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
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Computing and Visualization in Science
Erschienen in: Computing and Visualization in Science 6/2018

19.02.2018 | Original Article

Comparison of two local discontinuous Galerkin formulations for the subjective surfaces problem

verfasst von: Vadym Aizinger, Leon Bungert, Michael Fried

Erschienen in: Computing and Visualization in Science | Ausgabe 6/2018

Einloggen

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

search-config
loading …

Abstract

Based on the local discontinuous Galerkin method, two substantially different mixed formulations for the subjective surfaces problem are compared using a number of numerical tests of various types. The work also performs the energy stability analysis for both schemes.
Nächster Artikel Virtual reality in advanced medical immersive imaging: a workflow for introducing virtual reality as a supporting tool in medical imaging

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
Literatur
1.
Aizinger, V.: A geometry independent slope limiter for the discontinuous Galerkin method. In: Krause, E., Shokin, Y., Resch, M., Kröner, D., Shokina, N. (eds.) Computational Science and High Performance Computing IV, Volume 115 of Notes on Numerical Fluid Mechanics and Multidisciplinary Design, pp. 207–217. Springer, Berlin (2011)
2.
Aizinger, V., Dawson, C.: The local discontinuous Galerkin method for three-dimensional shallow water flow. Comput. Methods Appl. Mech. Eng. 196(4), 734746 (2007)MathSciNetMATH
3.
Aizinger, V., Kosik, A., Kuzmin, D., Reuter, B.: Anisotropic slope limiting for discontinuous Galerkin methods. Int. J. Numer. Methods Fluids 84(9), 543565 (2017)MathSciNetCrossRef
4.
Aizinger, V., Rupp, A., Schütz, J., Knabner, P.: Analysis of a mixed discontinuous Galerkin method for instationary Darcy flow. Comput. Geosci. 22(1), 179–194 (2018)MathSciNetCrossRef
5.
Arnold, D.N., Brezzi, F., Cockburn, B., Marini, L.D.: Analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39, 1749–1779 (2002)MathSciNetMATHCrossRef
6.
7.
Belhachmi, Z., Bernardi, C., Deparis, S.: Weighted Clément operator and application to the finite element discretization of the axisymmetric Stokes problem. Numer. Math. 105(2), 217–247 (2006)MathSciNetMATHCrossRef
8.
Bungert, L., Aizinger, V., Fried, M.: A discontinuous Galerkin method for the subjective surfaces problem. J. Math. Imaging Vis. 58(1), 147–161 (2017)CrossRef
9.
Caselles, V., Kimmel, R., Sapiro, G.: Geodesic active contours. Int. J. Comput. Vis. 22(1), 61–79 (1997)MATHCrossRef
10.
Chan, T.F., Moelich, M., Sandberg, B.: Some recent developments in variational image segmentation. In: Tai, X.-C., Lie, K.-A., Chan, T.F., Osher, S. (eds.) Image Processing Based on Partial Differential Equations, pp. 175–210. Springer, New York (2007)CrossRef
11.
Chan, T.F., Sandberg, B., Vese, L.A.: Active contours without edges for vector-valued images. J. Vis. Commun. Image Represent. 11(2), 130–141 (2000)CrossRef
12.
Chan, T.F., Vese, L.A.: Active contours without edges. IEEE Trans. Image Process. 10(2), 266–277 (2001)MATHCrossRef
13.
Cockburn, B., Dawson, C.: Some extensions of the local discontinuous Galerkin method for convection-diffusion equations in multidimensions. In: Whiteman, J. (eds.) Proceedings of the 10th Conference on the Mathematics of Finite Elements and Applications, pp. 225–238. Elsevier, Amsterdam (2000)
14.
Cockburn, B., Shu, C.: The local discontinuous Galerkin method for time-dependent convection-diffusion systems. SIAM J. Numer. Anal. 35(6), 2440–2463 (1998)MathSciNetMATHCrossRef
15.
Corsaro, S., Mikula, K., Sarti, A., Sgallari, F.: Semi-implicit covolume method in 3D image segmentation. SIAM J. Sci. Comput. 28, 2248–2265 (2006)MathSciNetMATHCrossRef
16.
Feng, X., Li, Y.: Analysis of symmetric interior penalty discontinuous Galerkin methods for the Allen–Cahn equation and the mean curvature flow. IMA J. Numer. Anal. 35, 1622–1651 (2014)MathSciNetMATHCrossRef
17.
18.
Frank, F., Reuter, B., Aizinger, V., Knabner, P.: FESTUNG: a MATLAB/GNU Octave toolbox for the discontinuous Galerkin method, part I—diffusion operator. Comput. Math. Appl. 70(1), 11–46 (2015)MathSciNetMATHCrossRef
19.
Fried, M.: Berechnung des Krmmungsflusses von Niveauflächen (in German). Master’s thesis, University of Freiburg (1993)
20.
Fried, M.: Multichannel image segmentation using adaptive finite elements. Comput. Vis. Sci. 12(3), 125–135 (2009)MathSciNetCrossRef
21.
Fried, M., Mikula, K.: Efficient subjective surfaces segmentation by adaptive finite elements. In: Lecture Presented at the IMI International Workshop on Computational Photography and Aesthetics, 12 (2009)
22.
23.
24.
Jaust, A., Reuter, B., Aizinger, V., Schütz, J., Knabner, P.: FESTUNG: a MATLAB/GNU Octave toolbox for the discontinuous Galerkin method, part III—hybridized discontinuous Galerkin (HDG) formulation. Submitted to Computers & Mathematics with Applications (2018)
25.
26.
Karasözen, B., Filibelioğlu, A.S., Uzunca, M.: Energy stable discontinuous Galerkin finite element method for the Allen–Cahn equation. arXiv preprint arXiv:​1409.​3997 (2014)
27.
Kass, M., Witkin, A., Terzopoulos, D.: Snakes: active contour models. Int. J. Comput. Vis. 1(4), 321–331 (1988)MATHCrossRef
28.
Kuzmin, D.: A vertex-based hierarchical slope limiter for adaptive discontinuous Galerkin methods. J. Comput. Appl. Math. 233(12), 3077–3085 (2010). Finite Element Methods in Engineering and Science (FEMTEC 2009)
29.
Mikula, K., Peyriéras, N., Remešíková, M., Sarti, A.: 3D embryogenesis image segmentation by the generalized subjective surface method using the finite volume technique. In: Eymard, R., Hérard, J.-M. (eds.) Finite Volumes for Complex Applications V, pp. 585–592. Wiley, New York (2008)
30.
Mikula, K., Sarti, A.: Parallel co-volume subjective surface method for 3D medical image segmentation. In: Suri, J.S., Farag, A.A. (eds.) Deformable Models, Topics in Biomedical Engineering. International Book Series, pp. 123–160. Springer, New York (2007)
31.
Mikula, K., Sarti, A., Sgallari, F.: Co-volume level set method in subjective surface based medical image segmentation. In: Suri, J.S., Wilson, D.L., Laxminarayan, S. (eds.) Handbook of Biomedical Image Analysis, pp. 583–626. Springer, New York (2005)CrossRef
32.
Mirabito, C., Dawson, C., Aizinger, V.: An a priori error estimate for the local discontinuous Galerkin method applied to two-dimensional shallow water and morphodynamic flow. Numer. Methods Partial Differ. Equ. 31(2), 397–421 (2015)MathSciNetMATHCrossRef
33.
Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Commun. Pure Appl. Math. 42(5), 577–685 (1989)MathSciNetMATHCrossRef
34.
Osher, S., Fedkiw, R.: Level Set Methods and Dynamic Implicit Surfaces (Applied Mathematical Sciences), 2003 Edition. Springer, New York (2002)
35.
Reed, H., Hill, T.R.: Triangular mesh methods for the neutron transport equation. Technical Report LA-UR-73-479, Los Alamos Scientific Laboratory, NM (1973)
36.
Reuter, B., Aizinger, V., Wieland, M., Frank, F., Knabner, P.: FESTUNG: a MATLAB/GNU Octave toolbox for the discontinuous Galerkin method, part II—advection operator and slope limiting. Comput. Math. Appl. 72(7), 1896–1925 (2016)MathSciNetMATHCrossRef
37.
Sapiro, G.: Geometric Partial Differential Equations and Image Analysis, 1st edn. Cambridge University Press, Cambridge (2001)MATHCrossRef
38.
Sarti, A., Citti, G.: Subjective surfaces and riemannian mean curvature flow graphs. Acta Math. Univ. Comen. 70, 85–104 (2001)MathSciNetMATH
39.
Sarti, A., Malladi, R., Sethian, J.A.: Subjective surfaces: a method for completing missing boundaries. Proc. Natl. Acad. Sci. 97(12), 6258–6263 (2000)MathSciNetMATHCrossRef
40.
Sarti, A., Malladi, R., Sethian, J.A.: Subjective surfaces: a geometric model for boundary completition. Int. J. Comput. Vis. 46(3), 201–221 (2002)MATHCrossRef
41.
Sethian, J.A.: Numerical algorithms for propagating interfaces: Hamilton–Jacobi equations and conservation laws. J. Differ. Geom. 31(1), 131–161 (1990)MathSciNetMATHCrossRef
42.
Sethian, J.A.: Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science, 2nd edn. Cambridge University Press, Cambridge (1999)MATH
43.
Xia, Y., Xu, Y., Shu, C.-W.: Local discontinuous Galerkin methods for the Cahn–Hilliard type equations. J. Comput. Phys. 227(1), 472–491 (2007)MathSciNetMATHCrossRef
44.
Xia, Y., Xu, Y., Shu, C.-W.: Application of the local discontinuous Galerkin method for the Allen–Cahn/Cahn–Hilliard system. Commun. Comput. Phys 5, 821–835 (2009)MathSciNetMATH
45.
Xu, Y., Shu, C.-W.: Local discontinuous Galerkin method for surface diffusion and Willmore flow of graphs. J. Sci. Comput. 40(1–3), 375–390 (2009)MathSciNetMATHCrossRef
Metadaten
Titel
Comparison of two local discontinuous Galerkin formulations for the subjective surfaces problem
verfasst von
Vadym Aizinger
Leon Bungert
Michael Fried
Publikationsdatum
19.02.2018
Verlag
Springer Berlin Heidelberg
Erschienen in
Computing and Visualization in Science / Ausgabe 6/2018
Print ISSN: 1432-9360
Elektronische ISSN: 1433-0369
DOI
https://doi.org/10.1007/s00791-018-0291-4