Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Bücher
Zeitschriften
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
MTZ-Fachkongress

Antriebe und Energiesysteme von morgen


Austausch von Automobil- und Energiewirtschaft

Am 14./15. Mai geht es in Chemnitz um die Mobilitätswende durch Elektro- und Wasserstofffahrzeuge.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
Introduction Kapitel lesen Erstes Kapitel lesen

2014 | OriginalPaper | Buchkapitel

3. Different Formulations of the Kansa Method: Domain Discretization

verfasst von : Wen Chen, Zhuo-Jia Fu, C. S. Chen

Erschienen in: Recent Advances in Radial Basis Function Collocation Methods

Verlag: Springer Berlin Heidelberg

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In contrast to the traditional meshed-based methods such as finite difference, finite element, and boundary element methods, the RBF collocation methods are mathematically very simple to implement and are truly free of troublesome mesh generation for high-dimensional problems involving irregular or moving boundary. This chapter introduces the basic procedure of the Kansa method, the very first domain-type RBF collocation method. Following this, several improved formulations of the Kansa method are described, such as the Hermite collocation method, the modified Kansa method, the method of particular solutions, the method of approximate particular solutions, and the localized RBF methods. Numerical demonstrations show the convergence rate and stability of these domain-type RBF collocation methods for several benchmark examples.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel Radial Basis Functions
Nächstes Kapitel Boundary-Type RBF Collocation Methods
Literatur
1.
E.J. Kansa, 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(8–9), 147–161 (1990)MathSciNetCrossRefMATH
2.
E.J. Kansa, Multiquadrics–A scattered data approximation scheme with applications to computational fluid-dynamics–I surface approximations and partial derivative estimates. Comput. Math. Appl. 19(8–9), 127–145 (1990)MathSciNetCrossRefMATH
3.
G.E. Fasshauer, Solving partial differential equations by collocation with radial basis functions. In: Surface Fitting and Multiresolution Methods, ed. by A. Mehaute, C. Rabut, L.L. Schumaker (Vanderbilt University Press, Nashville, 1997), pp. 131–138
4.
A.L. Fedoseyev, M.J. Friedman, E.J. Kansa, Improved multiquadric method for elliptic partial differential equations via PDE collocation on the boundary. Comput. Math. Appl. 43(3–5), 439–455 (2002)MathSciNetCrossRefMATH
5.
C.S. Chen, Y.C. Hon, R.S. Schaback, Radial basis functions with scientific computation. Department of Mathematics, University of Southern Mississippi, Mississippi (2007)
6.
C.S. Chen, A. Karageorghis, Y.S. Smyrlis, The Method of Fundamental Solutions – A Meshless Method (Dynamic Publishers, 2008)
7.
C.S. Chen, C.M. Fan, P.H. Wen The method of particular solutions for solving certain partial differential equations. Numerical Methods for Partial Differential Equations, 28, 506–522 (2012)
8.
S. Chantasiriwan, Investigation of the use of radial basis functions in local collocation method for solving diffusion problems. Int. Commun. Heat Mass Transfer 31(8), 1095–1104 (2004)CrossRef
9.
B. Sarler, R. Vertnik, Meshfree explicit local radial basis function collocation method for diffusion problems. Comput. Math. Appl. 51(8), 1269–1282 (2006)MathSciNetCrossRefMATH
10.
R. Vertnik, B. Sarler, Meshless local radial basis function collocation method for convective-diffusive solid-liquid phase change problems. Int. J. Numer. Meth. Heat Fluid Flow 16(5), 617–640 (2006)MathSciNetCrossRefMATH
11.
E. Divo, A.J. Kassab, An efficient localized radial basis function Meshless method for fluid flow and conjugate heat transfer. J. Heat Transf. Trans. ASME 129(2), 124–136 (2007)CrossRef
12.
B. Sarler, From global to local radial basis function collocation method for transport phenomena. Adv. Meshfree Techniq. 5, 257–282 (2007)MathSciNetCrossRef
13.
G. Kosec, B. Sarler, Local RBF collocation method for Darcy flow. CMES Comput. Model. Eng. Sci. 25(3), 197–207 (2008)
14.
Y. Sanyasiraju, G. Chandhini, Local radial basis function based gridfree scheme for unsteady incompressible viscous flows. J. Comput. Phys. 227(20), 8922–8948 (2008)MathSciNetCrossRefMATH
15.
C.K. Lee, X. Liu, S.C. Fan, Local multiquadric approximation for solving boundary value problems. Comput. Mech. 30, 396–409 (2003)MathSciNetCrossRefMATH
16.
G.M. Yao, Local radial basis function methods for solving partial differential equations. Ph.D. Dissertation, University of Southern Mississippi (2010)
17.
G.M. Yao, J. Kolibal, C.S. Chen, A localized approach for the method of approximate particular solutions. Comput. Math. Appl. 61, 2376–2387 (2011)MathSciNetCrossRefMATH
18.
G.R. Liu, Y.T. Gu, A local radial point interpolation method (LRPIM) for free vibration analyses of 2-D solids. J. Sound Vib. 246(1), 29–46 (2001)CrossRef
19.
J. Wertz, E.J. Kansa, L. Ling, The role of the multiquadric shape parameters in solving elliptic partial differential equations. Comput. Math. Appl. 51(8), 1335–1348 (2006)MathSciNetCrossRefMATH
20.
W. Chen, L.J. Ye, H.G. Sun, Fractional diffusion equations by the Kansa method. Comput. Math. Appl. 59(5), 1614–1620 (2010)MathSciNetCrossRefMATH
21.
M. Kindelan, F. Bernal, P. Gonzalez-Rodriguez, M. Moscoso, Application of the RBF Meshless method to the solution of the radiative transport equation. J. Comput. Phys. 229(5), 1897–1908 (2010)MathSciNetCrossRefMATH
22.
E.J. Kansa, R.C. Aldredge, L. Ling, Numerical simulation of two-dimensional combustion using mesh-free methods. Eng. Anal. Boundary Elem. 33(7), 940–950 (2009)MathSciNetCrossRefMATH
23.
Y. Zhang, K.R. Shao, Y.G. Guo, J.G. Zhu, D.X. Xie, J.D. Lavers, An improved multiquadric collocation method for 3-D electromagnetic problems. IEEE Trans. Magn. 43(4), 1509–1512 (2007)CrossRef
24.
Y. Duan, P.F. Tang, T.Z. Huang, S.J. Lai, Coupling projection domain decomposition method and Kansa’s method in electrostatic problems. Comput. Phys. Commun. 180(2), 209–214 (2009)CrossRefMATH
25.
S. Chantasiriwan, Multiquadric collocation method for time-dependent heat conduction problems with temperature-dependent thermal properties. J. Heat Transf. Trans. ASME 129(2), 109–113 (2007)CrossRef
26.
X. Zhou, Y.C. Hon, K.F. Cheung, A grid-free, nonlinear shallow-water model with moving boundary. Eng. Anal. Boundary Elem. 28(8), 967–973 (2004)CrossRefMATH
27.
A.J.M. Ferreira, C.M.C. Roque, P. Martins, Radial basis functions and higher-order shear deformation theories in the analysis of laminated composite beams and plates. Compos. Struct. 66(1–4), 287–293 (2004)CrossRef
28.
A.J.M. Ferreira, C.M.C. Roque, R.M.N. Jorge, Static and free vibration analysis of composite shells by radial basis functions. Eng. Anal. Boundary Elem. 30(9), 719–733 (2006)CrossRefMATH
29.
C.M.C. Roque, A.J.M. Ferreira, R.M.N. Jorge, A radial basis function approach for the free vibration analysis of functionally graded plates using a refined theory. J. Sound Vib. 300(3–5), 1048–1070 (2007)CrossRef
30.
P.H. Wen, Y.C. Hon, Geometrically nonlinear analysis of Reissner-Mindlin plate by Meshless computation. CMES Comput. Model. Eng. Sci. 21, 177–191 (2007)MathSciNetMATH
31.
H.J. Al-Gahtani, M. Naffa’a, RBF meshless method for large deflection of thin plates with immovable edges. Eng. Anal. Boundary Elem. 33(2), 176–183 (2009)MathSciNetCrossRefMATH
32.
S. Xiang, K.M. Wang, Free vibration analysis of symmetric laminated composite plates by trigonometric shear deformation theory and inverse multiquadric RBF. Thin Walled Struct. 47(3), 304–310 (2009)MathSciNetCrossRef
33.
S. Chantasiriwan, Performance of multiquadric collocation method in solving lid-driven cavity flow problem with low Reynolds number. CMES Comput. Model. Eng. Sci. 15(3), 137–146 (2006)
34.
I. Kovacevic, A. Poredos, B. Sarler, Solving the Stefan problem with the radial basis function collocation mehod. Nume. Heat Transf. Part B Fundament. 44(6), 575–599 (2003)CrossRef
35.
L. Vrankar, E.J. Kansa, L. Ling, F. Runovc, G. Turk, Moving-boundary problems solved by adaptive radial basis functions. Comput. Fluids 39(9), 1480–1490 (2010)MathSciNetCrossRefMATH
36.
Y. Liu, K.M. Liew, Y.C. Hon, X. Zhang, Numerical simulation and analysis of an electroactuated beam using a radial basis function. Smart Mater. Struct. 14(6), 1163–1171 (2005)CrossRef
37.
J. Li, Y. Chen, D. Pepper, Radial basis function method for 1-D and 2-D groundwater contaminant transport modeling. Comput. Mech. 32(1–2), 10–15 (2003)CrossRefMATH
38.
J.C. Li, C.S. Chen, Some observations on unsymmetric radial basis function collocation methods for convection-diffusion problems. Int. J. Numer. Meth. Eng. 57(8), 1085–1094 (2003)CrossRefMATH
39.
B. Sarler, J. Perko, C.S. Chen, Radial basis function collocation method solution of natural convection in porous media. Int. J. Numer. Meth. Heat Fluid Flow 14(2), 187–212 (2004)CrossRefMATH
40.
P.P. Chinchapatnam, K. Djidjeli, P.B. Nair, Unsymmetric and symmetric meshless schemes for the unsteady convection-diffusion equation. Comput. Methods Appl. Mech. Eng. 195(19–22), 2432–2453 (2006)MathSciNetCrossRefMATH
41.
Y.C. Hon, R. Schaback, On unsymmetric collocation by radial basis functions. Appl. Math. Comput. 119(2–3), 177–186 (2001)MathSciNetCrossRefMATH
42.
43.
A. LaRocca, A.H. Rosales, H. Power, Symmetric radial basis function meshless approach for time dependent PDEs. Boundary Elements Xxvi(19), 81–90 (2004)
44.
A. La Rocca, H. Power, V. La Rocca, M. Morale, A meshless approach based upon radial basis function hermite collocation method for predicting the cooling and the freezing times of foods. CMC Comput. Mater. Continua 2(4), 239–250 (2005)
45.
A. La Rocca, A.H. Rosales, H. Power, Radial basis function Hermite collocation approach for the solution of time dependent convection-diffusion problems. Eng. Anal. Boundary Elem. 29(4), 359–370 (2005)CrossRefMATH
46.
A.H. Rosales, A. La Rocca, H. Power, Radial basis function Hermite collocation approach for the numerical simulation of the effect of precipitation inhibitor on the crystallization process of an over-saturated solution. Numer. Methods Partial Differ. Eq. 22(2), 361–380 (2006)CrossRefMATH
47.
M. Naffa, H.J. Al-Gahtani, RBF-based meshless method for large deflection of thin plates. Eng. Anal. Boundary Elem. 31(4), 311–317 (2007)CrossRefMATH
48.
E. Larsson, B. Fornberg, A numerical study of some radial basis function based solution methods for elliptic PDEs. Comput. Math. Appl. 46(5–6), 891–902 (2003)MathSciNetCrossRefMATH
49.
X. Zhang, K.Z. Song, M.W. Lu, X. Liu, Meshless methods based on collocation with radial basis functions. Comput. Mech. 26, 333–343 (2000)CrossRefMATH
50.
W. Chen, New RBF collocation schemes and kernel RBFs with applications. Lect. Notes Comput. Sci. Eng. 26, 75–86 (2002)CrossRef
51.
K.E. Atkinson, The numerical evaluation of particular solutions for Poisson’s equation. IMA J. Numer. Anal. 5, 319–338 (1985)MathSciNetCrossRefMATH
52.
M.A. Golberg, A.S. Muleshkov, C.S. Chen, A.H.D. Cheng, Polynomial particular solutions for certain partial differential operators. Numer. Methods Partial Differ. Eq. 19(1), 112–133 (2003)MathSciNetCrossRefMATH
53.
C.S. Chen, M.A. Golberg, The method of fundamental solutions for potential, Helmholtz and diffusion problems, in Boundary Integral Method-Numerical and Mathematical Aspects, ed. by M.A. Golberg (Computational Mechanics Publications, Southampton, 1998), pp. 103–176
54.
G. Yao, C.H. Tsai, W. Chen, The comparison of three meshless methods using radial basis functions for solving fourth-order partial differential equations. Eng. Anal. Boundary Elem. 34(7), 625–631 (2010)MathSciNetCrossRefMATH
55.
M. Li, W. Chen, C.H. Tsai, A regularization method for the approximate particular solution of nonhomogeneous Cauchy problems of elliptic partial differential equations with variable coefficients. Eng. Anal. Boundary Elem. 36(3), 274–280 (2012)MathSciNetCrossRefMATH
56.
P. Hansen, Regularization tools: a matlab package for analysis and solution of discrete ill-posed problems. Numer. Algor. 6(1), 1–35 (1994)CrossRefMATH
57.
P.A. Ramachandran, Method of fundamental solutions: singular value decomposition analysis. Commun. Numer. Methods Eng. 18(11), 789–801 (2002)CrossRefMATH
58.
T. Wei, Y.C. Hon, L.V. Ling, Method of fundamental solutions with regularization techniques for Cauchy problems of elliptic operators. Eng. Anal. Boundary Elem. 31(4), 373–385 (2007)CrossRefMATH
59.
A. Emdadi, E.J. Kansa, N.A. Libre, M. Rahimian, M. Shekarchi, Stable PDE solution methods for large multiquadric shape parameters. CMES Comput. Model. Eng. Sci. 25(1), 23–41 (2008)MathSciNetMATH
60.
G.E. Fasshauer, Solving differential equations with radial basis functions: multilevel methods and smoothing. Adv. Comput. Math. 11, 139–159 (1999)MathSciNetCrossRefMATH
61.
Y.C. Hon, R.S. Schaback, X. Zhou, An adaptive greedy algorithm for solving large RBF collocation problems. Numer. Algor. 32(1), 13–25 (2003)MathSciNetCrossRefMATH
62.
R.S. Schaback, L. Ling, Stable and convergent unsymmetric meshless collocation methods. SIAM J. Numer. Anal. 46, 1097–1115 (2008)MathSciNetCrossRefMATH
63.
C.S. Huang, C.F. Lee, A.H.D. Cheng, Error estimate, optimal shape factor, and high precision computation of multiquadric collocation method. Eng. Anal. Boundary Elem. 31(7), 614–623 (2007)CrossRefMATH
64.
D. Brown, L. Ling, E. Kansa, J. Levesley, On approximate cardinal preconditioning methods for solving PDEs with radial basis functions. Eng. Anal. Boundary Elem. 29(4), 343–353 (2005)CrossRefMATH
65.
L.V. Ling, E.J. Kansa, A least-squares preconditioner for radial basis functions collocation methods. Adv. Comput. Math. 23(1–2), 31–54 (2005)MathSciNetCrossRefMATH
66.
Y.J. Liu, N. Nishimura, Z.H. Yao, A fast multipole accelerated method of fundamental solutions for potential problems. Eng. Anal. Boundary Elem. 29(11), 1016–1024 (2005)CrossRefMATH
67.
J.C. Carr, R.K. Beatson, J.B. Cherrie, T.J. Mitchell, W.R. Fright, B.C. McCallum, T.R. Evans, Reconstruction and representation of 3D objects with radial basis functions. SIGGRAPH '01 Proceedings of 28th annual conference on computer graphics and interactive techniques, ACM New York, 67–76 (2001)
68.
M. Bebendorf, Hierarchical Matrices: A Means to Efficiently Solve Elliptic Boundary Value Problems (Springer, Berlin, 2008)
69.
J.C. Li, Y.C. Hon, Domain decomposition for radial basis meshless methods. Numer. Methods Partial Differ. Eq. 20(3), 450–462 (2004)MathSciNetCrossRefMATH
70.
E. Divo, A. Kassab, Iterative domain decomposition meshless method modeling of incompressible viscous flows and conjugate heat transfer. Eng. Anal. Boundary Elem. 30(6), 465–478 (2006)CrossRefMATH
71.
H. Adibi, J. Es’haghi, Numerical solution for biharmonic equation using multilevel radial basis functions and domain decomposition methods. Appl. Math. Comput. 186(1), 246–255 (2007)MathSciNetCrossRefMATH
72.
P.P. Chinchapatnam, K. Djidjeli, P.B. Nair, Domain decomposition for time-dependent problems using radial based meshless methods. Numer. Methods Partial Differ. Eq. 23(1), 38–59 (2007)MathSciNetCrossRefMATH
73.
G. Gutierrez, W. Florez, Comparison between global, classical domain decomposition and local, single and double collocation methods based on RBF interpolation for solving convection-diffusion equation. Int. J. Mod. Phys. C 19(11), 1737–1751 (2008)CrossRefMATH
74.
P. Gonzalez-Casanova, J.A. Munoz-Gomez, G. Rodriguez-Gomez, Node adaptive domain decomposition method by radial basis functions. Numer. Methods Partial Differ. Eq. 25(6), 1482–1501 (2009)MathSciNetCrossRefMATH
75.
J.R. Phillips, J. White, A precorrected-FFT method for electrostatic analysis of complicated 3-D structures. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 16(10), 1059–1072 (1997)CrossRef
76.
77.
78.
S.M. Omohundro, Efficient algorithms with neural network behaviour. J. Complex Syst. 1, 273–347 (1987)MathSciNetMATH
79.
G.M. Yao, Z.Y. Yu, A localized meshless approach for modeling spatial-temporal calcium dynamics in ventricular myocytes. Int. J. Numer. Meth. Biomed. Eng. 28(2), 187–204 (2011)
80.
P. Indyk, R. Motwani, Approximate nearest neighbors: towards removing the curse of dimensionality. In: the 30th Annual ACM Symposium on Theory of Computing, 1998, pp. 604–613
81.
A. Guttman, R-trees: a dynamic index structure for spatial searching. In: The International Conference of Management of Data (ACM SIGMOD) (ACM Press, 1984), pp. 47–57
82.
L. Mai-Cao, T. Tran-Cong, A meshless IRBFN-based method for transient problems. CMES Comput. Model. Eng. Sci. 7(2), 149–171 (2005)MathSciNetMATH
83.
N. Mai-Duy, A. Khennane, T. Tran-Cong, Computation of laminated composite plates using integrated radial basis function networks. CMC Comput. Mater. Continua 5(1), 63–77 (2007)
84.
N. Mai-Duy, T. Tran-Cong, A multidomain integrated radial basis function collocation method for elliptic problems. Numer. Methods Partial Differ. Eq. 24, 1301–1320 (2008)MathSciNetCrossRefMATH
85.
N. Mai-Duy, T. Tran-Cong, Compact local integrated-RBF approximations for second-order elliptic differential problems. J. Comput. Phys. 230(12), 4772–4794 (2011)MathSciNetCrossRefMATH
86.
R.H. Chen, Z.M. Wu, Solving hyperbolic conservation laws using multiquadric quasi-interpolation. Numer. Methods Partial Differ. Eq. 22(4), 776–796 (2006)CrossRefMATH
87.
C. Shu, H. Ding, K.S. Yeo, Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Eng. 192, 941–954 (2003)CrossRefMATH
88.
S. Quan, Local RBF-based differential quadrature collocation method for the boundary layer problems. Eng. Anal. Boundary Elem. 34(3), 213–228 (2010)CrossRefMATH
89.
C. Shu, H. Ding, H.Q. Chen, T.G. Wang, An upwind local RBF-DQ method for simulation of inviscid compressible flows. Comput. Methods Appl. Mech. Eng. 194(18–20), 2001–2017 (2005)CrossRefMATH
90.
G.B. Wright, B. Fornberg, Scattered node compact finite difference-type formulas generated from radial basis functions. J. Comput. Phys. 212(1), 99–123 (2006)MathSciNetCrossRefMATH
91.
V. Bayona, M. Moscoso, M. Kindelan, Optimal constant shape parameter for multiquadric based RBF-FD method. J. Comput. Phys. 230(19), 7384–7399 (2011)MathSciNetCrossRefMATH
92.
V. Bayona, M. Moscoso, M. Carretero, M. Kindelan, RBF-FD formulas and convergence properties. J. Comput. Phys. 229(22), 8281–8295 (2010)CrossRefMATH
93.
N. Flyer, B. Fornberg, Radial basis functions: developments and applications to planetary scale flows. Comput. Fluids 46(1), 23–32 (2011)MathSciNetCrossRefMATH
94.
G.B. Wright, N. Flyer, D.A. Yuen, A hybrid radial basis function–pseudospectral method for thermal convection in a 3-D spherical shell. Geochem. Geophys. Geosyst. 11(7), n/a-n/a (2010)
95.
G.R. Liu, L. Yan, J.G. Wang, Y.T. Gu, Point interpolation method based on local residual formulation using radial basis functions. Struct. Eng. Mech. 14(6), 713–732 (2002)CrossRef
96.
J.G. Wang, G.R. Liu, A point interpolation meshless method based on radial basis functions. Int. J. Numer. Meth. Eng. 54(11), 1623–1648 (2002)CrossRefMATH
97.
Y. Liu, Y.C. Hon, K.M. Liew, A meshfree Hermite-type radial point interpolation method for Kirchhoff plate problems. Int. J. Numer. Meth. Eng. 66(7), 1153–1178 (2006)CrossRefMATH
98.
J.-S. Chen, L. Wang, H.-Y. Hu, S.-W. Chi, Subdomain radial basis collocation method for heterogeneous media. Int. J. Numer. Meth. Eng. 80(2), 163–190 (2009)MathSciNetCrossRefMATH
99.
C.H. Tsai, J. Kolibal, M. Li, The golden section search algorithm for finding a good shape parameter for meshless collocation methods. Eng. Anal. Boundary Elem. 34, 738–746 (2010)MathSciNetCrossRefMATH
Metadaten
Titel
Different Formulations of the Kansa Method: Domain Discretization
verfasst von
Wen Chen
Zhuo-Jia Fu
C. S. Chen
Copyright-Jahr
2014
Verlag
Springer Berlin Heidelberg
Buch
Recent Advances in Radial Basis Function Collocation Methods

Print ISBN: 978-3-642-39571-0

Electronic ISBN: 978-3-642-39572-7

Copyright-Jahr: 2014

DOI
https://doi.org/10.1007/978-3-642-39572-7_3

Premium Partner

    Bildnachweise