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Volumn 185, Issue 1, 2007, Pages 614-627

Solving partial differential equations by meshless methods using radial basis functions

Author keywords

Galerkin method; Meshless; Petrov Galerkin method; RBF; Subdomain method

Indexed keywords

COMPUTATIONAL COMPLEXITY; FUNCTIONS; GALERKIN METHODS; PROBLEM SOLVING;

EID: 33846914840     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.07.057     Document Type: Article
Times cited : (26)

References (30)
  • 1
    • 0025210711 scopus 로고
    • MultiquadricA scattered data approximation scheme with applications to computational fluid dynamics II
    • Kansa E.J. MultiquadricA scattered data approximation scheme with applications to computational fluid dynamics II. Comput. Math. Appl. 19 (1990) 147-161
    • (1990) Comput. Math. Appl. , vol.19 , pp. 147-161
    • Kansa, E.J.1
  • 3
    • 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. Comp. 22 (2000) 1717-1740
    • (2000) SIAM J. Sci. Comp. , vol.22 , pp. 1717-1740
    • Beatson, W.1    Cherrie, J.B.2    Mouat, T.3
  • 4
    • 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 1 (2000) 81-98
    • (2000) Int. J. Appl. Math. , vol.4 , Issue.1 , pp. 81-98
    • Hon, Y.C.1    Wu, Z.2
  • 5
    • 2342536532 scopus 로고    scopus 로고
    • Domain decomposition for radial basis meshless methods
    • Hon Y.C., and Li J. Domain decomposition for radial basis meshless methods. Numer. Meth. Part. D. E. 20 3 (2004) 450-462
    • (2004) Numer. Meth. Part. D. E. , vol.20 , Issue.3 , pp. 450-462
    • Hon, Y.C.1    Li, J.2
  • 6
    • 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
  • 7
    • 33846936413 scopus 로고    scopus 로고
    • Leevan Ling, Edward J. Kansa, A least-squares preconditioner for radial basis functions collocation methods, Adv. Comp. Math. (Preprint), 2003.
  • 8
    • 33846921463 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
    • 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
  • 10
    • 33846934367 scopus 로고    scopus 로고
    • L. Ling, M.R. Trummer, Multiquradric collocation method with integral formulation for boundary layer problems, Comp. Math. Appl. (Preprint), 2003.
  • 11
    • 85128507483 scopus 로고    scopus 로고
    • Mira Bozzini, Licia Lenarduzzi, R. Rossini, Robert Schaback, Interpolation by Basis Functions of Different Scales and Shapes, Calcolo 41 (2004) 77-87.
  • 12
    • 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. , vol.39 , pp. 123-137
    • Kansa, E.J.1    Hon, Y.C.2
  • 13
    • 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. , vol.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
  • 15
    • 0036467593 scopus 로고    scopus 로고
    • Boundary knot method: a meshless, exponential convergence, integration-free, and boundary-only RBF technique
    • Chen W., and Tanaka M. Boundary knot method: 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
  • 16
    • 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 311C324
    • (1999) Boundary Element Technology XIII
    • Schaback, R.1    Wendland, H.2
  • 17
    • 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
  • 18
    • 51649133223 scopus 로고
    • Hermite-Birkhoff interpolation of scattered data by radial basis function
    • Wu Z. Hermite-Birkhoff interpolation of scattered data by radial basis function. Approx. Theory Appl. 8 2 (1992)
    • (1992) Approx. Theory Appl. , vol.8 , Issue.2
    • Wu, Z.1
  • 19
    • 14544290310 scopus 로고
    • Local error estimates for radial basis function interpolation of scattered data
    • Wu Z., and Schaback R. Local error estimates for radial basis function interpolation of scattered data. IMA J. Numer. Anal. 13 (1993) 13-27
    • (1993) IMA J. Numer. Anal. , vol.13 , pp. 13-27
    • Wu, Z.1    Schaback, R.2
  • 20
    • 0001739142 scopus 로고
    • The theory of radial basis function approximation in 1990
    • Light W. (Ed), Oxford Science Publications, Oxford
    • Powell M.J.D. The theory of radial basis function approximation in 1990. In: Light W. (Ed). Advances in Numerical Analysis vol. II (1992), Oxford Science Publications, Oxford
    • (1992) Advances in Numerical Analysis , vol.II
    • Powell, M.J.D.1
  • 21
    • 84966244353 scopus 로고
    • Multivariate interpolation and conditionally positive definite functions
    • Madych W.R., and Nelson S.A. Multivariate interpolation and conditionally positive definite functions. Math. Comp. 54 (1990) 211-230
    • (1990) Math. Comp. , vol.54 , pp. 211-230
    • Madych, W.R.1    Nelson, S.A.2
  • 22
    • 30844437566 scopus 로고    scopus 로고
    • Characterization and construction of radial basis functions
    • Dyn N., Leviatan D., and Levin D. (Eds), Cambridge University Press, Cambridge
    • Schaback R., and Wendland H. Characterization and construction of radial basis functions. In: Dyn N., Leviatan D., and Levin D. (Eds). Eilat Proceedings (2000), Cambridge University Press, Cambridge
    • (2000) Eilat Proceedings
    • Schaback, R.1    Wendland, H.2
  • 23
    • 33846907986 scopus 로고    scopus 로고
    • L. Mai-Cao, T. Tran-Cong, Solving time-dependent PDEs with a meshless IRBFN-based method, in: Proceedings of the International Workshop on MeshFree Methods, 2003.
  • 24
    • 33845398201 scopus 로고    scopus 로고
    • Yunxin Zhang, Yongji Tan, Convergence of meshless Petrov-Galerkin method using radial basis functions, Appl. Math. Comp., in press, doi:10.1016/j.amc.2006.05.085.
  • 25
    • 33344475702 scopus 로고    scopus 로고
    • Solve partial differential equations by meshless subdomains method combined with RBFs
    • Zhang Y., and Tan Y. Solve partial differential equations by meshless subdomains method combined with RBFs. Appl. Math. Compt. 174 (2006) 700-709
    • (2006) Appl. Math. Compt. , vol.174 , pp. 700-709
    • Zhang, Y.1    Tan, Y.2
  • 26
    • 33646191542 scopus 로고    scopus 로고
    • Convergence of general meshless Schwarz method using radial basis functions
    • Zhang Y., and Tan Y. Convergence of general meshless Schwarz method using radial basis functions. Appl. Numer. Meth. 56 (2006) 916-936
    • (2006) Appl. Numer. Meth. , vol.56 , pp. 916-936
    • Zhang, Y.1    Tan, Y.2
  • 27
    • 33846921953 scopus 로고    scopus 로고
    • Convergence order of meshless collocation methods using radial
    • Franke C., and Schabake R. Convergence order of meshless collocation methods using radial. Basis Funct. (1997)
    • (1997) Basis Funct.
    • Franke, C.1    Schabake, R.2
  • 28
    • 0000136089 scopus 로고
    • Multivariate compactly supported positive definite radial functions
    • Wu Z. Multivariate compactly supported positive definite radial functions. Adv. Comp. Math. 4 (1995) 283-292
    • (1995) Adv. Comp. Math. , vol.4 , pp. 283-292
    • Wu, Z.1
  • 29
    • 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. Comp. Math. 4 (1995) 283-292
    • (1995) Adv. Comp. Math. , vol.4 , pp. 283-292
    • Wendland, H.1
  • 30
    • 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. , vol.70 , pp. 307-318
    • Buhmann, M.D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.