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1
Content available remote Supporting Product Modelling with “GraphTool”
Palacz w., Paszyńska A., Ślusarczyk G., Strug B., Grabska E.
Machine Dynamics Research
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2017
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Vol. 41, No. 4
135--147
EN
This paper presents the GraphTool system which supports all steps required to define graph grammars and to control their application. It provides graphical editors for graphs, graph transformation rules, and control diagrams. The considered graph grammars are based on different types of graphs (composite graphs, hierarchical graphs, hypergraphs and hierarchical hypergraphs) which can be labelled and attributed. In this tool, the standard approach to graphs and graph grammars is extended to graph grammar systems and graphs with layers. Adding layers allows the user to model graph structures composed of disjoint substructures, while adopting grammar systems allows for defining groups of grammars working together in a single derivation process. Graph structures obtained as the result of the graph derivations are used as knowledge representation in different application fields. This paper shows the versatility of GraphTool by presenting examples of its use in four different areas: computational grids, computer game states, Finite Element Method computations and architectural designs.
2
Content available remote Using the system of graph grammar for generation of quasi optimal element partition trees in two dimensions
Paszyńska A., Świderska I., Woźniak M., Jopek K., Paszyński M., Grabska E., Lenhart A., Nguyen D., Pingali K.
Computer Methods in Materials Science
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2016
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Vol. 16, No. 3
143--155
EN
The paper presents a graph grammar based approach for h-adaptive finite element method and multi-frontal solver algorithm. The multi-frontal solver is used for solving systems of linear equations created by finite element method. The multi-frontal solver is controlled by so-called ordering. The quality of ordering influences hardly the solver effectiveness. In our approach, the finite element mesh is represented by means of a hypergraph and corresponding element partition tree. The finite element operations like mesh generation or h-adaptation are modelled by graph grammar production. Additionally graph grammar productions have corresponding productions for the construction of the element partition tree. The element partition trees are transformed into the ordering that controlls execution of the solver algorithm. We show that the ordering resulting from our element partititon tree results in better performance of the parallel solver than the state of the art nested-dissection ordering available through MUMPS interface on the class of grids refined towards singularities.
PL
W artykule tym prezentujemy gramatykę grafową do modelowania algorytmów h adaptacyjnej metody elementów skończonych oraz solwera wielofrontalncgo. Solwer wielofronatlny używany jest do rozwiązania układu równań liniowych stworzonych przez metodę elementów skończonych. Solwer ten kontrolowany jest przez tak zwany porządek eliminacji. Jakość porządku eliminacji wpływa na efektywność solwera wielofrontalnego. W naszym podejściu siatka metody elementów skończonych reprezentowana jest przez hipergraf oraz związane z nim drzewo podziałów siatki. Operacje na elementach skończonych takie jak generacja siatki oraz h adaptacja modelowane są przez produkcję gramatyki grafowej. Dodatkowo, gramatyka grafowa posiada powiązane produkcje do generacji drzewa podziałów siatki. Drzewo podziałów siatki z kolei transformowane jest w porządek eliminacji, który kontroluje wykonanie algorytmu solwera. Pokazujemy że porządek eliminacji uzyskany na podstawie naszego drzewa podziałów siatki daje lepszą wydajność algorytmu solwera równoległego w porównaniu z klasycznym porządkiem nested- disseetions dostępnym w solwerze MUMPS, dla klas siatek adaptowalnych do lokalnych osobliwości.
3
Content available remote Engineering Design Supported by Many-Sorted First-Order Logic-Based Reasoning
Palacz W., Grabska E., Ślusarczyk G., Gajek S.
Machine Dynamics Research
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2015
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Vol. 39, No. 4
133-144
EN
This paper presents a computer system supporting conceptual design. The knowledge about designs saved in hierarchical hypergraphs allows the system to check if the current state of designs fulfills predefined constraints. The constraints are stored in external files, in the form of logic formulas. Originally, first-order logic was used; this paper proposes replacing it with many-sorted first-order logic.
4
Content available remote Graph Transformation Systems for Modeling Three Dimensional Finite Element Method. Part I
Ryszka I., Paszyńska A., Grabska E., Sieniek M., Paszyński M.
Fundamenta Informaticae
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2015
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Vol. 140, nr 2
129--172
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.
5
Content available remote Graph Transformation Systems for Modeling Three Dimensional Finite Element Method. Part 2
Ryszka I., Paszyńska A., Grabska E., Sieniek M., Paszyński M.
Fundamenta Informaticae
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2015
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Vol. 140, nr 2
173--203
EN
In this paper we introduce formal definitions for several graph transformation systems modeling three dimensional h-adaptive Finite Element Method (3D h-FEM) algorithms with tetrahedral finite elements. We introduce a composite graph representation of the computational mesh and graph transformation rules expressing the mesh operations. In particular, there are graph transformation rules expressing the generation of the initial mesh consisting with tetrahedral finite elements, graph transformation rules expressing the construction of an elimination tree for interfacing with multi-frontal direct solver algorithm, graph transformation rules selecting sub-graph representing finite elements for further refinements, graph transformation rules responsible for execution of mesh refinements. We also discuss several benefits of using graph transformation system instead of classical FEM approach, including the benefits from the viewpoint of multi-frontal direct solvers.
6
Content available Using a graph grammar system in the finite element method
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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Vol. 23, no. 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.
7
Content available remote Knowledge Representation for Human-Computer Interaction in a System Supporting Conceptual Design
Grabska E., Ślusarczyk G., Gajek S.
Fundamenta Informaticae
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2013
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Vol. 124, nr 1/2
91--110
EN
This paper deals with the conceptual stage of the design process related to civil engineering. Different types of design knowledge representation essential in visual aspects of a human-computer dialogue are considered. They comprise designer's drawings expressing forms, layouts and functionality of designed artifacts, internal graph-based data structures obtained automatically on the basis of these drawings and logic formulas extracted from the graph data structures. The reasoning mechanism based on the first-order logic enables the system to assess the compatibility of designs with specified requirements and constraints. The feedback given by the system along with visualizations of initial design ideas enforce the designer's constructive visual perception and creativity. The presented approach is illustrated on the example of designing an indoor swimming pool.
8
Content available remote A Graph GrammarModel of the hp Adaptive Three Dimensional Finite Element Method. Part I
Paszyńska A., Grabska E., Paszyński M.
Fundamenta Informaticae
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2012
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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).
9
Content available remote A Graph GrammarModel of the hp Adaptive Three Dimensional Finite Element Method. Part II
Paszyńska A., Grabska E., Paszyński M.
Fundamenta Informaticae
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2012
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Vol. 114, nr 2
183-201
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.
10
Content available remote Aesthetic Measure for Three-dimensional Objects
Tarko J., Grabska E.
Machine Graphics and Vision
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2011
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Vol. 20, No. 4
439-454
EN
This paper discusses a possible extension of Birkhoff's aesthetic measure in order to apply it to three-dimensional objects. Modified definitions of complexity and order, analogous to their two-dimensional equivalents, are proposed and used for calculation of aesthetic measure for both abstract and real-world three-dimensional objects.
11
Content available remote Supporting conceptual design in architecture by linguistic model
Borkowski A., Grabska E., Ozimek A., Ozimek P., Papiernik K.
Machine Graphics and Vision
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2007
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Vol. 16, No. 1/2
5-22
EN
It is shown that linguistic approach can be very useful when developing software supporting conceptual design in architecture. Treating primitives, like rooms, as letters of a certain language and capturing the knowledge about the architecture in a grammar allows us to implement automatic reasoning. It turns out that grammars describing hierarchical graphs are best suited for this purpose. The formalism underlying this approach is presented together with a prototype software that allows the user to convert functional requirements into layouts of the designed building, to visualise the resulting alternative solutions and to select the best one for the detailed design. The usage of this software is demonstrated on two examples.
12
Content available remote Hierarchical layout hypergraph operations and diagrammatic reasoning
Grabska E., Łachwa A., Ślusarczyk G., Grzesiak-Kopeć K., Lembas J.
Machine Graphics and Vision
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2007
|
Vol. 16, No. 1/2
23-38
EN
This paper deals with a new, computer-aided approach to floor-layout design. The approach proposes: firstly, a specific layout language with a syntactic knowledge defined by means of hierarchical hypergraphs; secondly, a correspondence between layout modifications and hypergraph operations. An initial layout drawn by the designer is automatically converted into a hypergraph and each designer's modification to the layout is reflected in the hypergraph structure. Our new approach is illustrated by a step by step example, where two complementary representations of the same floor-layout design are used.
13
Content available remote On Applying Model-Driven Engineering in Conceptual Design
Papiernik K., Grabska E., Borkowski A.
Machine Dynamics Problems
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2007
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Vol. 31, No. 3
58-65
EN
It is shown how decision support tools in the domain of conceptual design in architecture can be efficiently developed within the paradigm of Model-Driven Engineering (MDE). A prototype software is presented that allows the user to specify functional requirements for the designed building and then to map them onto certain subspaces. Hierarchical graphs and graph grammars serve as a knowledge representation tool. The final result is a 3D-view of the designed object coded automatically in the VRML and available on the screen. Hiding technicalities behind intuitive GUI we are able to win the interest of the designer and to convince him or her that the proposed tool increases productivity and creativity in the conceptual design phase.
14
Content available remote Fuzzy Interpretation of Layout Hypergraphs
Łachwa A., Grabska E., Ślusarczyk G.
Schedae Informaticae
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2006
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Vol. 15
165-173
EN
This paper presents a new approach to design floor-layouts with the use of computer. This approach is based on a special type of data structure in the form of a hierarchical hypergraph. This data structure describes the whole class of designs with fuzzy interpretation
15
Content available remote On computer-aided publication design
Grelowska K., Grabska E., Łachwa A.
Machine Graphics and Vision
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2004
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Vol. 13, No. 1/2
167-179
EN
The article presents a method of computer aided publication design. We consider text as a structure of mark displayed on a certain background, without paying attention to its meaning. Our approach is illustrated by a computer program generating layouts of covers with help of graph grammars.
16
Content available remote Design and reasoning with diagrams
Grabska E.
Machine Graphics and Vision
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2003
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Vol. 12, No. 1
5-16
EN
In this paper a new framework for conceptual design based on diagrammatic reasoning is sketched. The approach considers a dynamic context for design. The main phases of the design process are treated as different classes of situations in the appropriate world and as such they belong to their own classifications domains. The notion of classification allows one to model constraints that govern the construction diagrams to be drawn or generated.
17
Content available remote Hierarchical graph grammars in graphic print design and generation
Grabska E., Ślusarczyk G., Niewiadomska A.
Machine Graphics and Vision
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2001
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Vol. 10, No. 4
519-536
EN
The paper deals with graphic prints in Escher's style and hierarchical graphs. Escher prints are based on regular plane divisions, while hierarchical graphs represent plane division structures. The paper is illustrated by graphic prints generated by the system ESCHER_GRAPHICS.
18
Content available remote Hierarchical graphs in creative design
Grabska E., Palacz W., Szyngiera P.
Machine Graphics and Vision
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2000
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Vol. 9, No. 1/2
115-122
EN
This paper is concerned with computational aspects of creative design. We propose a new representation of artifacts' structures: hierarchical graphs. This type of graphs enables to define a gluing operation. The proposed operation is illustrated by an example of designing gardens.
19
Content available remote Function-structure computer-aided design model
Borkowski A., Grabska E., Hliniak G.
Machine Graphics and Vision
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1999
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Vol. 8, No. 3
367-381
EN
This paper considers defining functional requirements of the designed object and transforming them into the object structure. The proposed Function Structure Editor (FSE) enables to bridge the gap between the design specification and the object structure. When utilising FSE the designer uses graph operations which are automatically transformed into graph rules allowing one to generate potential solutions of a given design problem. The proposed methodology is illustrated by examples of designing the teapot and the floor-layout of the house.
20
Content available remote Graphics prints design using graph grammars
Grabska E., Hliniak G.
Machine Graphics and Vision
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1998
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Vol. 7, No. 1/2
345-353
EN
The syntactic and semantic aspects of graphic design process are considered. The syntactic structures of prints are represented by graphs. Hence, graph grammars are tools for generation of graph representations of Escher's prints. The possible ways of a realisation of those representations are specified by a realisation scheme which maps into graphic print. The implementation of Escher's prints is also discussed.
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