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Volumn 33, Issue 2, 2009, Pages 200-208

Use of singularity capturing functions in the solution of problems with discontinuous boundary conditions

Author keywords

Discontinuous boundary conditions; Radial basis function; Stokes problem

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; FEEDFORWARD NEURAL NETWORKS; NUMERICAL METHODS; PROBABILITY DENSITY FUNCTION; RADIAL BASIS FUNCTION NETWORKS;

EID: 56949103650     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2008.05.002     Document Type: Article
Times cited : (17)

References (32)
  • 1
    • 0000562261 scopus 로고
    • The treatment of singularities of partial differential equations by relaxation methods
    • Motz H. The treatment of singularities of partial differential equations by relaxation methods. Quart Appl Math 4 (1947) 373-377
    • (1947) Quart Appl Math , vol.4 , pp. 373-377
    • Motz, H.1
  • 2
    • 30244562604 scopus 로고
    • The relaxation treatment of singular points in Poisson's equation
    • Woods L.C. The relaxation treatment of singular points in Poisson's equation. Quart J Mech Appl Math 6 (1953) 163-174
    • (1953) Quart J Mech Appl Math , vol.6 , pp. 163-174
    • Woods, L.C.1
  • 3
    • 1842632053 scopus 로고    scopus 로고
    • An accurate semi-analytic finite difference scheme for two-dimensional elliptic problems with singularities
    • Yosibash Z., Arad M., Yakhot A., and Ben-Dor G. An accurate semi-analytic finite difference scheme for two-dimensional elliptic problems with singularities. Numer Meth Partial Differential Equations 14 (1998) 281-296
    • (1998) Numer Meth Partial Differential Equations , vol.14 , pp. 281-296
    • Yosibash, Z.1    Arad, M.2    Yakhot, A.3    Ben-Dor, G.4
  • 4
    • 0012145451 scopus 로고
    • Higher order Rayleigh-Ritz approximations
    • Fix G. Higher order Rayleigh-Ritz approximations. J Math Mech 18 (1969) 645-658
    • (1969) J Math Mech , vol.18 , pp. 645-658
    • Fix, G.1
  • 5
    • 0001586518 scopus 로고
    • An efficient finite element method for treating singularities in Laplace's equation
    • Olson L.G., Georgiou G.C., and Schultz W.W. An efficient finite element method for treating singularities in Laplace's equation. J Comput Phys 96 (1991) 391-410
    • (1991) J Comput Phys , vol.96 , pp. 391-410
    • Olson, L.G.1    Georgiou, G.C.2    Schultz, W.W.3
  • 6
    • 0003168091 scopus 로고
    • Corner singularities in elliptic problems by finite element methods
    • Wait R., and Mitchell A.R. Corner singularities in elliptic problems by finite element methods. J Comput Phys 8 (1971) 45
    • (1971) J Comput Phys , vol.8 , pp. 45
    • Wait, R.1    Mitchell, A.R.2
  • 7
    • 0001238123 scopus 로고    scopus 로고
    • A finite-element method for Laplace and Helmholtz-type boundary value problems with singularities
    • Wu X., and Han H. A finite-element method for Laplace and Helmholtz-type boundary value problems with singularities. Quart SIAM J Numer Anal 34 (1997) 1037-1050
    • (1997) Quart SIAM J Numer Anal , vol.34 , pp. 1037-1050
    • Wu, X.1    Han, H.2
  • 9
    • 0032114681 scopus 로고    scopus 로고
    • Computing flux intensity factors by a boundary method for elliptic equations with singularities
    • Arad M., Yosibash Z., Ben-Dor G., and Yakhot A. Computing flux intensity factors by a boundary method for elliptic equations with singularities. Commun Numer Meth Eng 14 (1998) 657-670
    • (1998) Commun Numer Meth Eng , vol.14 , pp. 657-670
    • Arad, M.1    Yosibash, Z.2    Ben-Dor, G.3    Yakhot, A.4
  • 10
    • 0036496997 scopus 로고    scopus 로고
    • The solution of Laplace problems over L-shaped domains with a singular function boundary integral method
    • Elliotis M., Georgiou G., and Xenophontos C. The solution of Laplace problems over L-shaped domains with a singular function boundary integral method. Commun Numer Meth Eng 18 (2002) 213-222
    • (2002) Commun Numer Meth Eng , vol.18 , pp. 213-222
    • Elliotis, M.1    Georgiou, G.2    Xenophontos, C.3
  • 11
    • 0002703242 scopus 로고
    • The numerical solution of plane potential problems by improved boundary integral equation methods
    • Hingham D.B., Heggs P.J., and Manzoor M. The numerical solution of plane potential problems by improved boundary integral equation methods. J Comput Phys 42 (1981) 77-98
    • (1981) J Comput Phys , vol.42 , pp. 77-98
    • Hingham, D.B.1    Heggs, P.J.2    Manzoor, M.3
  • 13
    • 32544445023 scopus 로고    scopus 로고
    • Crack analysis using an enriched MFS domain decomposition technique
    • Alves C.J.S., and Leitão V.M.A. Crack analysis using an enriched MFS domain decomposition technique. Eng Anal Boundary Elements 30 3 (2006) 160-166
    • (2006) Eng Anal Boundary Elements , vol.30 , Issue.3 , pp. 160-166
    • Alves, C.J.S.1    Leitão, V.M.A.2
  • 14
    • 0025229330 scopus 로고
    • Multiquadrics, a scattered data approximation scheme with applications to computational fluid dynamics. I. Surface approximations and partial derivatives estimates
    • Kansa E.J. Multiquadrics, a scattered data approximation scheme with applications to computational fluid dynamics. I. Surface approximations and partial derivatives estimates. Comput Math Appl 19 (1990) 127-145
    • (1990) Comput Math Appl , vol.19 , pp. 127-145
    • Kansa, E.J.1
  • 15
    • 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
    • Kansa E.J. 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 (1990) 147-161
    • (1990) Comput Math Appl , vol.19 , pp. 147-161
    • Kansa, E.J.1
  • 16
    • 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., and Yeo K.S. Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier-Stokes equations. Comput Meth Appl Mech Eng 192 3 (2003) 941-954
    • (2003) Comput Meth Appl Mech Eng , vol.192 , Issue.3 , pp. 941-954
    • Shu, C.1    Ding, H.2    Yeo, K.S.3
  • 17
    • 0002567674 scopus 로고
    • Bounds on multivariate polynomials and exponential error estimates for multiquadric interpolation
    • Madych W.D., and Nelson S.A. Bounds on multivariate polynomials and exponential error estimates for multiquadric interpolation. J Approx Theory 70 (1992) 94-114
    • (1992) J Approx Theory , vol.70 , pp. 94-114
    • Madych, W.D.1    Nelson, S.A.2
  • 19
    • 34249710855 scopus 로고    scopus 로고
    • Error estimate, optimal shape factor, and high precision computation of multiquadric collocation method
    • Huang C.-S., Lee C.-F., and Cheng A.H.-D. Error estimate, optimal shape factor, and high precision computation of multiquadric collocation method. Eng Anal Boundary Elements 31 (2007) 614-623
    • (2007) Eng Anal Boundary Elements , vol.31 , pp. 614-623
    • Huang, C.-S.1    Lee, C.-F.2    Cheng, A.H.-D.3
  • 20
    • 0034173976 scopus 로고    scopus 로고
    • Circumventing the ill-conditioning problem with multiquadric radial basis functions: applications to elliptic partial differential equations
    • Kansa E.J., and Hon Y.C. Circumventing the ill-conditioning problem with multiquadric radial basis functions: applications 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
  • 21
    • 0036467591 scopus 로고    scopus 로고
    • Observation of the behavior of radial basis function approximations near boundaries
    • Fornberg B., Driscoll T.A., Wright G., and Charles R. Observation of the behavior of radial basis function approximations near boundaries. Comput Math Appl 43 (2002) 473-490
    • (2002) Comput Math Appl , vol.43 , pp. 473-490
    • Fornberg, B.1    Driscoll, T.A.2    Wright, G.3    Charles, R.4
  • 22
    • 56949091899 scopus 로고    scopus 로고
    • An RBF meshless method for injection molding modelling en Meshfree Methods for Partial Differential Equations III
    • Griebel y M., and Schweitzer M.A. (Eds), Springer, Berlin
    • Bernal F., and Kindelan M. An RBF meshless method for injection molding modelling en Meshfree Methods for Partial Differential Equations III. In: Griebel y M., and Schweitzer M.A. (Eds). Lecture notes in computational science and engineering (2006), Springer, Berlin 41-56
    • (2006) Lecture notes in computational science and engineering , pp. 41-56
    • Bernal, F.1    Kindelan, M.2
  • 23
    • 34548140161 scopus 로고    scopus 로고
    • RBF meshless modeling of non-Newtonian Hele-Shaw flow
    • Bernal F., and Kindelan M. RBF meshless modeling of non-Newtonian Hele-Shaw flow. Eng Anal Boundary Elements 31 (2007) 863-874
    • (2007) Eng Anal Boundary Elements , vol.31 , pp. 863-874
    • Bernal, F.1    Kindelan, M.2
  • 25
    • 0036468097 scopus 로고    scopus 로고
    • Improved multiquadric method for elliptic partial differential equations via PDE collocation on the Boundary
    • Fedoseyev A.I., Friedman M.J., and Kansa E.J. Improved multiquadric method for elliptic partial differential equations via PDE collocation on the Boundary. Comput Math Appl 43 (2002) 439-455
    • (2002) Comput Math Appl , vol.43 , pp. 439-455
    • Fedoseyev, A.I.1    Friedman, M.J.2    Kansa, E.J.3
  • 26
    • 33846263053 scopus 로고    scopus 로고
    • A note on the Gibbs phenomenon with multiquadric radial basis functions
    • Jung J.H. A note on the Gibbs phenomenon with multiquadric radial basis functions. Appl Numer Math 57 2 (2007) 213-229
    • (2007) Appl Numer Math , vol.57 , Issue.2 , pp. 213-229
    • Jung, J.H.1
  • 27
    • 10644280743 scopus 로고    scopus 로고
    • Computing eigenmodes of elliptic operators using radial basis functions
    • Platte R., and Driscoll T.A. Computing eigenmodes of elliptic operators using radial basis functions. Comput Math Appl 48 (2004) 561-576
    • (2004) Comput Math Appl , vol.48 , pp. 561-576
    • Platte, R.1    Driscoll, T.A.2
  • 28
    • 27544432416 scopus 로고    scopus 로고
    • Radial basis collocation methods for elliptic boundary value problems
    • Hu H.Y., Li Z.C., and Cheng A.H.D. Radial basis collocation methods for elliptic boundary value problems. Comput Math Appl 50 (2005) 289-320
    • (2005) Comput Math Appl , vol.50 , pp. 289-320
    • Hu, H.Y.1    Li, Z.C.2    Cheng, A.H.D.3
  • 29
    • 33847663404 scopus 로고    scopus 로고
    • Solutions to harmonic and biharmonic problems with discontinuous boundary conditions by collocation methods using multiquadrics as basis functions
    • Chantasiriwan S. Solutions to harmonic and biharmonic problems with discontinuous boundary conditions by collocation methods using multiquadrics as basis functions. Int Comm Heat Mass Transfer 34 3 (2007) 313-320
    • (2007) Int Comm Heat Mass Transfer , vol.34 , Issue.3 , pp. 313-320
    • Chantasiriwan, S.1
  • 30
    • 10644233898 scopus 로고    scopus 로고
    • Particular solutions of Laplace's equations on polygons and new models involving mild singularities
    • Li Z.-C., Lu T.-T., Hu H.-Y., and Cheng A.H.-D. Particular solutions of Laplace's equations on polygons and new models involving mild singularities. Eng Anal Boundary Elements 29 (2005) 59-75
    • (2005) Eng Anal Boundary Elements , vol.29 , pp. 59-75
    • Li, Z.-C.1    Lu, T.-T.2    Hu, H.-Y.3    Cheng, A.H.-D.4
  • 32
    • 0027386854 scopus 로고
    • The eddy structure in Stokes flow in a cavity
    • Shankar P.N. The eddy structure in Stokes flow in a cavity. J Fluid Mech 250 (1993) 371-383
    • (1993) J Fluid Mech , vol.250 , pp. 371-383
    • Shankar, P.N.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.