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This paper addresses the problem of controlling a large group of robots in a 2-D pattern generation task. Different from previous methodologies, our approach can be used in generic static environments, where obstacles may appear. This approach is based on the analogy with the simulation of fluids in electrostatic fields. By means of a weak coupling between the smoothed particle hydrodynamics and the finite element method we derive a scalable solution where decentralized controllers are provided. Index Terms--Electric fields, hydrodynamics, mobile robots.

This paper presents improvements in surface mesh of models generated by Boolean and assembly operations or surface reconstruction methods. The general concept consists of applying local mesh modification operators on the surface mesh to improve the shape quality of the elements without losing geometric information. To guarantee the model geometric characteristics, a smooth surface approximation of the model is evaluated and coupled to the operators of local mesh modifications. The approximation uses mesh information to generate the B-splines patches. Index Terms--Finite-element method (FEM), mesh generation, solid modelers.

A meshless method for electromagnetic field computation is developed based on the multiquadric interpolation technique. A global approximation to the solution is built based only on the discretization of the domain in nodes and the differential equations describing the problem in the domain and its boundary. An attractive characteristic of the multiquadric solution is that it is continuous and it has infinitely continuous derivatives. This is particularly important to obtain field quantities in electromagnetic analysis. The method is also capable of dealing with physical discontinuities present at the interface between different materials. The formulation is presented in the Cartesian and polar coordinates, which can be extended to other systems. We applied the formulation in the analysis of an electrostatic micromotor and a microstrip. The results demonstrate good agreement with other numerical technique, showing the adequacy of the proposed methodology for electromagnetic analysis. Index Terms--Collocation methods, interface conditions, mesh-free methods, meshless methods, multiquadrics.

This article presents a simple efficient algorithm for the subdivision of a d-dimensional simplex in [k.sup.d] simplices, where k is any positive integer number. The algorithm is an extension of Freudenthal's subdivision method. The proposed algorithm deals with the more general case of [k.sup.d] subdivision, and is considerably simpler than the RedRefinementND algorithm for implementation of Freudenthal's strategy. The proposed simplex subdivision algorithm is motivated by a problem in the field of robust control theory: the computation of a tight upper bound of a dynamical system performance index by means of a branch-and-bound algorithm. Categories and Subject Descriptors: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling--Geometric algorithms, languages, and systems General Terms: Algorithms Additional Key Words and Phrases: Simplex subdivision, mesh generation

This note presents a new approach to robust "D-stability analysis of linear time-invariant systems with polytope-bounded uncertainty. The proposed approach combines sufficient conditions for robust D-stability in terms of feasibility problems with linear matrix inequalities (LMI) constraints and a new polytope partition technique. If the initial polytope does not attain the robust D-stability sufficient condition, the polytope is successively subdivided until all subpolytopes attain the sufficient condition, in the case of robustly D-stable uncertain system, or it is found a subpolytope vertex that does not attain the regional pole-placement constraints, in the case of an uncertain system that is not robustly D-stable. It is presented a new general format polytope partition technique that allows the implementation of the proposed approach. The efficiency of the proposed approach is verified by means of illustrative examples and three different LMI-based analysis formulations. Index Terms--Polytope-bounded uncertainty, robust D-stability, robust stability, simplex subdivision.

This paper addresses the problem of mobile robot navigation using artificial potential fields. Many potential field based methodologies are found in the robotics literature, but most of them have problems with spurious local minima, which cause the robot to stop before reaching its target position. Although some free of local minima methodologies are found in the literature, none of them are easy to implement and generalize for complex shaped environments and robots. We propose a perfect analogy between electrostatic field computation and robot path planning. Thus, an easy solution to the problem, which is based on standard finite-element methods, can be applied with generic geometries and can even take into account the robot's orientation. To demonstrate the elegance of the proposed methodology, several experimental results with actual mobile robots are included. Index Terms--Finite element methods, mobile robots, motion-planning.

The element-free Galerkin (EFG) meshless method is being widely used in problems where it is difficult to construct a good mesh or remeshing is needed. Although most of these problems include three-dimensional (3-D) domains, few works are found using the EFG in three dimensions in all areas, including electromagnetism. In this paper, we present the formulation and numerical results concerning EFG parameters in a 3-D electromagnetic problem. Index Terms--Electromagnetics, element-free Galerkin (EFG), Laplace's equation, meshless, three-dimensional (3-D).

The element-free Galerkin method (EFG) has specific characteristics that require the usage of techniques and data structures in order to provide efficient calculation. This paper address two problems concerning the EFG implementation. The point location problem, which must find in which subdomain the integration point is located, and the influence domain problem, which must find the nearest nodes to build an influence domain and construct the shape functions. This work proposes the use of new data structures and algorithms in order to solve these problems, speeding up the method and providing a fast and correct influence domain construction. Index Terms--Data structures, element-free Galerkin, kd-tree, meshless, trapezoidal map.

This paper presents an object-oriented platform developed for teaching finite element pre-processor programming and design. The main techniques that can be learned with this tool are computer graphics programming, object-oriented analysis and design, data structures for CAD, data file interchange formats, automatic mesh generation and parametrization techniques. The platform structure is presented and its main characteristics are emphasized. This open platform has its code freely disposable on the Internet. Index Terms - Computer aided engineering, object-oriented programming, design automation software, finite element methods, software development, educational technology.

This paper describes the potential solution offered by object-oriented programming (OOP) to solve problems of data management. The practical examples are discussed with particular reference to finite element method. The main aim is to show the potentiality of the technology based on objects in systems that use complex data structure. Class descriptions are given. The codes are presented using the OOP language C++.

This paper describes the integrated use of two design strategies for controlling the permittivity and permeability of a transformation electromagnetics two-dimensional cloak. This hybrid process permits more freedom in the choice of the constitutive properties, which could simplify the implementation with metamaterials. Because simplicity of materials and scattering performance are inherently conflicting characteristics, a multi-objective genetic algorithm is applied to optimize them. According to the presented results for a transverse-magnetic layered cloak, it is possible to have a good performance in terms of scattering even with an approximated reduced set of parameters with unitary axial permeability. [ABSTRACT FROM AUTHOR]

An out-of-plane coordinate transformation can avoid singular materials in a two-dimensional electromagnetic cloak. Based on numerical simulations of elliptical cylinders, in this paper we show that the use of two different constants to define the out-of-plane stretching can result in anisotropic materials with lower values and yet with a better scattering reduction for a given incident wave direction. [ABSTRACT FROM AUTHOR]

New vectorial shape functions for the edge meshless method are introduced. The theory to develop these functions is based on Nédélec's elements of the first type in the H(curl;Ω) space. The mathematical formulation to construct the shape functions is presented and the method's main characteristics in two dimensions are verified numerically. As a result, it is shown that the numerical solution is not corrupted by spurious modes and that the new shape functions are less dependent on edges distribution in the problem domain. Furthermore, it is possible to generate consistent approximations even when the length of the edges tends to zero. [ABSTRACT FROM AUTHOR]

A singular coordinate transformation leads to extreme materials in a transformation-based cloak. If a non-singular transformation is used, the perfect invisibility is lost. The invisibility is also influenced by the homogenization process. In this paper, we investigate these two influences in 2-D circular cylindrical cloaks, obtained from different non-singular mappings. Considering a further deterministic optimization, we also conclude that it is better to use a non-singular cloak based on a mapping scale up to 20%, since it has lower scattering and simpler materials when compared with cloaks based on other mappings. [ABSTRACT FROM AUTHOR]