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

• Autorzy: Paszyńska A. , Grabska E. , Paszyński M.
• Języki publikacji: EN

Abstrakty

EN

This paper presents a composite programmable graph grammar model of the three dimensional self-adaptive hp Finite Element Method (hp-FEM) algorithms. The computational mesh composed of hexahedral finite elements is represented by a composite graph. The operations performed over the mesh are expressed by composite graph grammar productions. The three dimensional model is based on the extension of the two dimensional model for rectangular finite elements. This paper is concluded with numerical examples, presenting the generation of the optimal mesh for simulation of the Step-and-Flash Imprint Lithography (SFIL), the modern patterning process.

Słowa kluczowe

EN

graph grammar; automatic hp adaptivity; finite element model; Step-and-Flash Imprint Lithography

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2012
• Tom: Vol. 114, nr 2
• Strony: 183--201
• Opis fizyczny: Bibliogr. 17 poz., wykr.

Twórcy

autor

Paszyńska A.

autor

Grabska E.

autor

Paszyński M.

• AGH, University of Science and Technology, Al.Mickiewicza 30, 30-059, Kraków, Poland

Bibliografia

• [1] Bailey T.C., Colburn M. E. , Choi B. J. , Grot A., Ekerdt J. G., Sreenivasan J. G., Willson C. G., Step and Flash Imprint Lithography: A Low-Pressure, Room Temperature Nanoimprint Patterning Process. Alternative Lithography. Unleashing the Potentials of Nanotechnol-ogy. C. Sotomayor Torres, Editor, Elsevier (2002)
• [2] Burns R. L., Johnson S. C., Schmid G. M. , Kim E. K., Dickey D. M. D. , Meiring J., Burns S. D. , Stacey N. A., Willson C. G., Mesoscale modeling for SFIL simulating polymerization kinetics and densification. Proceeding of SPIE (2004)
• [3] ColburnM. E., Step and Flash Imprint Lithograpy: A Low Pressure, RoomTemperatureNonoimprint Lithography. PhD. Thesis, The University of Texas in Austin (2000)
• [4] Colburn M. E. , Suez I., Choi B. J., Meissi M. , Bailey T., Sreeni-vasan S. V. , Ekerdt J. E., Willson C. G., Characterization and mod-eling of volumetric and mechanical properties for SFIL photopoly-mers, Journal of Vacuum Science and Technology, B 19(6) (2001)
• [5] 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) in press.
• [6] Foster I., Designing and Building Parallel Programs (available online).
• [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, Hliniak G., Structural Aspects of CP-Graph Languages. Schedae Informaticae 5 (1993) 81-100
• [10] Hughes T. J. R., The Finite Element Method. Linear Statics and Dynamics Finite Element Method Analysis. Dover (2000)
• [11] 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.
• [12] PaszyńskiM., On the Parallelization of Self-Adaptive hp-Finite ElementMethods, Part II. Partitioning, Communication, Agglomeration,Mapping Analysis, Fundamenta Informaticae 43(9) (2009) 435-457
• [13] Paszyński M., Barabasz B., Schaefer R., Efficient adaptive strategy for solving inverse problems,May 2007, Lecture Notes in Computer Science 4488 (2007) 342-349.
• [14] 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)
• [15] Paszyński M., Schaefer R., Graph GrammarDriven Parallel PartialDifferential Equation Solver, Concurrency & Computations, Partice & Experience (2009) in press.
• [16] Szymczak A., Paszyński M., Graph grammar-based Petri nets model of concurrency for the self-adaptive hp-Finite Element Method with rectangular elements, International Conference on Computational Science, Baton Rouge, LA, USA, May 2008, Lecture Notes in Computer Science 5544 (2009)
• [17] Szymczak A., Paszyński M., Graph grammar-based Petri nets model of concurrency for the self-adaptive hp-Finite Element Method with triangular elements, Parallel Processing and Applied Mathematics, Wroclaw, Poland, September 2009, Lecture Notes in Computer Science (2009) in press.