Alexandre R. Fonseca

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

Robot Navigation in Multi-terrain Outdoor Environments

This paper presents a methodology for motion planning in outdoor environments that takes into account specific characteristics of the terrain. Instead of decomposing the robot configuration space into “free” and “occupied”, we consider the existence of several regions with different navigation costs. In this paper, costs are determined experimentally by navigating the robot through the regions and measuring the influence of the terrain on its motion. We measure the robots vertical acceleration, which reflects the terrain roughness. The paper presents a hybrid (discrete—continuous) approach to guide and control the robot. After decomposing the map into triangular cells, a path planning algorithm is used to determine a discrete sequence of cells that minimizes the navigation cost. Robot control is accomplished by a fully continuous vector field that drives the robot through the sequence of triangular cells. This vector field allows smooth robot trajectories from any position inside the sequence to the goal, even for a small number of large cells. Moreover, the vector field is terrain dependent in the sense it changes the robot velocity according to the characteristics of the terrain. Experimental results with a differential driven, all-terrain mobile robot illustrate the proposed approach.

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.

Meshless Local Petrov-Galerkin in solving microwave guide problems

This paper describes a meshless approach to obtain accurate solutions for propagating microwave problems. The Meshless Local Petrov-Galerkin (MLPG) method, with the Heaviside step test functions and Radial basis point interpolation method (RPIM) shape functions, is used. Results are obtained for a two-dimensional model and are compared with a consolidated Finite Element Method (FEM).

Application of Local Point Interpolation Method to Electromagnetic Problems With Material Discontinuities Using a New Visibility Criterion

In this paper, the local point interpolation method (LPIM) is used with a modified visibility criterion to handle material discontinuities. In general, visibility criterion is applied only to shape function generation over support nodes selection. We present a modified version where it is also applied to the integration process. The method is simpler and more robust than other techniques often employed on multimaterials problems, with a straight-forward implementation.

Parallel Implementation of a Combined Moment Expansion and Spherical-Multipole Time-Domain Near-Field to Far-Field Transformation

A time-domain spherical-multipole near-to-far-field algorithm running in a parallelized code version is introduced in this paper. Such an approach is employed to obtain UWB antenna radiated fields and radiation patterns directly in time domain, which is more convenient to perform a unified characterization in time and frequency domains. We propose the use of the OpenMP, an application program interface that permits the code parallelization with almost no intervention. The results show that the proposed technique allows a code running 28 times faster when using a computer with 24 processors, each one with two threads, when compared with the sequential one. It also suggested a moment expansion technique to improve the accuracy and computational efficiency when using Gaussian pulse excitation when compared with the Fourier transform.