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A Graph GrammarModel of the hp Adaptive Three Dimensional Finite Element Method. Part I

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The first part of our paper presents a composite programmable graph grammar model for the self-adaptive two dimensional hp Finite Element Method algorithms (2D hp-FEM) with mixed triangular and rectangular finite elements. The two dimensional model is a starting point for the three dimensional model of self-adaptive hp-FEM presented in the second part of this paper. A computational mesh is represented by a composite graph. The operations performed over the mesh are expressed by the graph grammar rules. The three dimensional model is based on the extension of the two dimensional model with rectangular finite elements. In the second part of this paper, we conclude the presentation with numerical examples concerning the generation of the optimal mesh for simulation of the Step-and-Flash Imprint Lithography (SFIL).
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149--182
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Bibliogr. 32 poz., wykr.
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autor
Bibliografia
  • [1] Beal M. W., Shephard M. S., A General Topology-Based Mesh Data Structure, International Journal for Numerical Methods in Engineering, 40 (1997) 1573-1596.
  • [2] Demkowicz L., Computing with hp-Adaptive Finite Elements, Vol. I. One and Two Dimensional Elliptic and Maxwell Problems, Chapman & Hall/Crc Applied Mathematics & Nonlinear Science (2006).
  • [3] Demkowicz L., Kurtz J., Pardo D., Paszyński 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)
  • [4] Diekert V., Rozenberg G., The book of traces, World Scientific Publishing (1995)
  • [5] 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.
  • [6] Gawad J., Paszyński M., Matuszyk P.,Madej L., Cellular automata coupled with hp-adaptive Finite Element Method applied to simulation of austenite-ferrite phase transformation with a moving interface, Steel Research, ISSN 1611-3683, 79 (2008) 579586.
  • [7] Grabska E., Theoretical Concepts of Graphical Modeling. Part One: Realization of CP-Graphs. Machine Graphics and Vision 2, 1 (1993) 3-38.
  • [8] Grabska E., Theoretical Concepts of Graphical Modeling. Part Two: CP-Graph Grammars and Languages. Machine Graphics and Vision 2, 2 (1993) 149-178.
  • [9] Grabska E., Graphs and Designing, Graph Transformation in Computer Science, H.J. Schneider and H.Ehrig (Eds.), Lecture Notes in Computer Science, Springer-Verlag, 776, 1994.
  • [10] Grabska E, Hliniak G., Structural Aspects of CP-Graph Languages. Schedae Informaticae 5 (1993) 81-100
  • [11] Habel A, Hyperedge Replacement: Grammars and Languages, Lectures Notes in Computer Science, 643, Springer, 1992.
  • [12] Olkusnik R., Edytor graficzny do projektowania gramatyk grafowych. Msc Thesis, Jagiellonian University, Krakow, (1996).
  • [13] Obrok P., Pierzchala P., Szymczak A., Paszyński M., Graph grammar-based multi-thread multi-frontal parallel solver with trace theory-based scheduler, Procedia Computer Science, 1, 1, (2010) 1993-2001.
  • [14] Pardo D., Demkowicz L., Torres-Verdin C., Paszyński M., Simulation of Resistivity Logging-While-Drilling (LWD) Measurements Using a Self-Adaptive Goal-Oriented hp-Finite Element Method, SIAM Journal on Applied Mathematics 66 (2006) 2085-2106.
  • [15] Pardo D., Demkowicz L., Torres-VerdinC., PaszyńskiM., A Goal Oriented hp-Adaptive Finite Element Strategy with Electromagnetic Applications. Part II: Electrodynamics. Computer Methods in Applied Mechanics and Engineering, special issue in honor of Prof. Ivo Babu´ska, 196 (2007) 3585-3597.
  • [16] Pardo D., Torres-Verdin C., Paszyński M., Simulation of 3D DC Borehole Resistivity Measurements with a Goal-Oriented hp Finite Element Method. Part II: Through-Casing Resistivity Instruments, Computational Geophysics, 12 (2008) 83-89.
  • [17] Paszyńska A., Paszyński M., Grabska E., Graph transformations for modeling hp-adaptive Finite Element Method with triangular elements, International Conference on Computational Science, Kraków, Poland, June 2008, Lecture Notes in Computer Science 5103 (2008) 612-613
  • [18] Paszyńska A., Paszyński M., Grabska E., Graph transformations for modeling hp-adaptive Finite Element Method with mixed triangular and rectangular elements, International Conference on Computational Science, Baton Rouge, LA, USA, May 2008, Lecture Notes in Computer Science 5544 (2009) 875-884
  • [19] Paszyński M., On the Parallelization of Self-Adaptive hp-Finite Element Methods, Part I. Composite Programmable Graph Grammar Model, Fundamenta Informaticae 93(4) (2009) 411-434.
  • [20] PaszyńskiM., On the Parallelization of Self-Adaptive hp-Finite ElementMethods, Part II. Partitioning, Communication, Agglomeration,Mapping Analysis, Fundamenta Informaticae 93(4) (2009) 435-457
  • [21] PaszyńskiM., Demkowicz L., Parallel Fully Automatic hp-Adaptive 3D Finite Element Package, Engineering with Computers, 22, 3-4 (2006) 255-276.
  • [22] Paszyński M., Demkowicz L., Pardo D., Verification of Goal-Oriented hp-Adaptivity, Computers and Mathematics with Applications, 50, 8-9 (2005) 1395-1404.
  • [23] Paszyński M., Kurtz J., Demkowicz L., Parallel Fully Automatic hp-Adaptive 2D Finite Element Package, Computer Methods in Applied Mechanics and Engineering, 195, 7-8 (2006) 711-741.
  • [24] Paszyński M., Maciol P., Application of the Fully Automatic 3D hp Adaptive Code to Orthotropic Heat Transfer in Structurally Graded Materials, Journal of Material Processing Technology, 177, 1-3 (2006) 68-71.
  • [25] Paszyński M., Pardo D., Torres-Verdin C., Demkowicz L, Calo V, A Parallel Direct Solver for Self-Adaptive hp Finite Element Method, Journal of Parallel and Distributed Computing (2009) in press.
  • [26] Paszyński M., Romkes A., Collister E., Meiring J., Demkowicz L., Willson, C. G., On the Modeling of Step-and-Flash Imprint Lithography using Molecular Statics Models, ICES Report 05-38 (2005).
  • [27] PaszyńskiM., PaszyńskaA., Graph transformations formodeling parallel hp-adaptive Finite ElementMethod computations, Parallel Processing and Applied Mathematics, Gdańsk, Poland, September 2007, Lecture Notes in Computer Science 4967 (2008) 1313-1322.
  • [28] PaszyńskiM., Schaefer R., Graph GrammarDriven Parallel Partial Differential Equation Solver, Concurrency & Computations, Partice & Experience, 22, 9 (2009) 1063-1097.
  • [29] 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.
  • [30] Szymczak A., PaszyńskiM., Grach grammar based model of concurrency for self-adaptive hp Finite Element Method, Lecture Notes in Computer Science, vol. 6067, 2010, 95-104.
  • [31] Szymczak A., Paszyńska A., Paszyński M, Pardo D, Preventing deadlock during anisotropic 2D mesh adaptation in hp-adaptive Finite Element Method, accepted to Journal of Computational Science, 2011
  • [32] Szymczak A., Paszyński M., Pardo D., Graph grammar based Petri nets controlled direct solver algorithm, Computer Science, 11 (2010) 65-79.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS8-0028-0003
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