nach oben

Cluster Computing

Erschienen in:

31.01.2018

The simulation by using bivariate splines for solving two dimensional non-classical diffusion problem

verfasst von: Kai Qu, Jiawei Xuan, Ning Wang, Mengdi Zhang

Erschienen in: Cluster Computing | Sonderheft 4/2019

Einloggen

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

search-config

KI-gestützte Suche

Aus

Abstract

In this paper, a high order method using bivariate spline finite elements on domains defined by NURBS is proposed for solving two dimensional non-classical diffusion problem. Bivariate spline proper subspace of \(S_4^{2,3} (\Delta _{mn}^{(2)} )\) satisfying homogeneous boundary conditions on type-2 triangulations and quadratic B-spline interpolating boundary functions are primarily constructed. Two examples are solved to assess the accuracy of the method. The simulation obtained, indicates that spline method is reliable and yields results compatible with the exact solutions and consistent with other existing numerical methods.

Vorheriger Artikel Intelligence algorithm for optimization design of the low wind speed airfoil for wind turbine

Nächster Artikel Adaptive multiple classifiers fusion for inertial sensor based human activity recognition

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

Li, Z., Jieqing, T., Xianyu, G., Guo, Z.: Generalized B-splines’ geometric iterative fitting method with mutually different weights. J. Comput. Appl. Math. 329, 331–343 (2018)MathSciNetMATHCrossRef

Mingzeng, L., Baojun, L., Qingjie, G., Zhu Chungang, H., Ping, S.Y.: Progressive iterative approximation for regularized least square bivariate B-spline surface fitting. J. Comput. Appl. Math. 327, 175–187 (2018)MathSciNetMATHCrossRef

Christopher, P.: B-splines collocation for plate bending eigenanalysis. J. Mech. Mater. Struct. 12(4), 353–371 (2017)MathSciNetCrossRef

Alaattin, E., Orkun, T.: Numerical solution of time fractional Schrödinger equation by using quadratic B-spline finite elements. Ann. Math. Sil. 31(1), 83–98 (2017)MathSciNetMATH

Jalil, R., Sanaz, J.: Collocation method based on modified cubic B-spline for option pricing models. Math. Commun. 22(1), 89–102 (2017)MathSciNetMATH

Kai, Q., Wang, Z., Jiang, B.: A finite element method by using bivariate splines for one dimensional heat equations. J. Inf. Comput. Sci. 10(12), 3659–3666 (2013)CrossRef

Ole, C.: Goh Say Song: From dual pairs of Gabor frames to dual pairs of wavelet frames and vice versa. Appl. Comput. Harmon. Anal. 36(2), 198–214 (2014)MathSciNetMATHCrossRef

Annalisa, B., Carlotta, G.: Adaptive isogeometric methods with hierarchical splines: optimality and convergence rates. Math. Models Methods Appl. Sci. 27(14), 2781–2802 (2017)MathSciNetMATHCrossRef

Annalisa, B., Garau, E.M.: Refinable spaces and local approximation estimates for hierarchical splines. IMA J. Numer. Anal. 37(3), 1125–1149 (2017)MathSciNetMATH

10.

Annalisa, B., Carlotta, G.: Adaptive isogeometric methods with hierarchical splines: error estimator and convergence. Math. Models Methods Appl. Sci. 26(1), 1–25 (2016)MathSciNetMATHCrossRef

11.

Andrea, B., Annalisa, B., Giancarlo, S.: Characterization of analysis-suitable T-splines. Comput. Aided Geom. Design 39, 17–49 (2015)MathSciNetMATHCrossRef

12.

Annalisa, B., Vázquez, R.H., Sangalli, G., Beirão da Veiga, L.: Approximation estimates for isogeometric spaces in multipatch geometries. Numer. Methods Partial Differ. Equ. 31(2), 422–438 (2015)MathSciNetMATHCrossRef

13.

Deepesh, T., Hendrik, S., Hughes Thomas, J.R.: Smooth cubic spline spaces on unstructured quadrilateral meshes with particular emphasis on extraordinary points: geometric design and isogeometric analysis considerations. Comput. Methods Appl. Mech. Eng. 327, 411–458 (2017)MathSciNetCrossRef

14.

Deepesh, T., Hendrik, S., Hiemstra René, R., Hughes Thomas, J.R.: Multi-degree smooth polar splines: a framework for geometric modeling and isogeometric analysis. Comput. Methods Appl. Mech. Eng. 316, 1005–1061 (2017)MathSciNetCrossRef

15.

Kamensky, D., Hsu, M.-C., Yu, Y., Evans, J.A., Sacks, M.S., Hughes, T.J.R.: Immersogeometric cardiovascular fluid-structure interaction analysis with divergence-conforming B-splines. Comput. Methods Appl. Mech. Eng. 314, 408–472 (2017)MathSciNetCrossRef

16.

Kruse, R., Nguyen-Thanh, N., De Lorenzis, L., Hughes, T.J.R.: Isogeometric collocation for large deformation elasticity and frictional contact problems. Comput. Methods Appl. Mech. Eng. 2296, 73–112 (2015)MathSciNetMATHCrossRef

17.

Kanca, F.: The inverse problem of the heat equation with periodic boundary and integral over determination conditions. J. Inequal. Appl. 18, 1–9 (2013)MathSciNetMATH

18.

Martín, V.J., Queiruga, D.A., Encinas, A.H.: Numerical algorithms for diffusion-reaction problems with non-classical conditions. Appl. Math. Comput. 218(9), 5487–5495 (2012)MathSciNetMATH

19.

Dehghan, M.: Efficient techniques for the second-order parabolic equation subject to nonlocal specifications. Appl. Numer. Math. 52, 39–62 (2005)MathSciNetMATHCrossRef

20.

Martin-Vaquero, J., Vigo-Aguiar, J.: A note on efficient techniques for the second-order parabolic equation subject to non-local conditions. Appl. Numer. Math. 59(6), 1258–1264 (2009)MathSciNetMATHCrossRef

21.

Khaliq, A.Q.M., Martín, V.J., Wade, B.A., Yousuf, M.: Smoothing schemes for reaction-diffusion systems with nonsmooth data. J. Comput. Appl. Math. 223(1), 374–386 (2009)MathSciNetMATHCrossRef

22.

Li, X., Wu, B.: New algorithm for non-classical parabolic problems based on the reproducing kernel method. Math. Sci. 7, 4–8 (2013)MATHCrossRef

23.

Dehghan, M.: On the numerical solution of the diffusion equation with a nonlocal boundary condition. Math. Probl. Eng. 2, 81–92 (2003)MathSciNetMATHCrossRef

24.

Dehghan, M.: A computational study of the one-dimensional parabolic equation subject to non-classical boundary specifications. Numer. Methods Partial Differ. Equ. 22, 220–257 (2006)MATHCrossRef

25.

Tatari, M., Dehghan, M.: On the solution of the non-local parabolic partial differential equations via radial basis functions. Appl. Math. Model. 33, 1729–1738 (2009)MathSciNetMATHCrossRef

26.

Golbabai, A., Javidi, M.: A numerical solution for non-classical parabolic problem based on Chebyshev spectral collocation method. Appl. Math. Comput. 190, 179–185 (2007)MathSciNetMATH

27.

Raunak, B., Charbel, F., Radek, T.: A discontinuous Galerkin method with Lagrange multipliers for spatially-dependent advection-diffusion problems. Comput. Methods Appl. Mech. Eng. 327, 93–117 (2017)MathSciNetMATHCrossRef

28.

Abbasbandy, S., Shirzadi, A.: MLPG method for two-dimensional diffusion equation with Neumann’s and non-classical boundary conditions. Appl. Numer. Math. 61(2), 170–180 (2011)MathSciNetMATHCrossRef

29.

Wang, R.H., Li, C.J.: Bivariate quartic spline spaces and quasi-interpolation operators. J. Comput. Appl. Math. 190, 325–338 (2006)MathSciNetMATHCrossRef

Titel: The simulation by using bivariate splines for solving two dimensional non-classical diffusion problem
verfasst von: Kai Qu
Jiawei Xuan
Ning Wang
Mengdi Zhang
Publikationsdatum: 31.01.2018
Verlag: Springer US
Erschienen in: Cluster Computing / Ausgabe Sonderheft 4/2019
Print ISSN: 1386-7857
Elektronische ISSN: 1573-7543
DOI: https://doi.org/10.1007/s10586-017-1636-3

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

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

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Weitere Artikel der Sonderheft 4/2019

A conceptual model of profitability determinants in online deal promotions for online-to-offline restaurant merchants

Fixed-point twin support vector machine

Performance of image transmission over MC-CDMA based on super resolution technique

Priority based prediction mechanism for ranking providers in federated cloud architecture

Concepts recommendation for searching scientific papers

Research on discontinuous guidance and hardware-in-the-loop simulation for unmanned underwater vehicle