메뉴 건너뛰기




Volumn 51, Issue 3, 2009, Pages 213-238

A Cartesian-grid discretisation scheme based on local integrated RBFNs for two-dimensional elliptic problems

Author keywords

Integrated RBFNs; Local approximations; Point collocation; Second order differential problems; Subregion collocation

Indexed keywords

DIFFERENTIAL PROBLEMS; INTEGRATED RBFNS; LOCAL APPROXIMATION; POINT COLLOCATION; SECOND ORDERS;

EID: 77449102023     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (13)

References (33)
  • 1
    • 69949108106 scopus 로고    scopus 로고
    • Adaptive support domain implementation on the moving least squares approximation for mfree methods applied on elliptic and parabolic pde problems using strong-form description
    • Bourantas, G. C.; Skouras, E. D.; Nikiforidis, G. C. (2009): Adaptive support domain implementation on the moving least squares approximation for mfree methods applied on elliptic and parabolic pde problems using strong-form description. CMES: Computer Modeling in Engineering & Sciences, vol.43, no.1, pp. 1-26.
    • (2009) CMES: Computer Modeling in Engineering & Sciences , vol.43 , Issue.1 , pp. 1-26
    • Bourantas, G.C.1    Skouras, E.D.2    Nikiforidis, G.C.3
  • 2
    • 4744345897 scopus 로고    scopus 로고
    • Investigation of the use of radial basis functions in local collocation method for solving diffusion problems
    • Chantasiriwan, S. (2004): Investigation of the use of radial basis functions in local collocation method for solving diffusion problems. International Communications in Heat and Mass Transfer, vol.31, no.8, pp. 1095-1104.
    • (2004) International Communications in Heat and Mass Transfer , vol.31 , Issue.8 , pp. 1095-1104
    • Chantasiriwan, S.1
  • 4
    • 76249103596 scopus 로고    scopus 로고
    • A Galerkin-RBF approach for the streamfunction-vorticity-temperature formulation of natural convection in 2D enclosured domains
    • Ho-Minh, D.; Mai-Duy, N.; Tran-Cong, T. (2009): A Galerkin-RBF approach for the streamfunction-vorticity-temperature formulation of natural convection in 2D enclosured domains. CMES: Computer Modeling in Engineering & Sciences, vol.44, pp. 219-248.
    • (2009) CMES: Computer Modeling in Engineering & Sciences , vol.44 , pp. 219-248
    • Ho-Minh, D.1    Mai-Duy, N.2    Tran-Cong, T.3
  • 6
    • 0001827481 scopus 로고    scopus 로고
    • A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
    • Johansen, H.; Colella, P. (1998): A Cartesian grid embedded boundary method for Poisson's equation on irregular domains. Journal of Computational Physics, vol.147, no.1, pp. 60-85.
    • (1998) Journal of Computational Physics , vol.147 , Issue.1 , pp. 60-85
    • Johansen, H.1    Colella, P.2
  • 7
    • 10244227858 scopus 로고    scopus 로고
    • The embedded finite difference method for the Poisson equation in a domain with an irregular boundary and Dirichlet boundary conditions
    • Jomaa, Z.; Macaskill, C. (2005): The embedded finite difference method for the Poisson equation in a domain with an irregular boundary and Dirichlet boundary conditions. Journal of Computational Physics, vol.202, no.2, pp. 488-506.
    • (2005) Journal of Computational Physics , vol.202 , Issue.2 , pp. 488-506
    • Jomaa, Z.1    MacAskill, C.2
  • 8
    • 0000954713 scopus 로고
    • Multigrid calculation of steady, viscous flow in a triangular cavity
    • Jyotsna, R.; Vanka, S. P. (1995): Multigrid calculation of steady, viscous flow in a triangular cavity. Journal of Computational Physics, vol.122, no.1, pp. 107-117.
    • (1995) Journal of Computational Physics , vol.122 , Issue.1 , pp. 107-117
    • Jyotsna, R.1    Vanka, S.P.2
  • 9
    • 33745434509 scopus 로고    scopus 로고
    • A flow-condition-based interpolation finite element procedure for triangular grids
    • Kohno, H.; Bathe, K.-J. (2006): A flow-condition-based interpolation finite element procedure for triangular grids. International Journal for Numerical Methods in Fluids, vol.51, no.6, pp. 673-699.
    • (2006) International Journal for Numerical Methods in Fluids , vol.51 , Issue.6 , pp. 673-699
    • Kohno, H.1    Bathe, K.-J.2
  • 12
    • 77449110168 scopus 로고    scopus 로고
    • An effective integrated-RBFN Cartesian-grid discretisation for the stream function-vorticity-temperature formulation in non-rectangular domains
    • Part B
    • Le-Cao, K.; Mai-Duy, N.; Tran-Cong, T. (2009): An effective integrated-RBFN Cartesian-grid discretisation for the stream function-vorticity-temperature formulation in non-rectangular domains. Numerical Heat Transfer, Part B, vol.55, pp. 480-502.
    • (2009) Numerical Heat Transfer , vol.55 , pp. 480-502
    • Le-Cao, K.1    Mai-Duy, N.2    Tran-Cong, T.3
  • 13
    • 0038604335 scopus 로고    scopus 로고
    • Local multiquadric approximation for solving boundary value problems
    • Lee, C. K.; Liu, X.; Fan, S. C. (2003): Local multiquadric approximation for solving boundary value problems. Computational Mechanics, vol.30, no.5-6, pp. 396-409.
    • (2003) Computational Mechanics , vol.30 , Issue.5-6 , pp. 396-409
    • Lee, C.K.1    Liu, X.2    Fan, S.C.3
  • 14
    • 13244255578 scopus 로고    scopus 로고
    • Solving high order ordinary differential equations with radial basis function networks
    • DOI 10.1002/nme.1220
    • Mai-Duy, N. (2005): Solving high order ordinary differential equations with radial basis function networks. International Journal for Numerical Methods in Engineering, vol.62, pp. 824-852. (Pubitemid 40195781)
    • (2005) International Journal for Numerical Methods in Engineering , vol.62 , Issue.6 , pp. 824-852
    • Mai-Duy, N.1
  • 15
    • 15844392773 scopus 로고    scopus 로고
    • An effective high order interpolation scheme in BIEM for biharmonic boundary value problems
    • Mai-Duy, N.; Tanner, R. I. (2005): An effective high order interpolation scheme in BIEM for biharmonic boundary value problems. Engineering Analysis with Boundary Elements, vol.29, pp. 210-223.
    • (2005) Engineering Analysis with Boundary Elements , vol.29 , pp. 210-223
    • Mai-Duy, N.1    Tanner, R.I.2
  • 16
    • 0035137045 scopus 로고    scopus 로고
    • Numerical solution of differential equations using multiquadric radial basis function networks
    • DOI 10.1016/S0893-6080(00)00095-2, PII S0893608000000952
    • Mai-Duy, N.; Tran-Cong, T. (2001): Numerical solution of differential equations using multiquadric radial basis function networks. Neural Networks, vol.14, no.2, pp. 185-199. (Pubitemid 32157010)
    • (2001) Neural Networks , vol.14 , Issue.2 , pp. 185-199
    • Mai-Duy, N.1    Tran-Cong, T.2
  • 18
    • 31044436186 scopus 로고    scopus 로고
    • Solving biharmonic problems with scattered-point discretisation using indirect radial-basis-function networks
    • Mai-Duy, N.; Tran-Cong, T. (2006): Solving biharmonic problems with scattered-point discretisation using indirect radial-basis-function networks. Engineering Analysis with Boundary Elements, vol.30, no.2, pp. 77-87.
    • (2006) Engineering Analysis with Boundary Elements , vol.30 , Issue.2 , pp. 77-87
    • Mai-Duy, N.1    Tran-Cong, T.2
  • 19
    • 78650150367 scopus 로고    scopus 로고
    • A control volume technique based on integrated RBFNs for the convection-diffusion equation
    • accepted
    • Mai-Duy, N.; Tran-Cong, T. (2009a): A control volume technique based on integrated RBFNs for the convection-diffusion equation. Numerical Methods for Partial Differential Equations (accepted).
    • (2009) Numerical Methods for Partial Differential Equations
    • Mai-Duy, N.1    Tran-Cong, T.2
  • 20
    • 77449085516 scopus 로고    scopus 로고
    • A numerical study of 2D integrated RBFNs incorporating Cartesian grids for solving 2D elliptic differential problems
    • accepted
    • Mai-Duy, N.; Tran-Cong, T. (2009b): A numerical study of 2D integrated RBFNs incorporating Cartesian grids for solving 2D elliptic differential problems. Numerical Methods for Partial Differential Equations(accepted).
    • (2009) Numerical Methods for Partial Differential Equations
    • Mai-Duy, N.1    Tran-Cong, T.2
  • 21
    • 39349099522 scopus 로고    scopus 로고
    • Improving volume element methods by meshless radial basis function techniques
    • Orsini, P.; Power, H.; Morvan, H. (2008): Improving volume element methods by meshless radial basis function techniques. CMES: Computer Modeling in Engineering & Sciences, vol.23, pp. 187-208.
    • (2008) CMES: Computer Modeling in Engineering & Sciences , vol.23 , pp. 187-208
    • Orsini, P.1    Power, H.2    Morvan, H.3
  • 22
    • 39049089022 scopus 로고    scopus 로고
    • Investigation of multi geometric uncertainties by different polynomial chaos methodologies using a fictitious domain solver
    • Parussini, L.; Pediroda, V. (2008): Investigation of multi geometric uncertainties by different polynomial chaos methodologies using a fictitious domain solver. CMES: Computer Modeling in Engineering & Sciences, vol.23, no.1, pp. 29-52.
    • (2008) CMES: Computer Modeling in Engineering & Sciences , vol.23 , Issue.1 , pp. 29-52
    • Parussini, L.1    Pediroda, V.2
  • 23
    • 58149517230 scopus 로고    scopus 로고
    • Solutions for incompressible viscous flow in a triangular cavity using cartesian grid method
    • Pasquim, B. M.; Mariani, V. C. (2008): Solutions for incompressible viscous flow in a triangular cavity using cartesian grid method. CMES: Computer Modeling in Engineering & Sciences, vol.35, no.2, pp. 113-132.
    • (2008) CMES: Computer Modeling in Engineering & Sciences , vol.35 , Issue.2 , pp. 113-132
    • Pasquim, B.M.1    Mariani, V.C.2
  • 26
    • 50249093768 scopus 로고    scopus 로고
    • Local radial basis function based gridfree scheme for unsteady incompressible viscous flows
    • Sanyasiraju, Y. V. S. S.; Chandhini, G. (2008): Local radial basis function based gridfree scheme for unsteady incompressible viscous flows. Journal of Computational Physics, vol.227, no.20, pp. 8922-8948.
    • (2008) Journal of Computational Physics , vol.227 , Issue.20 , pp. 8922-8948
    • Sanyasiraju, Y.V.S.S.1    Chandhini, G.2
  • 27
    • 33746113026 scopus 로고    scopus 로고
    • Integrated multiquadric radial basis function approximation methods
    • Sarra, S. A. (2006): Integrated multiquadric radial basis function approximation methods. Computers & Mathematics with Applications, vol.51, no.8, pp. 1283- 1296.
    • (2006) Computers & Mathematics with Applications , vol.51 , Issue.8 , pp. 1283-1296
    • Sarra, S.A.1
  • 28
    • 0037436111 scopus 로고    scopus 로고
    • Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier-Stokes equations
    • Shu, C.; Ding, H.; Yeo, K. S. (2003): Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering, vol.192, pp. 941-954.
    • (2003) Computer Methods in Applied Mechanics and Engineering , vol.192 , pp. 941-954
    • Shu, C.1    Ding, H.2    Yeo, K.S.3
  • 29
    • 15544371314 scopus 로고    scopus 로고
    • Computation of incompressible navierstokes equations by local RBF-based differential quadrature method
    • Shu, C.; Ding, H.; Yeo, K. S. (2005): Computation of incompressible navierstokes equations by local RBF-based differential quadrature method. CMES: Computer Modeling in Engineering & Sciences, vol.7, pp. 195-206.
    • (2005) CMES: Computer Modeling in Engineering & Sciences , vol.7 , pp. 195-206
    • Shu, C.1    Ding, H.2    Yeo, K.S.3
  • 30
    • 3042722159 scopus 로고    scopus 로고
    • On using radial basis functions in a "finite difference mode" with applications to elasticity problems
    • Tolstykh, A. I.; Shirobokov, D. A. (2003): On using radial basis functions in a "finite difference mode" with applications to elasticity problems. Computational Mechanics, vol.33, no.1, pp. 68-79.
    • (2003) Computational Mechanics , vol.33 , Issue.1 , pp. 68-79
    • Tolstykh, A.I.1    Shirobokov, D.A.2
  • 33
    • 29144437684 scopus 로고    scopus 로고
    • Scattered node compact finite differencetype formulas generated from radial basis functions
    • Wright, G. B.; Fornberg, B. (2006): Scattered node compact finite differencetype formulas generated from radial basis functions. Journal of Computational Physics, vol.212, no.1, pp. 99-123.
    • (2006) Journal of Computational Physics , vol.212 , Issue.1 , pp. 99-123
    • Wright, G.B.1    Fornberg, B.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.