Elson J. Silva

The element-free Galerkin method in three-dimensional electromagnetic problems

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

Robot navigation based on electrostatic field computation

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 robots orientation. To demonstrate the elegance of the proposed methodology, several experimental results with actual mobile robots are included

An object-oriented finite-element program for electromagnetic field computation

The purpose of this paper is to illustrate how the concepts of object-oriented programming can be applied to the finite element method, and to illustrate the advantages of this approach. The basic concepts of the object-oriented programming method are also presented. A 3-D magnetostatic program that uses nodal elements and edge elements has been developed and implemented using the C++ language. >

On Computing Complex Navigation Functions

This paper addresses the problem of efficiently computing robot navigation functions. Navigation functions are potential functions free of spurious local minima that present an exact solution to the robot motion planning and control problem. Although some methodologies were found in the literature, none of them are easy to implement and generalize for complex shaped workspaces and robots. We discuss some of the difficulties encountered in the current methodologies and propose a novel approach using a Finite Element method for potential field computation.

Efficient algorithms and data structures for element-free Galerkin method

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

Improving the Mixed Formulation for Meshless Local Petrov–Galerkin Method

The meshless local Petrov-Galerkin method (MLPG) with a mixed formulation to impose Dirichlet boundary conditions is investigated in this paper. We propose the use of Shepard functions for inner nodes combined with the radial point interpolation method with polynomial terms (RPIMp) for nodes over the Dirichlet boundaries. Whereas the Shepard functions have lower computational costs, the RPIMp imposes the essential boundary conditions in a direct manner. Results show that the proposed technique leads to a good tradeoff between computational time and precision.

Meshless Local Petrov-Galerkin Approach in Solving Microwave Guide Problems

This paper describes a meshless approach to obtain solutions for propagating microwave problems. The Meshless Local Petrov-Galerkin (MLPG) method is used, based on a local weak form tested with the Heaviside step function. The field is approximated by the Point Interpolation method using radial basis function with additional polynomial basis (RPIMp). TEAM workshop problem 18 is solved and its solution is compared with references from the literature. The results are in good agreement, showing that MLPG can be used as a good alternative to finite elements for this kind of problems.

The Nonconforming Point Interpolation Method Applied to Electromagnetic Problems

Nonconforming point interpolation method (NPIM) is a meshless method that has been applied to problems in mechanics in the last years. In this paper, we investigate NPIM in electromagnetism. We present its formulation and shape functions, which are generated by the radial point interpolation method with polynomial terms. The numerical results are compared to the ones obtained by the finite flement method (FEM) and the element-free Galerkin method (EFG).

Adaptive time-stepping analysis of nonlinear microwave heating problems

This paper presents a three-dimensional computational model for nonlinear microwave heating problems. In order to reduce the computational costs, a new finite element method adaptive time-stepping scheme is proposed. Numerical results are compared with experimental measurements on a problem of dielectric heating of water.

Data management in finite element analysis programs using object-oriented techniques

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++.