Wyniki wyszukiwania - Biblioteka Nauki

1

Using a graph grammar system in the finite element method

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Strug B. , Paszyńska A. , Paszyński M. , Grabska E.

International Journal of Applied Mathematics and Computer Science

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2013

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tom 23

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nr 4

839-853

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.

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On the Parallelization of Self-Adaptive hp-Finite Element Methods Part I. Composite Programmable Graph Grammar Model

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Paszyński M.

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2009

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tom Vol. 93, nr 4

411-434

EN

The paper presents a general methodology for an efficient parallelization of the fully automatic hp-adaptive Finite Element Method (hp-FEM). The self-adaptive hp-FEM algorithm expressed in terms of the graph grammar productions is analyzed by utilizing the Partitioning Communication Agglomeration Mapping (PCAM) model. The computational tasks are defined over a graph model of the computational mesh. It is done for all parts of the algorithm: the generation of an initial mesh, direct solver (including the integration and elimination of degrees of freedom), mesh transformations (including the h and p refinements), as well as the selection of the optimal refinements. The computation and communication complexities of the resulting parallel algorithms are analyzed. The paper is concluded with the sequence of massive parallel computations. >From the performed tests it implies that the code scales well up to 200 processors

3

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

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Paszyńska A. , Grabska E. , Paszyński M.

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2012

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tom Vol. 114, nr 2

149-182

EN

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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On the Parallelization of Self-Adaptive hp-Finite Element Methods Part II. Partitioning Communication Agglomeration Mapping (PCAM) Analysis

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Paszyński M.

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2009

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tom Vol. 93, nr 4

435-457

EN

The paper presents a general methodology for an efficient parallelization of the fully automatic hp-adaptive Finite Element Method (hp-FEM). The self-adaptive hp-FEM algorithm expressed in terms of the graph grammar productions is analyzed by utilizing the Partitioning Communication Agglomeration Mapping (PCAM) model. The computational tasks are defined over a graph model of the computational mesh. It is done for all parts of the algorithm: the generation of an initial mesh, direct solver (including the integration and elimination of degrees of freedom), mesh transformations (including the h and p refinements), as well as the selection of the optimal refinements. The computation and communication complexities of the resulting parallel algorithms are analyzed. The paper is concluded with the sequence of massive parallel computations. >From the performed tests it implies that the code scales well up to 200 processors.