Graph Transformation Systems for Modeling Three Dimensional Finite Element Method. Part I

• Autorzy: Ryszka I. , Paszyńska A. , Grabska E. , Sieniek M. , Paszyński M.

Identyfikatory

DOI

10.3233/FI-2015-1248

• Języki publikacji: EN

Abstrakty

EN

In this paper we present several graph transformation systems modeling three dimensional h-adaptive Finite Element Method (3D h-FEM) algorithms with tetrahedral finite elements. In our approach a computational mesh is represented by a composite graph and mesh operations are expressed by the graph transformation rules. Each graph transformation system is responsible for different kind of operations. In particular, there is a graph transformation system expressing generation of an initial mesh, generating element matrices and elimination trees for interfacing with direct solver algorithm, a graph transformation system deciding which elements have to be further refined, as well as a graph transformation system responsible for execution of mesh refinements. These graph transformation systems are tested using a graph transformation tool (called GRAGRA), which provides a graphical environment for defining graphs, graph transformation rules and graph transformation systems. In this paper we illustrate the concepts by using an exemplary derivation for a three dimensional projection problem, based on a set of graph transformation rules.

Słowa kluczowe

EN

graph transformation system; automatic h adaptivity; finite element method

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2015
• Tom: Vol. 140, nr 2
• Strony: 129--172
• Opis fizyczny: Bibliogr. 34 poz., rys.

Twórcy

autor

Ryszka I.

• Faculty of Physics, Astronomy and Applied Computer Science Jagiellonian University Reymonta 4, 30-059, Krak´ow, Poland

autor

Paszyńska A.

• Faculty of Physics, Astronomy and Applied Computer Science Jagiellonian University Reymonta 4, 30-059, Kraków, Poland

autor

Grabska E.

• Faculty of Physics, Astronomy and Applied Computer Science Jagiellonian University Reymonta 4, 30-059, Kraków, Poland

autor

Sieniek M.

• Department of Computer Science Faculty of Computer Science, Electronics and Telecommunications AGH University of Science and Technology Al.Mickiewicza 30, 30-059, Kraków, Poland

autor

Paszyński M.

• Department of Computer Science Faculty of Computer Science, Electronics and Telecommunications AGH University of Science and Technology Al.Mickiewicza 30, 30-059, Kraków, Poland

Bibliografia

• [1] Amestoy, P. R. Duff, I. S. L’Excellent, J.-Y.: Multifrontal parallel distributed symmetric and unsymmetric solvers. Computer Methods in Applied Mechanics and Engineering, 184(2) (2000) 501–500
• [2] Amestoy, P. R. Duff, I. S. L’Excellent, J.-Y. Pralet S.: A fully asynchronous multifrontal solver using distributed dynamic scheduling, SIAM Journal on Matrix Analysis and Applications, 23(1) (2001) 15–41
• [3] Amestoy, P. R. Guermouche, A. L’Excellent, J.-Y. Pralet S.: Hybrid scheduling for the parallel solution of linear systems, Parallel Computing 32(2) (2006) 136–156
• [4] Bao, G. Hu, G. Liu, D.: An h-adaptive finite element solver for the calculations of the electronic structures. Journal of Computational Physics, 231(14) (2012) 4967–4979
• [5] Csuhaj-Varjú E.,Dassow J., Paun Gh., Dynamically controlled cooperating/distributed grammar systems. Information Sciences, 69(1-2) (1993) 1-25
• [6] Csuhaj-Varjú E., Dassow J., Kelemen J., Paun Gh., Grammar systems. A grammatical approach to distribution and cooperation. Topics in Computer Mathematics 8. Gordon and Breach Science Publishers, Yverdon (1994)
• [7] E. Csuhaj-Varjiú,Vaszil Gy. On context-free parallel communicating grammar systems: Synchronization, communication, and normal forms. Theoretical Computer Science, 255(1-2) (2001) 511-538
• [8] Csuhaj-Varjú E., Grammar systems: A short survey, Proceedings of Grammar SystemsWeek 2004,Budapest, Hungary, July 5-9, (2004) 141-157
• [9] Demkowicz L., Kurtz J., Pardo D., Paszy´nski M., Rachowicz W., Zdunek A., Computing with hp-Adaptive Finite Elements, Vol. II. Frontiers: Three Dimensional Elliptic and Maxwell Problems with Applications, Chapman & Hall/Crc Applied Mathematics & Nonlinear Science (2007)
• [10] Flasiński M., Schaefer R., Quasi context sensitive graph grammars as a formal model of FE mesh generation, Computer-Assisted Mechanics and Engineering Science, 3 (1996) 191-203
• [11] Grabska E., Theoretical Concepts of Graphical Modeling. Part One: Realization of CP-Graphs. Machine Graphics and Vision 2, 1 (1993) 3-38
• [12] Grabska E., Theoretical Concepts of Graphical Modeling. Part Two: CP-Graph Grammars and Languages. Machine Graphics and Vision 2, 2 (1993) 149-178
• [13] Grabska E, Hliniak G., Structural Aspects of CP-Graph Languages, Schedae Informaticae 5 (1993) 81-100
• [14] Grabska E., Strug B., Applying Cooperating Distributed Graph Grammars in Computer Aided Design, R. Wyrzykowski et al. (eds.): PPAM 2005, LNCS 3911 (2005) 567-574
• [15] Gurgul, P. Sieniek, M. Paszyński, M. Madej, L. Collier, N.: Two-dimensional HP-adaptive Algorithm for Continuous Approximations of Material Data Using Space Projection. Computer Science, 14(1) (2013) 97–112
• [16] Kelemen J., Syntactical models of cooperating/distributed problem solving. Journal of Experimental and Theoretical AI, 3(1) (1991) 1-10
• [17] Martín-Vide C, Mitrana V. Cooperation in contextual grammars. In A. Kelemenová, editor, Proceedings of the MFCS’98 Satellite Workshop on Grammar Systems, Silesian University, Opava (1998) 289-302
• [18] MUlti-frontal Massivelly Parallel Sparse direct solver (MUMPS) http://graal.ens-lyon.fr/MUMPS/
• [19] Paszynska A., Grabska E., Paszynski M., A Graph Grammar Model of the hp Adaptive Three dimensional Finite Element Method, Part I. Fundamenta Informaticae 114(2) (2012) 149-182
• [20] Paszynska A., Grabska E., Paszynski M., A Graph Grammar Model of the hp Adaptive Three dimensional Finite Element Method, Part II. Fundamenta Informaticae 114(2) (2012) 183-201
• [21] Paszyński,M.: Minimizing the memory usage with parallel out-of-coremulti-frontal direct solver, Computer Assisted Methods in Engineering and Science 20(1) (2013) 15–41
• [22] Paszyński M., On the Parallelization of Self-Adaptive hp-Finite Element Methods, Part I. Composite Programmable Graph Grammar Model, Fundamenta Informaticae 43(9) (2009) 411-434
• [23] PaszyńskiM., On the Parallelization of Self-Adaptive hp-Finite Element Methods, Part II. Partitioning, Communication, Agglomeration, Mapping Analysis, Fundamenta Informaticae 43(9) (2009) 435-457
• [24] Plaszewski, P. Banaś, K. Paszyński, M, Architecture of iterative solvers for hp-adaptive finite element codes, Computer Assisted Methods in Engineering and Science 20(1) (2013) 43-54
• [25] Paszyński, M. Pardo, D. Calo, V. M, A direct solver with reutilization of LU factorizations for h-adaptive finite element grids with point singularities, Computers and Mathematics with Applications, 65(8) (2013) 1140-1151
• [26] Paszyński, M. Pardo, D. Paszyńska A, Parallel multi-frontal solver for p adaptive finite element modeling of multi-physics computational problems, Journal of Computational Science 1(1) (2010) 48-54
• [27] Paszyński, M. Pardo, D. Paszyńska, A. Demkowicz, L, Out-of-core multi-frontal solver for multi-physics hp adaptive problems, Procedia Computer Science 4 (2011) 1788-1797
• [28] Paszyński, M. Schaefer, R, Graph grammar driven parallel partial differential equation solver, 22(9) (2010) 1063–1097
• [29] Rozenberg, G., Handbook of graph grammars and computing by graph transformation, vol I: Foundations. World Scientific, (1997)
• [30] Ryszka, I., Paszyńska,A., Grabska, E., Sieniek, M., Paszyński, M. Graph transformation systems for modeling three dimensional finite element method. Part II, submitted to Fundamenta Informaticae
• [31] Sieniek, M. Paszyński M.: Subtree reuse in multi-frontal solvers for regular grids in Step-and-Flash Imprint Nanolithography modelling, accepted to Advanced EngineeringMaterials (2013)
• [32] Ślusarczyk, G., Paszyńska, A., HypergraphGrammars in hp-adaptive Finite Element Method, Procedia Computer Science, 18 (2013) 1545-1554
• [33] Spicher A., Michel O., Giavitto J., Declarative Mesh Subdivision Using Topological Rewriting in MGS, International Conference on Graph Transformation, Enschede, The Netherlands, September 2010, Lecture Notes in Computer Science 6372 (2010) 298-313
• [34] Simeoni M., Staniszkis M.: Cooperating Graph Grammar Systems. Grammatical Models of Multi-Agent Systems (1999) 193-217