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This paper presents a novel parallel-GPU discontinuous Galerkin time domain (DGTD) method with a third-order local time stepping (LTS) scheme for the solution of multi-scale electromagnetic problems. The parallel-GPU implementations were developed based on NVIDIA's recommendations to guarantee the optimal GPU performance, and an LTS scheme based on the third-order Runge–Kutta (RK3) method was used to accelerate the solution of multi-scale problems further. This LTS scheme used third-order interpolation polynomials to ensure the continuity of the time solution. The numerical results indicate that the strategy with the parallel-GPU DGTD and LTS maintains the order of precision of standard global time stepping (GTS) and reduces the execution time by about 78% for a complex multi-scale electromagnetic scattering problem. [ABSTRACT FROM AUTHOR]

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 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]

Abstract: The purpose of this work is to apply a previously developed ultra weak variational formulation (UWVF) to the solution of the Helmholtz equation in electromagnetic scattering problems. The variational form is based on discontinuous Galerkin with plane wave basis functions in 2‐dimensional finite element mesh. We present a general strategy, which allows to adjust the number of wave directions based on both the element size and the local conditioning number. This provides a cost‐effective mechanism for application of UWVF using nonuniform meshes. Through simulation of scattering of a dielectric‐coated circular cylinder, it is shown that the process significantly improves the UWVF performance. [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]

The generalized finite-element method (GFEM) enriched by plane waves has been proved suitable to solve the 2-D Helmholtz equation. However, when the number of unknowns increases, some difficulties arise, such as bad condition number. Therefore, developing a pre-processing methodology to identify an appropriate number of degrees of freedom for each problem could be useful. This paper presents a systematic approach to determine the optimal number of plane waves for each problem to be used in GFEM solution. It is based on the analysis of the traditional FEM solution with a poor mesh resolution using the fast discrete curvelet transform. The results indicate that the adopted strategy can guarantee accurate and converging responses for GFEM in complex problems, along with remarkable reductions of the computational cost. [ABSTRACT FROM AUTHOR]