메뉴 건너뛰기




Volumn 19, Issue 5, 2003, Pages 333-347

Radial basis functions for solving near singular Poisson problems

Author keywords

Compactly supported radial basis functions; Dual reciprocity method; Method of fundamental solutions; Near singular problems; Particular solution; Radial basis functions

Indexed keywords

MATHEMATICAL MODELS; POISSON EQUATION; RADIAL BASIS FUNCTION NETWORKS;

EID: 0037534039     PISSN: 10698299     EISSN: None     Source Type: Journal    
DOI: 10.1002/cnm.593     Document Type: Article
Times cited : (21)

References (28)
  • 2
    • 84968515237 scopus 로고
    • Scattered data interpolation: Tests of some methods
    • Franke R. Scattered data interpolation: tests of some methods. Mathematics of Computation 1982; 48:181-200.
    • (1982) Mathematics of Computation , vol.48 , pp. 181-200
    • Franke, R.1
  • 3
    • 34250122797 scopus 로고
    • Interpolation of scattered data: Distance matrices and conditionally positive definite functions
    • Micchelli CA. Interpolation of scattered data: distance matrices and conditionally positive definite functions. Constructive Approximation 1986; 2(1):11-12.
    • (1986) Constructive Approximation , vol.2 , Issue.1 , pp. 11-12
    • Micchelli, C.A.1
  • 4
    • 0001680399 scopus 로고    scopus 로고
    • On the efficiency of interpolation by radial basis functions
    • Le Méhauté A, Rabut C, Schumaiker LL (eds). Vanderbilt University Press: Nashville
    • Schaback R. On the efficiency of interpolation by radial basis functions. In Surface Fitting and Multiresolution Methods, Le Méhauté A, Rabut C, Schumaiker LL (eds). Vanderbilt University Press: Nashville, 1997; 309-318.
    • (1997) Surface Fitting and Multiresolution Methods , pp. 309-318
    • Schaback, R.1
  • 5
    • 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. Advances in Computational Mathematics 1995; 4:389-396.
    • (1995) Advances in Computational Mathematics , vol.4 , pp. 389-396
    • Wendland, H.1
  • 6
    • 0000136089 scopus 로고
    • Multivariate compactly supported positive definite radial functions
    • Wu Z. Multivariate compactly supported positive definite radial functions. Advances in Computational Mathematics 1995; 4:283-292.
    • (1995) Advances in Computational Mathematics , vol.4 , pp. 283-292
    • Wu, Z.1
  • 8
    • 0041593773 scopus 로고    scopus 로고
    • Solving differential equations with radial basis functions: Multilevel methods and smoothing
    • Fasshauer GE. Solving differential equations with radial basis functions: multilevel methods and smoothing. Advances in Computational Mathematics 1999; 11:139-159.
    • (1999) Advances in Computational Mathematics , vol.11 , pp. 139-159
    • Fasshauer, G.E.1
  • 10
    • 0001987050 scopus 로고
    • The theory of radial basis functions applied to the BEM for inhomogeneous partial differential equations
    • Golberg MA, Chen CS. The theory of radial basis functions applied to the BEM for inhomogeneous partial differential equations. Boundary Elements Communications 1994; 5:57-61.
    • (1994) Boundary Elements Communications , vol.5 , pp. 57-61
    • Golberg, M.A.1    Chen, C.S.2
  • 11
    • 0032025676 scopus 로고    scopus 로고
    • Some comments on the use of radial basis functions in the dual reciprocity method
    • Golberg MA, Chen CS, Bowman H, Power H. Some comments on the use of radial basis functions in the dual reciprocity method. Computational Mechanics 1998; 21:141-148.
    • (1998) Computational Mechanics , vol.21 , pp. 141-148
    • Golberg, M.A.1    Chen, C.S.2    Bowman, H.3    Power, H.4
  • 12
    • 0000776101 scopus 로고    scopus 로고
    • The method of fundamental solutions for potential, Helmholtz and diffusion problems
    • Golberg MA (ed.). WIT Press: Southampton
    • Golberg MA, Chen CS. The method of fundamental solutions for potential, Helmholtz and diffusion problems. In Boundary Integral Methods: Numerical and Mathematical Aspects, Golberg MA (ed.). WIT Press: Southampton, 1998; 103-176.
    • (1998) Boundary Integral Methods: Numerical and Mathematical Aspects , pp. 103-176
    • Golberg, M.A.1    Chen, C.S.2
  • 13
    • 0025210711 scopus 로고
    • Multiquadrics: A scattered data approximation scheme with applications to computational fluid-dynamics
    • Kansa E. Multiquadrics: a scattered data approximation scheme with applications to computational fluid-dynamics. Computers and Mathematics with Applications 1990; 19:147-161.
    • (1990) Computers and Mathematics With Applications , vol.19 , pp. 147-161
    • Kansa, E.1
  • 16
    • 0004665984 scopus 로고
    • Collocation methods for second kind integral equations with non-compact operators
    • Amini S, Sloan I. Collocation methods for second kind integral equations with non-compact operators. Journal of Integral Equations and Applications 1989; 2:1-30.
    • (1989) Journal of Integral Equations and Applications , vol.2 , pp. 1-30
    • Amini, S.1    Sloan, I.2
  • 17
    • 0003223536 scopus 로고
    • A survey of boundary integral equation methods for the numerical solution of Laplace's equation in three dimensions
    • Chapter 1, Golberg MA (ed.). Plenum: New York
    • Atkinson KE. A survey of boundary integral equation methods for the numerical solution of Laplace's equation in three dimensions. In Numerical Solution of Integral Equations, Chapter 1, Golberg MA (ed.). Plenum: New York, 1990.
    • (1990) Numerical Solution of Integral Equations
    • Atkinson, K.E.1
  • 18
    • 0001705710 scopus 로고
    • The method of fundamental solutions for the numerical solution of the biharmonic equation
    • Fairweather G, Karageorghis A. The method of fundamental solutions for the numerical solution of the biharmonic equation. Journal of Computational Physics 1987: 69:435-459.
    • (1987) Journal of Computational Physics , vol.69 , pp. 435-459
    • Fairweather, G.1    Karageorghis, A.2
  • 19
    • 0026692321 scopus 로고
    • Modified methods of fundamental solutions for harmonic and biharmonic problems with boundary singularities
    • Karageorghis A. Modified methods of fundamental solutions for harmonic and biharmonic problems with boundary singularities. Numerical Methods for Partial Differential Equations 1992; 8:1-19.
    • (1992) Numerical Methods for Partial Differential Equations , vol.8 , pp. 1-19
    • Karageorghis, A.1
  • 20
    • 0032073925 scopus 로고    scopus 로고
    • Method of fundamental solutions for harmonic and biharmonic boundary value problems
    • Poullikkas A, Karageorghis A, Georgiou G. Method of fundamental solutions for harmonic and biharmonic boundary value problems. Computational Mechanics 1998; 21:416-423.
    • (1998) Computational Mechanics , vol.21 , pp. 416-423
    • Poullikkas, A.1    Karageorghis, A.2    Georgiou, G.3
  • 22
    • 0033100545 scopus 로고    scopus 로고
    • Stress singularity at a crack tip for various intermediate solids and structures
    • Mushuris GS. Stress singularity at a crack tip for various intermediate solids and structures. International Journal of Solids and Structures 1999; 36:999-1015.
    • (1999) International Journal of Solids and Structures , vol.36 , pp. 999-1015
    • Mushuris, G.S.1
  • 23
    • 0035248089 scopus 로고    scopus 로고
    • Interface crack and nonideal interface concept (Mode III)
    • Mushuris GS. Interface crack and nonideal interface concept (Mode III). International Journal of Fracture 2001; 107:279-296.
    • (2001) International Journal of Fracture , vol.107 , pp. 279-296
    • Mushuris, G.S.1
  • 24
    • 23044530600 scopus 로고    scopus 로고
    • Asymptotic behavior of the elastic solution near the tip of a crack situated at a nonideal interface
    • Mushuris GS, Kuhn G. Asymptotic behavior of the elastic solution near the tip of a crack situated at a nonideal interface. Zeitschrift für Angewandte Mathematic und Mechanik 2001; 81:811-826.
    • (2001) Zeitschrift für Angewandte Mathematic und Mechanik , vol.81 , pp. 811-826
    • Mushuris, G.S.1    Kuhn, G.2
  • 25
    • 0343826595 scopus 로고    scopus 로고
    • Particular solutions of the 3D modified Helmholtz-type equations using compactly supported radial basis functions
    • Golberg MA, Chen CS, Ganesh M. Particular solutions of the 3D modified Helmholtz-type equations using compactly supported radial basis functions. Engineering Analysis with Boundary Elements 2000; 24:539-547.
    • (2000) Engineering Analysis With Boundary Elements , vol.24 , pp. 539-547
    • Golberg, M.A.1    Chen, C.S.2    Ganesh, M.3
  • 26
    • 0032687680 scopus 로고    scopus 로고
    • Particular solutions of Helmholtz-type operators using higher order Poly harmonic splines
    • Muleshkov AS, Golberg MA, Chen CS. Particular solutions of Helmholtz-type operators using higher order Poly harmonic splines. Computational Mechanics 1999; 23:411-419.
    • (1999) Computational Mechanics , vol.23 , pp. 411-419
    • Muleshkov, A.S.1    Golberg, M.A.2    Chen, C.S.3
  • 28
    • 0030571096 scopus 로고    scopus 로고
    • Multistep scattered data interpolation using compactly supported radial basis functions
    • Floater MS, Iske A. Multistep scattered data interpolation using compactly supported radial basis functions Journal of Computational and Applied Mathematics 1996; 73:65-78.
    • (1996) Journal of Computational and Applied Mathematics , vol.73 , pp. 65-78
    • Floater, M.S.1    Iske, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.