메뉴 건너뛰기




Volumn 88, Issue 3, 2012, Pages 183-209

Numerical investigation on Direct MLPG for 2D and 3D potential problems

Author keywords

Generalized moving least squares; Meshless methods; Poisson problem; Radial basis functions; Tensor product functions

Indexed keywords

GENERALIZED MOVING LEAST SQUARES; MESH-LESS METHODS; POISSON PROBLEM; RADIAL BASIS FUNCTIONS; TENSOR PRODUCTS;

EID: 84872102142     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (29)

References (36)
  • 2
    • 0042964833 scopus 로고    scopus 로고
    • The meshless local Petrov-Galerkin (MLPG) method: A simple & less-costly alternative to the finite element and boundary element methods
    • Atluri, S. N.; Zhu, T. (2002): The meshless local Petrov-Galerkin (MLPG) method: A simple & less-costly alternative to the finite element methods. Computer Modeling in Engineering and Sciences, vol. 3, no. 1, pp. 11-51. (Pubitemid 135695145)
    • (2002) CMES - Computer Modeling in Engineering and Sciences , vol.3 , Issue.1 , pp. 11-51
    • Atluri, S.N.1    Shen, S.2
  • 3
    • 84872108473 scopus 로고    scopus 로고
    • Survey of meshless and generalized finite element methods: A unified approach
    • One Liberty Center, 875 North Randolph Street Suite 1425, Arlington, VA, 22203-1995, 2005
    • Babuska, I.; Banerjee, U.; Osborn, J. E. (2005): Survey of meshless and generalized finite element methods: A unified approach. Technical report, Office of Naval Research, One Liberty Center, 875 North Randolph Street Suite 1425, Arlington, VA, 22203-1995, 2005.
    • (2005) Technical Report, Office of Naval Research
    • Babuska, I.1    Banerjee, U.2    Osborn, J.E.3
  • 6
    • 3042799255 scopus 로고    scopus 로고
    • volume 12 of Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, Cambridge
    • Buhmann, M. D. (2003): Radial Basis Functions: Theory and Implementation, volume 12 of Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, Cambridge.
    • (2003) Radial Basis Functions: Theory and Implementation
    • Buhmann, M.D.1
  • 7
    • 0036608933 scopus 로고    scopus 로고
    • A truly meshless Galerkin method based on a moving least squares quadrature
    • DOI 10.1002/cnm.503
    • Duflot, M.; Nguyen-Dang, H. (2002): A truly meshless method based on a moving least squares quadrature. Commun. Numer. Methods Eng., vol. 18, pp. 441-449. (Pubitemid 34718546)
    • (2002) Communications in Numerical Methods in Engineering , vol.18 , Issue.6 , pp. 441-449
    • Duflot, M.1    Nguyen-Dang, H.2
  • 8
    • 85115723184 scopus 로고    scopus 로고
    • volume 6 of Interdisciplinary Mathematical Sciences. World Scientific Publishing Co., pub-WORLD-SCI:adr. With 1 CD-ROM (Windows, Macintosh and UNIX)
    • Fasshauer, G. E. (2007): Meshfree approximation methods with MATLAB, volume 6 of Interdisciplinary Mathematical Sciences. World Scientific Publishing Co., pub-WORLD-SCI:adr. With 1 CD-ROM (Windows, Macintosh and UNIX).
    • (2007) Meshfree Approximation Methods with MATLAB
    • Fasshauer, G.E.1
  • 9
    • 84857500034 scopus 로고    scopus 로고
    • Shifted FSAI preconditioner for the efficient parallel solution of non-linear groundwater flow models
    • Ferronato, M.; Janna, C.; Pini, G. (2012): Shifted FSAI preconditioner for the efficient parallel solution of non-linear groundwater flow models. International Journal for Numerical Methods in Engineering, vol. 89, pp. 1707-1719.
    • (2012) International Journal for Numerical Methods in Engineering , vol.89 , pp. 1707-1719
    • Ferronato, M.1    Janna, C.2    Pini, G.3
  • 11
    • 0002020770 scopus 로고
    • On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals
    • Halton, J. H. (1960): On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numer. Math., vol. 2, pp. 84-90.
    • (1960) Numer. Math. , vol.2 , pp. 84-90
    • Halton, J.H.1
  • 12
    • 0002497330 scopus 로고
    • The incomplete Cholesky-conjugate gradient method for the iterative solution of systems of linear equations
    • Kershaw, D. S. (1978): The incomplete Cholesky-conjugate gradient method for the iterative solution of systems of linear equations. J. Comp. Phys., vol. 26, pp. 43-65.
    • (1978) J. Comp. Phys. , vol.26 , pp. 43-65
    • Kershaw, D.S.1
  • 13
    • 84966237423 scopus 로고
    • Surfaces generated by moving least squares methods
    • Lancaster, P.; Salkauskas, K. (1981): Surfaces generated by moving least squares methods. Math. Comp., vol. 37, no. 155, pp. 141-158.
    • (1981) Math. Comp. , vol.37 , Issue.155 , pp. 141-158
    • Lancaster, P.1    Salkauskas, K.2
  • 14
    • 0032381035 scopus 로고    scopus 로고
    • The approximation power of moving least-squares
    • Levin, D. (1998): The approximation power of moving least-squares. Math. Comp., vol. 67, no. 234, pp. 1517-1531. (Pubitemid 128383317)
    • (1998) Mathematics of Computation , vol.67 , Issue.224 , pp. 1517-1531
    • Levin, D.1
  • 15
    • 84872102374 scopus 로고    scopus 로고
    • 2012. Last accessed: September 7, 2012
    • Li, S.; Demmel, J.; Gilbert, J.; Grigori, L. (2012): SuperLU. http: //crd-legacy.lbl.gov/~xiaoye/SuperLU/, 2012. Last accessed: September 7, 2012.
    • SuperLU. , vol.2012
    • Li, S.1    Demmel, J.2    Gilbert, J.3    Grigori, L.4
  • 17
    • 0028400170 scopus 로고
    • A new implementation of the element free Galerkin method
    • Lu, Y. Y.; Belytschko, T.; Gu, L. (1994): A new implementation of the element free Galerkin method. Comp. Methods App. Mech. Eng., vol. 113, pp. 397-414.
    • (1994) Comp. Methods App. Mech. Eng. , vol.113 , pp. 397-414
    • Lu, Y.Y.1    Belytschko, T.2    Gu, L.3
  • 18
    • 71649107095 scopus 로고    scopus 로고
    • Product Gauss quadrature rules vs cubature rules in the meshless local Petrov-Galerkin method
    • Mazzia, A.; Pini, G. (2010): Product Gauss quadrature rules vs cubature rules in the meshless local Petrov-Galerkin method. Journal of Complexity, vol. 26, pp. 82-101.
    • (2010) Journal of Complexity , vol.26 , pp. 82-101
    • Mazzia, A.1    Pini, G.2
  • 19
    • 35248878498 scopus 로고    scopus 로고
    • Comparison of 3D flow fields arising in mixed and standard unstructured finite elements
    • et al., P. S.(Ed), volume 2657 of Lecture Notes in Computer Sciences, Berlin. Springer-Verlag
    • Mazzia, A.; Pini, G.; Putti, M.; Sartoretto, F. (2003): Comparison of 3D flow fields arising in mixed and standard unstructured finite elements. In et al., P. S.(Ed): Computational Science - ICCS 2003, volume 2657 of Lecture Notes in Computer Sciences, pp. 560-567, Berlin. Springer-Verlag.
    • (2003) Computational Science - ICCS 2003 , pp. 560-567
    • Mazzia, A.1    Pini, G.2    Putti, M.3    Sartoretto, F.4
  • 21
    • 79851499691 scopus 로고    scopus 로고
    • Meshless solution of potential problems by combining radial basis functions and tensor product ones
    • Mazzia, A.; Sartoretto, F. (2010): Meshless solution of potential problems by combining radial basis functions and tensor product ones. Computer Modeling in Engineering & Sciences, vol. 68, no. 1, pp. 95-112.
    • (2010) Computer Modeling in Engineering & Sciences , vol.68 , Issue.1 , pp. 95-112
    • Mazzia, A.1    Sartoretto, F.2
  • 24
    • 84863955808 scopus 로고    scopus 로고
    • On generalized moving least squares and diffuse derivatives
    • Mirzaei, D.; Schaback, R.; Dehghan, M. (2011): On generalized moving least squares and diffuse derivatives. IMA Journal of Numerical Analysis, vol. 32, no. 3, pp. 983-1000.
    • (2011) IMA Journal of Numerical Analysis , vol.32 , Issue.3 , pp. 983-1000
    • Mirzaei, D.1    Schaback, R.2    Dehghan, M.3
  • 26
    • 2442521260 scopus 로고    scopus 로고
    • Meshless local Petrov-Galerkin method and its application to electromagnetic field computations
    • Ni, G.; Ho, S. L.; Yang, S.; Ni, P. (2004): Meshless local Petrov-Galerkin method and its application to electromagnetic field computations. International Journal of Applied Electromagnetics and Mechanics, vol. 19, no. 1, pp. 111-117.
    • (2004) International Journal of Applied Electromagnetics and Mechanics , vol.19 , Issue.1 , pp. 111-117
    • Ni, G.1    Ho, S.L.2    Yang, S.3    Ni, P.4
  • 27
    • 84872102108 scopus 로고    scopus 로고
    • Last accessed: September 7, 2012
    • PARDISO solver project. http://www.pardiso-project.org/, 2012. Last accessed: September 7, 2012.
    • (2012)
  • 28
    • 84985399736 scopus 로고
    • Preconditioned iterative algorithms for large sparse unsymmetric problems
    • Pini, G.; Zilli, G. (1989): Preconditioned iterative algorithms for large sparse unsymmetric problems. Numerical Methods for Partial Differential Equations, vol. 5, pp. 107-120.
    • (1989) Numerical Methods for Partial Differential Equations , vol.5 , pp. 107-120
    • Pini, G.1    Zilli, G.2
  • 29
    • 44249108544 scopus 로고    scopus 로고
    • Meshless solution of a diffusion equation with parameter optimization and error analysis
    • DOI 10.1016/j.enganabound.2007.10.002, PII S0955799707001622
    • Sterk, M.; Trobec, R. (2008): Meshless solution of a diffusion equation with parameter optimization and error analysis. Engineering Analysis with Boundary Elements, vol. 32, pp. 567-577. (Pubitemid 351726443)
    • (2008) Engineering Analysis with Boundary Elements , vol.32 , Issue.7 , pp. 567-577
    • Sterk, M.1    Trobec, R.2
  • 31
    • 44349097640 scopus 로고    scopus 로고
    • Meshless numerical method based on tensor product
    • Sun, H.;Wang, Y.; Miao, Y. (2008): Meshless numerical method based on tensor product. Front. Archit. Civ. Eng. China, vol. 2, no. 2, pp. 166-171.
    • (2008) Front. Archit. Civ. Eng. China , vol.2 , Issue.2 , pp. 166-171
    • Sun, H.1    Wang, Y.2    Miao, Y.3
  • 32
    • 0000005482 scopus 로고
    • Bi-CGSTAB: A fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems
    • van der Vorst, H. A. (1992): Bi-CGSTAB: A fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., vol. 13, pp. 631-644.
    • (1992) SIAM J. Sci. Stat. Comput. , vol.13 , pp. 631-644
    • Van Der Vorst, H.A.1
  • 33
    • 0035127997 scopus 로고    scopus 로고
    • Hierarchical enrichment for bridging scales and mesh-free boundary conditions
    • DOI 10.1002/1097-0207(20010130)50:3<507::AID-NME33>3.0.CO;2-B
    • Wagner, G. J.; Liu, W. K. (2001): Hierarchical enrichment for bridging scales and mesh-free boundary conditions. Int. J. Numer. Methods Eng., vol. 50, no. 3, pp. 507-524. (Pubitemid 32138354)
    • (2001) International Journal for Numerical Methods in Engineering , vol.50 , Issue.3 , pp. 507-524
    • Wagner, G.J.1    Liu, W.K.2
  • 34
    • 33845792142 scopus 로고    scopus 로고
    • A general meshsize fourth-order compact difference discretization scheme for 3D Poisson equation
    • DOI 10.1016/j.amc.2006.06.028, PII S009630030600614X
    • Wang, J.; Zhong, W.; Zhang, J. (2006): A general meshsize fourth-order compact difference discretization scheme for 3D Poisson equation. Applied Mathematics and Computation, vol. 183, no. 2, pp. 804-812. (Pubitemid 46014633)
    • (2006) Applied Mathematics and Computation , vol.183 , Issue.2 , pp. 804-812
    • Wang, J.1    Zhong, W.2    Zhang, J.3
  • 35
    • 0037196181 scopus 로고    scopus 로고
    • Essential boundary condition enforcement in meshless methods: Boundary flux collocation method
    • DOI 10.1002/nme.267
    • Wu, C.-K. C.; Plesha, M. E. (2002): Essential boundary condition enforcement in meshless methods: boundary flux collocation method. Int. J. Numer. Meth. Engng., vol. 53, pp. 499-514. (Pubitemid 34039611)
    • (2002) International Journal for Numerical Methods in Engineering , vol.53 , Issue.3 , pp. 499-514
    • Wu, C.-K.C.1    Plesha, M.E.2
  • 36
    • 1542434257 scopus 로고    scopus 로고
    • Meshless analysis of potential problems in three dimensions with the hybrid boundary node method
    • Zhang, J.; Tanaka, M.; Endo, M. (2004): Meshless analysis of potential problems in three dimensions with the hybrid boundary node method. International Journal for Numerical Methods in Engineering., vol. 59, pp. 1147-1166. (Pubitemid 38335646)
    • (2004) International Journal for Numerical Methods in Engineering , vol.59 , Issue.9 , pp. 1147-1166
    • Zhang, J.1    Tanaka, M.2    Matsumoto, T.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.