The paper is the next attempt to formalize an ontology-based knowledge framework helpful for CAD process. Our previous research has showed the need for a more expressive specification in order to capture the intended models corresponding to a certain design conceptualization. This paper presents a more general approach to ontological framework which will be illustrated with examples of designing floor-layouts. This formal framework can be useful for many different applications, for instance to biological systems, cultural heritage and economical aspects.

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.

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.

This paper continues development of ontological approach to conceptual visual design aided by computer. Design ideas during the conceptualization phase are externalized by the designer in the form of diagrams on the monitor screen and automatically transformed by the system into data structures being hyper-graphs. Hyper-graph structures are combined with logic-based knowledge representation techniques. Different types (sorts) are used to represent knowledge from diagrams and many-sorted first order languages for their formal specification. The paper is the next attempt to formalize ontology-based knowledge framework for CAD process. The proposed method is illustrated with an exemplary of design of floor-layouts aided by the prototype of the System, so called HSSDR (Hyper-graph System Supporting Design and Reasoning).

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.

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).

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.