메뉴 건너뛰기




Volumn 183, Issue 1, 2006, Pages 307-321

Convergence of meshless Petrov-Galerkin method using radial basis functions

Author keywords

Meshless; Petrov Galerkin method; RBF

Indexed keywords

NUMERICAL METHODS; RADIAL BASIS FUNCTION NETWORKS;

EID: 33845398201     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.05.085     Document Type: Article
Times cited : (9)

References (27)
  • 1
    • 1842853059 scopus 로고    scopus 로고
    • The method of fundamental solutions for solving Poisson problems
    • Alves C.J.S., and Chen C.S. The method of fundamental solutions for solving Poisson problems. Int. Ser. Adv. Bound. Elem. XXIV 13 (2002) 67-76
    • (2002) Int. Ser. Adv. Bound. Elem. , vol.XXIV , Issue.13 , pp. 67-76
    • Alves, C.J.S.1    Chen, C.S.2
  • 3
    • 0028483749 scopus 로고
    • Special finite element methods for a class of second order elliptic problems with rough coefficients
    • Babuška I., Caloz G., and Osborn J.E. Special finite element methods for a class of second 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
  • 4
    • 0034775741 scopus 로고    scopus 로고
    • Fast solution of the radial basis function interpolation methods: domain decomposition methods
    • Beatson W., Cherrie J.B., and Mouat T. Fast solution of the radial basis function interpolation methods: domain decomposition methods. SIAM J. Sci. Comput. 22 (2000) 1717-1740
    • (2000) SIAM J. Sci. Comput. , Issue.22 , pp. 1717-1740
    • Beatson, W.1    Cherrie, J.B.2    Mouat, T.3
  • 5
    • 33845436980 scopus 로고    scopus 로고
    • Mira Bozzini, Licia Lenarduzzi, R. Rossini, Robert Schaback, Interpolation by basis functions of different scales and shapes, 2001.
  • 6
    • 0035606001 scopus 로고    scopus 로고
    • A new class of radial basis functions with compact support
    • Buhmann M.D. A new class of radial basis functions with compact support. Math. Comput. 70 (2001) 307-318
    • (2001) Math. Comput. , Issue.70 , pp. 307-318
    • Buhmann, M.D.1
  • 7
    • 0036467593 scopus 로고    scopus 로고
    • A meshless, exponential convergence, integration-free, and boundary-only RBF technique
    • Chen W., and Tanaka M. A meshless, exponential convergence, integration-free, and boundary-only RBF technique. Comput. Math. Appl. 43 (2002) 379-391
    • (2002) Comput. Math. Appl. , vol.43 , pp. 379-391
    • Chen, W.1    Tanaka, M.2
  • 8
    • 33845444952 scopus 로고    scopus 로고
    • Gregory E. Fasshauer, Approximate moving least-squares approximation with compactly supported radial weights, in: Numerical Algorithms, Lecture Notes in Computer Science and Engineering, vol. 26, 2002, pp. 105-116.
  • 9
    • 1842441315 scopus 로고    scopus 로고
    • Matrix-free multilevel moving least-squares methods
    • Chui C.K., Schumaker L.L., and Stöckler J. (Eds), Vanderbilt University Press
    • Fasshauer G.E. Matrix-free multilevel moving least-squares methods. In: Chui C.K., Schumaker L.L., and Stöckler J. (Eds). Approximation Theory X: Wavelets, Splines, and Applications (2002), Vanderbilt University Press 271-281
    • (2002) Approximation Theory X: Wavelets, Splines, and Applications , pp. 271-281
    • Fasshauer, G.E.1
  • 10
    • 33845453569 scopus 로고    scopus 로고
    • Gregory E. Fasshauer, Approximate moving least-squares approximation for time- dependent PDEs in WCCM V, in: H.A. Mang, F.G. Rammerstorfer, J. Eberhardsteiner (Eds.), Fifth World Congress on Computational Mechanics, Vienna University of Technology, 2002. Available from: .
  • 11
    • 1842597969 scopus 로고    scopus 로고
    • Approximate moving least-squares approximation: a fast and accurate multivariate approximation method
    • Cohen A., Merrien J.-L., and Schumaker L.L. (Eds), Nashboro Press
    • Fasshauer G.E. Approximate moving least-squares approximation: a fast and accurate multivariate approximation method. In: Cohen A., Merrien J.-L., and Schumaker L.L. (Eds). Curve and Surface Fitting: Saint-Malo 2002 (2002), Nashboro Press 139-148
    • (2002) Curve and Surface Fitting: Saint-Malo 2002 , pp. 139-148
    • Fasshauer, G.E.1
  • 12
    • 3142763671 scopus 로고    scopus 로고
    • Additive Schwarz domain decomposition with radial basis approximation
    • Hon Y.C., and Wu Z. Additive Schwarz domain decomposition with radial basis approximation. Int. J. Appl. Math. 4 (2002) 81-98
    • (2002) Int. J. Appl. Math. , Issue.4 , pp. 81-98
    • Hon, Y.C.1    Wu, Z.2
  • 13
    • 33845456976 scopus 로고    scopus 로고
    • Y.C.Hon, Jichun Li, Domain decomposition for radial basis meshless methods, Numer. Methods Partial Diff. Equat., submitted for publication.
  • 14
    • 0035311996 scopus 로고    scopus 로고
    • On unsysmetric collocation by radial basis functions
    • Hon Y.C., and Schaback R. On unsysmetric collocation by radial basis functions. Appl. Math. Comput. 119 (2001) 177-186
    • (2001) Appl. Math. Comput. , Issue.119 , pp. 177-186
    • Hon, Y.C.1    Schaback, R.2
  • 15
    • 0025210711 scopus 로고
    • Multiquadric: a scattered data approximation scheme with applications to computational fluid dynamics II
    • Kansa E.J. Multiquadric: a scattered data approximation scheme with applications to computational fluid dynamics II. Comput. Math. Appl. 19 (1990) 147-161
    • (1990) Comput. Math. Appl. , Issue.19 , pp. 147-161
    • Kansa, E.J.1
  • 16
    • 0034173976 scopus 로고    scopus 로고
    • Circumventing the ill-conditioning problem with multiquadric radial basis functions: application to elliptic partial differential equations
    • Kansa E.J., and Hon Y.C. Circumventing the ill-conditioning problem with multiquadric radial basis functions: application to elliptic partial differential equations. Comput. Math. Appl. 39 (2000) 123-137
    • (2000) Comput. Math. Appl. , Issue.39 , pp. 123-137
    • Kansa, E.J.1    Hon, Y.C.2
  • 17
    • 33845384318 scopus 로고    scopus 로고
    • Leevan Ling, Edward J. Kansa, A least-squares preconditioner for radial basis functions collocation methods, Adv. Comput. Math. Preprint, 2003.
  • 18
    • 33845389221 scopus 로고    scopus 로고
    • Leevan Ling, Manfred R. Trummer, Multiquadric collocation method with integral formulation for boundary layer problems, Computers Math. Applic. Preprint, 2003.
  • 20
    • 3142684323 scopus 로고    scopus 로고
    • Using compactly supported radial basis functions to solve partial differential equations
    • Chen C., Brebbia C.A., and Pepper D.W. (Eds), WitPress, Southampton, Boston
    • Schaback R., and Wendland H. Using compactly supported radial basis functions to solve partial differential equations. In: Chen C., Brebbia C.A., and Pepper D.W. (Eds). Boundary Element Technology XIII (1999), WitPress, Southampton, Boston 311-324
    • (1999) Boundary Element Technology XIII , pp. 311-324
    • Schaback, R.1    Wendland, H.2
  • 21
    • 23044522578 scopus 로고    scopus 로고
    • Adaptive greedy techniques for approximate solution of large RBF systems
    • Schaback R., and Wendland H. Adaptive greedy techniques for approximate solution of large RBF systems. Numerical Algorithms (2000)
    • (2000) Numerical Algorithms
    • Schaback, R.1    Wendland, H.2
  • 22
    • 0033465031 scopus 로고    scopus 로고
    • Meshless Galerkin methods using radial basis functions
    • Wendland H. Meshless Galerkin methods using radial basis functions. Math. Comput. 68 228 (2002) 1521-1531
    • (2002) Math. Comput. , vol.68 , Issue.228 , pp. 1521-1531
    • Wendland, H.1
  • 23
    • 0346847275 scopus 로고
    • Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree
    • Wendland H. Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree. Adv. Comput. Math. 4 (1995) 283-292
    • (1995) Adv. Comput. Math. , Issue.4 , pp. 283-292
    • Wendland, H.1
  • 24
    • 0033115928 scopus 로고    scopus 로고
    • Multizone decomposition for simulation of time-dependent problems using the multiquadric scheme
    • Wong A.S.M., Hon Y.C., Li T.S., Chung S.L., and Kansa E.J. Multizone decomposition for simulation of time-dependent problems using the multiquadric scheme. Comput. Math. Appl. 37 (1999) 23-43
    • (1999) Comput. Math. Appl. , Issue.37 , pp. 23-43
    • Wong, A.S.M.1    Hon, Y.C.2    Li, T.S.3    Chung, S.L.4    Kansa, E.J.5
  • 25
    • 0000136089 scopus 로고
    • Multivariate compactly supported positive definite radial functions
    • Wu Z. Multivariate compactly supported positive definite radial functions. Adv. Comput. Math. 4 (1995) 283-292
    • (1995) Adv. Comput. Math. , Issue.4 , pp. 283-292
    • Wu, Z.1
  • 26
    • 0037215232 scopus 로고    scopus 로고
    • Overlapping domain decomposition method by radial basis functions
    • Zhou X., Hon Y.C., and Li J. Overlapping domain decomposition method by radial basis functions. Appl. Numer. Math. 44 1-2 (2003) 241-255
    • (2003) Appl. Numer. Math. , vol.44 , Issue.1-2 , pp. 241-255
    • Zhou, X.1    Hon, Y.C.2    Li, J.3
  • 27
    • 33645783427 scopus 로고
    • Finite element methods for the solution of problems with rough data
    • Singularities and Constructive Methods for Their Treatment. Grisvard P., Wendland W., and Whiteman J.K. (Eds), Springer-Verlag, Berlin-New York
    • Finite element methods for the solution of problems with rough data. In: Grisvard P., Wendland W., and Whiteman J.K. (Eds). Singularities and Constructive Methods for Their Treatment. Lecture Notes in Mathematics vol. 1121 (1985), Springer-Verlag, Berlin-New York 1-18
    • (1985) Lecture Notes in Mathematics , vol.1121 , pp. 1-18


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.