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2013 | 23 | 4 | 839-853
Tytuł artykułu

Using a graph grammar system in the finite element method

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The paper presents a system of Composite Graph Grammars (CGGs) modelling adaptive two dimensional hp Finite Element Method (hp-FEM) algorithms with rectangular finite elements. A computational mesh is represented by a composite graph. The operations performed over the mesh are defined by the graph grammar rules. The CGG system contains different graph grammars defining different kinds of rules of mesh transformations. These grammars allow one to generate the initial mesh, assign values to element nodes and perform h- and p-adaptations. The CGG system is illustrated with an example from the domain of geophysics.
Rocznik
Tom
23
Numer
4
Strony
839-853
Opis fizyczny
Daty
wydano
2013
otrzymano
2013-02-20
poprawiono
2013-07-10
Twórcy
  • Department of Physics, Astronomy and Applied Computer Science, Jagiellonian University, ul. Reymonta 4, 30-059 Kraków, Poland
  • Department of Physics, Astronomy and Applied Computer Science, Jagiellonian University, ul. Reymonta 4, 30-059 Kraków, Poland
  • Department of Computer Science, AGH University of Science and Technology, al. A. Mickiewicza 30, 30-059 Kraków, Poland
autor
  • Department of Physics, Astronomy and Applied Computer Science, Jagiellonian University, ul. Reymonta 4, 30-059 Kraków, Poland
Bibliografia
  • Albers, B., Savidis, S.A., Taşan, E., von Estorff, O. and Gehlken, M. (2012). BEM and FEM results of displacements in a poroelastic column, International Journal of Applied Mathematics and Computer Science 22(4): 883-896, DOI: 10.2478/v10006-012-0065-y.
  • Barboteu, M., Bartosz, K. and Kalita, P. (2013). An analytical and numerical approach to a bilateral contact problem with nonmonotone friction, International Journal of Applied Mathematics and Computer Science 23(2): 263-276, DOI: 10.2478/amcs-2013-0020.
  • Csuhaj-Varjú, E. (2004). Grammar systems: A short survey, Proceedings of Grammar Systems Week 2004, Budapest, Hungary, pp. 141-157.
  • Csuhaj-Varjú, E., Dassow, J., Kelemen, J. and Paun, G. (1994). Grammar Systems. A Grammatical Approach to Distribution and Cooperation, Topics in Computer Mathematics 8, Gordon and Breach Science Publishers, Yverdon.
  • Csuhaj-Varjú, E., Dassow, J. and Paun, G. (1993). Dynamically controlled cooperating/distributed grammar systems, Information Sciences 69(1-2): 1-25.
  • Demkowicz, L. (2006). Computing with hp-Adaptive Finite Elements, Vol. I: One and Two Dimensional Elliptic and Maxwell Problems, Chapman and Hall/CRC Applied Mathematics and Nonlinear Science, Taylor & Franics Group, Boca Raton, FL/London/New York, NY.
  • Druskin, V., Knizhnerman, A. and Lee, P. (1999). New spectral Lanczos decomposition method for induction modeling in arbitrary 3-d geometry, Geophysics 64(3): 701-706.
  • Flasiński, M. and Schaefer, R. (1996). Quasi context sensitive graph grammars as a formal model of FE mesh generation, Computer-Assisted Mechanics and Engineering Science 3: 191-203.
  • Grabska, E. (1993). Theoretical concepts of graphical modeling, Part two: cp-graph grammars and languages, Machine Graphics and Vision 2(2): 149-178.
  • Grabska, E. and Strug, B. (2005). Applying cooperating distributed graph grammars in computer aided design, in R. Wyrzykowski, J. Dongarra, N. Meyer and J. Waśniewski (Eds.), Parallel Processing and Applied Mathematics, Lecture Notes in Computer Science, Vol. 3911, Springer, Berlin/Heidelberg, pp. 567-574.
  • Hild, P. (2011). A sign preserving mixed finite element approximation for contact problems, International Journal of Applied Mathematics and Computer Science 21(3): 487-498, DOI: 10.2478/v10006-011-0037-7.
  • Kelemen, J. (1991). Syntactical models of cooperating/distributed problem solving, Journal of Experimental and Theoretical AI 3(1): 1-10.
  • Kukluk, J., Holder, L. and Cook, D. (2008). Inferring graph grammars by detecting overlap in frequent subgraphs, International Journal of Applied Mathematics and Computer Science 18(2): 241-250, DOI: 10.2478/v10006-008-0022-y.
  • Martín-Vide, C. and Mitrana, V. (1998). Cooperation in contextual grammars, Proceedings of the MFCS'98 Satellite Workshop on Grammar Systems, Brno, Czech Republic, pp. 289-302.
  • Newman, G. and Alumbaugh, D. (2002). Three-dimensional induction logging problems, Part 2: A finite-difference solution, Geophysics 67(2): 484-491.
  • Pardo, D., Demkowicz, L., Torres-Verdín, C. and Paszynski, M. (2006). Two-dimensional high-accuracy simulation of resistivity logging-while-drilling (LWD) measurements using a self-adaptive goal-oriented hp finite element method, SIAM Journal on Applied Mathematics 66(6): 2085-2106.
  • Pardo, D., Demkowicz, L., Torres-Verdín, C. and Paszynski, M. (2007). A self-adaptive goal-oriented hp-finite element method with electromagnetic applications, Part II: Electrodynamics, Computer Methods in Applied Mechanics and Engineering 196(37): 3585-3597.
  • Pardo, D., Torres-Verdín, C. and Paszynski, M. (2008). Simulations of 3d DC borehole resistivity measurements with a goal-oriented hp finite-element method, Part II: Through-casing resistivity instruments, Computational Geosciences 12(1): 83-89.
  • Paszynska, A., Grabska, E. and Paszynski, M. (2012a). A graph grammar model of the hp adaptive three dimensional finite element method, Part I, Fundamenta Informaticae 114(2): 149-182.
  • Paszynska, A., Grabska, E. and Paszynski, M. (2012b). A graph grammar model of the hp adaptive three dimensional finite element method, Part II, Fundamenta Informaticae 114(2): 183-201.
  • Paszynska, A., Paszynski, M. and Grabska, A. (2008). Graph transformations for modeling hp-adaptive finite element method with triangular elements, in M. Bubak, G.D. Albada, J. Dongarra and P.M.A. Sloot (Eds.), ICCS 2008, Lecture Notes in Computer Science, Vol. 5103, Springer, Berlin/Heidelberg, pp. 604-613.
  • Paszynska, A., Paszynski, M. and Grabska, E. (2009). Graph transformations for modeling hp-adaptive finite element method with mixed triangular and rectangular elements, in G. Allen, J. Nabrzyski, E. Seidel, G.D. Albada, J. Dongarra and P.M.A. Sloot (Eds.), ICCS 2009, Lecture Notes in Computer Science, Vol. 5545, Springer, Berlin/Heidelberg, pp. 875-884.
  • Paszynski, M. (2009a). On the parallelization of self-adaptive hp-finite element methods, Part I: Composite programmable graph grammar model, Fundamenta Informaticae 93(4): 411-434.
  • Paszynski, M. (2009b). On the parallelization of self-adaptive hp-finite element methods, Part II: Partitioning communication agglomeration mapping (PCAM) analysis, Fundamenta Informaticae 93(4): 435-457.
  • Paszynski, M., Pardo, D. and Calo, V. (2013). A direct solver with reutilization of LU factorizations for h-adaptive finite element grids with point singularities, Computers & Mathematics with Applications 65(8): 1140-1151.
  • Paszynski, M., Pardo, D. and Paszynska, A. (2011). Out-of-core multi-frontal solver for multi-physics hp adaptive problems, Procedia Computer Science 4: 1788-1797.
  • Paszynski, M. and Schaefer, R. (2010). Graph grammar-driven parallel partial differential equation solver, ComputerAssisted Mechanics and Engineering Science 22(9): 1063-1097.
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  • Szymczak, A., Paszynska, A. and Paszynski, M. (2011). Anisotropic 2d mesh adaptation in hp-adaptive FEM, Procedia Computer Science 4: 1818-1827.
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv23z4p839bwm
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