEMENT METHOD; DECODING; DECOMPOSITION; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

EID: 28244455875     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2005.07.003     Document Type: Article
Times cited : (35)

References (33)
  • 1
    • 0035541165 scopus 로고    scopus 로고
    • Fast evaluation of radial basis functions: Methods for four-dimensional polyharmonic splines
    • R.K. Beatson, J.B. Cherrie, and D.L. Ragozin Fast evaluation of radial basis functions: methods for four-dimensional polyharmonic splines SIAM J Math Anal 32 6 2001 1272 1310 (electronic)
    • (2001) SIAM J Math Anal , vol.32 , Issue.6 , pp. 1272-1310
    • Beatson, R.K.1    Cherrie, J.B.2    Ragozin, D.L.3
  • 2
    • 28244458795 scopus 로고    scopus 로고
    • Good point/bad point iterations for solving the thin-plate spline interpolation equations
    • Approximation theory, X (St. Louis, MO, 2001) Vanderbilt University Press Nashville, TN
    • R.K. Beatson, and J. Levesley Good point/bad point iterations for solving the thin-plate spline interpolation equations Approximation theory, X (St. Louis, MO, 2001) Innov. Appl. Math. 2001 Vanderbilt University Press Nashville, TN p. 17-25
    • (2001) Innov. Appl. Math.
    • Beatson, R.K.1    Levesley, J.2
  • 3
    • 18144408028 scopus 로고    scopus 로고
    • On approximate cardinal preconditioning methods for solving PDEs with radial basis functions
    • D. Brown, L. Ling, E.J. Kansa, and J. Levesley On approximate cardinal preconditioning methods for solving PDEs with radial basis functions Eng Anal Boundary Elements 29 4 2005 343 353
    • (2005) Eng Anal Boundary Elements , vol.29 , Issue.4 , pp. 343-353
    • Brown, D.1    Ling, L.2    Kansa, E.J.3    Levesley, J.4
  • 4
    • 0000098430 scopus 로고
    • Multivariate cardinal interpolation with radial-basis functions
    • M.D. Buhmann Multivariate cardinal interpolation with radial-basis functions Constr Approx 6 3 1990 225 255
    • (1990) Constr Approx , vol.6 , Issue.3 , pp. 225-255
    • Buhmann, M.D.1
  • 5
    • 0002851869 scopus 로고
    • Multivariate interpolation in odd-dimensional Euclidean spaces using multiquadrics
    • M.D. Buhmann Multivariate interpolation in odd-dimensional Euclidean spaces using multiquadrics Constr Approx 6 1 1990 21 34
    • (1990) Constr Approx , vol.6 , Issue.1 , pp. 21-34
    • Buhmann, M.D.1
  • 6
    • 0036605241 scopus 로고    scopus 로고
    • Symmetric boundary knot method
    • W. Chen Symmetric boundary knot method Eng Anal Boundary Elements 26 6 2002 489 494
    • (2002) Eng Anal Boundary Elements , vol.26 , Issue.6 , pp. 489-494
    • Chen, W.1
  • 7
    • 0037432707 scopus 로고    scopus 로고
    • Numerical convergence of boundary knot method in the analysis of helmholtz, modified helmholtz, and convection-diffusion problems
    • W. Chen, and Y.C. Hon Numerical convergence of boundary knot method in the analysis of helmholtz, modified helmholtz, and convection-diffusion problems Comput Methods Appl Mech Eng 192 2003 1859 1875
    • (2003) Comput Methods Appl Mech Eng , vol.192 , pp. 1859-1875
    • Chen, W.1    Hon, Y.C.2
  • 8
    • 0042334783 scopus 로고    scopus 로고
    • Exponential convergence and h-c multiquadric collocation method for partial differential equations
    • A.H.-D. Cheng, M.A. Golberg, E.J. Kansa, and G. Zammito Exponential convergence and h-c multiquadric collocation method for partial differential equations Numer Methods Partial Differential Eq 19 5 2003 571 594
    • (2003) Numer Methods Partial Differential Eq , vol.19 , Issue.5 , pp. 571-594
    • Cheng, A.H.-D.1    Golberg, M.A.2    Kansa, E.J.3    Zammito, G.4
  • 9
    • 0036467951 scopus 로고    scopus 로고
    • Interpolation in the limit of increasingly flat radial basis functions
    • T.A. Driscoll, and B. Fornberg Interpolation in the limit of increasingly flat radial basis functions Comput Math Appl 43 3-5 2002 413 422
    • (2002) Comput Math Appl , vol.43 , Issue.3-5 , pp. 413-422
    • Driscoll, T.A.1    Fornberg, B.2
  • 10
    • 0036468097 scopus 로고    scopus 로고
    • Improved multiquadric method for elliptic partial differential equations via PDE collocation on the boundary
    • A.I. Fedoseyev, M.J. Friedman, and E.J. Kansa Improved multiquadric method for elliptic partial differential equations via PDE collocation on the boundary Comput Math Appl 43 3-5 2002 439 455
    • (2002) Comput Math Appl , vol.43 , Issue.3-5 , pp. 439-455
    • Fedoseyev, A.I.1    Friedman, M.J.2    Kansa, E.J.3
  • 11
    • 0036467591 scopus 로고    scopus 로고
    • Observations on the behavior of radial basis function approximations near boundaries
    • B. Fornberg, T.A. Driscoll, G. Wright, and R. Charles Observations on the behavior of radial basis function approximations near boundaries Comput Math Appl 43 3-5 2002 473 490
    • (2002) Comput Math Appl , vol.43 , Issue.3-5 , pp. 473-490
    • Fornberg, B.1    Driscoll, T.A.2    Wright, G.3    Charles, R.4
  • 12
    • 14644431037 scopus 로고    scopus 로고
    • Stable computation of multiquadric interpolants for all values of the shape parameter
    • B. Fornberg, and G. Wright Stable computation of multiquadric interpolants for all values of the shape parameter Comput Math Appl 48 5-6 2004 853 867
    • (2004) Comput Math Appl , vol.48 , Issue.5-6 , pp. 853-867
    • Fornberg, B.1    Wright, G.2
  • 13
    • 0942300715 scopus 로고    scopus 로고
    • Some observations regarding interpolants in the limit of flat radial basis functions
    • B. Fornberg, G. Wright, and E. Larsson Some observations regarding interpolants in the limit of flat radial basis functions Comput Math Appl 47 1 2004 37 55
    • (2004) Comput Math Appl , vol.47 , Issue.1 , pp. 37-55
    • Fornberg, B.1    Wright, G.2    Larsson, E.3
  • 14
    • 0025206382 scopus 로고
    • Theory and applications of the multiquadric-biharmonic method. 20 years of discovery 1968-1988
    • R.L. Hardy Theory and applications of the multiquadric-biharmonic method. 20 years of discovery 1968-1988 Comput Math Appl 19 (8-9) 1988 163 208
    • (1988) Comput Math Appl , vol.19 , Issue.89 , pp. 163-208
    • Hardy, R.L.1
  • 15
    • 0008061154 scopus 로고    scopus 로고
    • Multiquadric collocation method with adaptive technique for problems with boundary layer
    • Y.C. Hon Multiquadric collocation method with adaptive technique for problems with boundary layer Int J Appl Sci Comput 6 3 1999 173 184
    • (1999) Int J Appl Sci Comput , vol.6 , Issue.3 , pp. 173-184
    • Hon, Y.C.1
  • 16
    • 0002879831 scopus 로고    scopus 로고
    • An efficient numerical scheme for Burgers' equation
    • Y.C. Hon, and X.Z. Mao An efficient numerical scheme for Burgers' equation Appl Math Comput 95 1 1998 37 50
    • (1998) Appl Math Comput , vol.95 , Issue.1 , pp. 37-50
    • Hon, Y.C.1    Mao, X.Z.2
  • 17
    • 0035311996 scopus 로고    scopus 로고
    • On unsymmetric collocation by radial basis functions
    • Y.C. Hon, and R. Schaback On unsymmetric collocation by radial basis functions Appl Math Comput 119 2-3 2001 177 186
    • (2001) Appl Math Comput , vol.119 , Issue.2-3 , pp. 177-186
    • Hon, Y.C.1    Schaback, R.2
  • 18
    • 0033133932 scopus 로고    scopus 로고
    • Multiquadric solution for shallow water equations
    • Y.C. Hon, K.F. Cheung, X.Z. Mao, and E.J. Kansa Multiquadric solution for shallow water equations ASCE J Hydr Engrg 125 5 1999 524 533
    • (1999) ASCE J Hydr Engrg , vol.125 , Issue.5 , pp. 524-533
    • Hon, Y.C.1    Cheung, K.F.2    Mao, X.Z.3    Kansa, E.J.4
  • 19
    • 0025229330 scopus 로고
    • Multiquadrics - A scattered data approximation scheme with applications to computational fluid-dynamics. I. Surface approximations and partial derivative estimates
    • E.J. Kansa Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. I. Surface approximations and partial derivative estimates Comput Math Appl 19 8-9 1990 127 145
    • (1990) Comput Math Appl , vol.19 , Issue.8-9 , pp. 127-145
    • Kansa, E.J.1
  • 20
    • 0025210711 scopus 로고
    • Multiquadrics - A scattered data approximation scheme with applications to computational fluid-dynamics. II. Solutions to parabolic, hyperbolic and elliptic partial differential equations
    • E.J. Kansa Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. II. Solutions to parabolic, hyperbolic and elliptic partial differential equations Comput Math Appl 19 8-9 1990 147 161
    • (1990) Comput Math Appl , vol.19 , Issue.8-9 , pp. 147-161
    • Kansa, E.J.1
  • 21
    • 0242667184 scopus 로고    scopus 로고
    • A numerical study of radial basis functions based solution methods for elliptic PDEs
    • E. Larsson, and B. Fornberg A numerical study of radial basis functions based solution methods for elliptic PDEs Comput Math Appl 46 5-6 2003 891 902
    • (2003) Comput Math Appl , vol.46 , Issue.5-6 , pp. 891-902
    • Larsson, E.1    Fornberg, B.2
  • 22
    • 0037370546 scopus 로고    scopus 로고
    • A comparison of efficiency and error convergence of multiquadric collocation method and finite element method
    • J. Li, A.H.D. Cheng, and C.-S. Chen A comparison of efficiency and error convergence of multiquadric collocation method and finite element method Eng Anal Boundary Elements 27 3 2003 251 257
    • (2003) Eng Anal Boundary Elements , vol.27 , Issue.3 , pp. 251-257
    • Li, J.1    Cheng, A.H.D.2    Chen, C.-S.3
  • 23
    • 0000972395 scopus 로고    scopus 로고
    • Comparative accuracy of da and hdq methods for three-dimensional vibration analysis of rectangular plates
    • K.M. Liew, T.M. Teo, and J.-B. Han Comparative accuracy of da and hdq methods for three-dimensional vibration analysis of rectangular plates Int J Numer Meth Eng 45 1999 1831 1848
    • (1999) Int J Numer Meth Eng , vol.45 , pp. 1831-1848
    • Liew, K.M.1    Teo, T.M.2    Han, J.-B.3
  • 24
    • 18144408406 scopus 로고    scopus 로고
    • Preconditioning for radial basis functions with domain decomposition methods
    • L. Ling, and E.J. Kansa Preconditioning for radial basis functions with domain decomposition methods Math Comput Modelling 40 13 2005 1413 1427 [2004]
    • (2005) Math Comput Modelling , vol.40 , Issue.13 , pp. 1413-1427
    • Ling, L.1    Kansa, E.J.2
  • 25
    • 16244376155 scopus 로고    scopus 로고
    • A least-squares preconditioner for radial basis functions collocation methods
    • L. Ling, and E.J. Kansa A least-squares preconditioner for radial basis functions collocation methods Adv Comput Math 23 1-2 2005 31 54
    • (2005) Adv Comput Math , vol.23 , Issue.1-2 , pp. 31-54
    • Ling, L.1    Kansa, E.J.2
  • 26
    • 14644407531 scopus 로고    scopus 로고
    • Multiquadratic collocation method with integral formulation for boundary layer problems
    • L. Ling, and M.R. Trummer Multiquadratic collocation method with integral formulation for boundary layer problems Comput Math Appl 48 5-6 2004 927 941
    • (2004) Comput Math Appl , vol.48 , Issue.5-6 , pp. 927-941
    • Ling, L.1    Trummer, M.R.2
  • 27
    • 0000172493 scopus 로고
    • Miscellaneous error bounds for multiquadric and related interpolators
    • W.R. Madych Miscellaneous error bounds for multiquadric and related interpolators Comput Math Appl 24 12 1992 121 138
    • (1992) Comput Math Appl , vol.24 , Issue.12 , pp. 121-138
    • Madych, W.R.1
  • 28
    • 0035885009 scopus 로고    scopus 로고
    • Numerical solution of navier-stokes equations using multiquadric radial basis function networks
    • N. Mai-Duy, and T. Tran-Cong Numerical solution of navier-stokes equations using multiquadric radial basis function networks Int J Numer Meth Fluid 37 2001 65 86
    • (2001) Int J Numer Meth Fluid , vol.37 , pp. 65-86
    • Mai-Duy, N.1    Tran-Cong, T.2
  • 29
    • 51249166702 scopus 로고
    • Error estimates and condition numbers for radial basis function interpolation
    • R. Schaback Error estimates and condition numbers for radial basis function interpolation Adv Comput Math 3 3 1995 251 264
    • (1995) Adv Comput Math , vol.3 , Issue.3 , pp. 251-264
    • Schaback, R.1
  • 33
    • 2942542888 scopus 로고    scopus 로고
    • A grid-free, nonlinear shallow-water model with moving boundary
    • X. Zhou, Y.C. Hon, and K.F. Cheung A grid-free, nonlinear shallow-water model with moving boundary Eng Anal Boundary Elements 28 9 2004 1135 1147
    • (2004) Eng Anal Boundary Elements , vol.28 , Issue.9 , pp. 1135-1147
    • Zhou, X.1    Hon, Y.C.2    Cheung, K.F.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.