Search

Meshless methods construct their shape functions based on scattered nodes in the domain. One drawback of this approach is the presence of nonphysical modes in the numerical solution when dealing with vector problems due to the lack of the divergence free condition, in a similar way that occurs with the node-based finite-element method. On the other hand, vector radial basis functions were developed to produce numerical approximations that satisfy the divergence free condition. This paper presents the usage of those functions in conjunction with weak forms to solve vector electromagnetic problems. Numerical tests involving the Maxwell eigenvalue problem and the wave propagation in a waveguide are solved to demonstrate that the numerical solution is not corrupted with spurious modes.

A challenge in meshless methods dealing with vector electromagnetic problems is to produce numerical solutions that are free of spurious modes given that the generated vector field does not satisfy the condition of zero divergence. The edge meshless method (EMM) constructs its approximations using special shape functions based on edges to produce vector fields that are divergence free and to guarantee the continuity of the tangential field components. This paper presents the application of the EMM to solve vector electromagnetic problems. The 2-D Maxwell eigenvalue problem with anisotropic medium is tested to demonstrate that the technique produces correct numerical solution without spurious modes.

We propose a meshfree procedure for the time-harmonic analysis of electromagnetic wave scattering from conducting targets.We provide a novel formulation and also a totally meshfree discretization scheme.The problem is described by the vector wave equation with a divergence-free constraint.We propose a mixed formulation whose unknowns are the electric field vector and a Lagrange multiplier.The well-posedness of the variational problem is investigated, and compatible meshfree function spaces are given. We propose a completely meshfree procedure aimed at the time-harmonic analysis of electromagnetic wave scattering from conducting targets. The problem is described by the vector wave equation with a divergence-free constraint. We propose a mixed formulation whose unknowns are the electric field vector and a Lagrange multiplier. We investigate the well-posedness of the variational problem and construct compatible meshfree function spaces able to describe solutions in any geometry, in two and three dimensions. The method does not depend on any kind of parameter tuning. We illustrate its performance in a number of solutions through experimentally derived convergence rates and comparisons with other techniques.

There are important concerns about the problems caused by high values of low-frequency magnetic field in urban centers. Two of them have received particular attention: the electromagnetic interference in sensitive equipment and the potential adverse health effects on human beings. In this way, many solutions to mitigate the magnetic field generated by these lines have been proposed. In this context, this work presents several computational results about the effectiveness of the main forms to reduce the magnetic field generated by underground power cables. The analysis addresses not only the field attenuation levels, but also the impact on the rated current due to the presence of shielding devices. From these results, it is possible to choose the best shielding arrangement for each specific situation, in order to achieve the required attenuation levels with the least ampacity loss. The thermal-magnetic model was implemented in the (free) software FEMM 4.2, which employs the finite element method.

A possible strategy for avoiding singular material parameters in a transformation-based invisibility cloak involves an out-of-plane stretching, calculated to compensate the in-plane singular transformation. In this paper, we used numerical simulations to analyze the relation among the out-of-plane transformation, the resulting material anisotropy, and the total scattering cross width. Moreover, we show how this information can be used to optimize a cloak with homogeneous anisotropic layers.

In this paper, a strategy to parallelize the meshless local Petrov–Galerkin (MLPG) method is developed. It is executed in a high parallel architecture, the well known graphics processing unit. The MLPG algorithm has many variations depending on which combination of trial and test functions is used. Two types of interpolation schemes are explored in this paper to approximate the trial functions and a Heaviside step function is used as test function. The first scheme approximates the trial function through a moving least squares interpolation, and the second interpolates using the radial point interpolation method with polynomial reproduction (RPIMp). To compare these two approaches, a simple electromagnetic problem is solved, and the number of nodes in the domain is increased while the time to assemble the system of equations is obtained. Results shows that with the parallel version of the algorithm it is possible to achieve an execution time 20 times smaller than the CPU execution time, for the MLPG using RPIMp versions of the method.

Cable models for high-frequency studies require the calculation of per-unit-length parameters in a wide frequency range. Analytical methods, such as the one implemented in the Line/Cable Constants routine available in the Alternative Transients Program (ATP), are frequently used for this purpose. However, they are valid only for specific geometries, in which the cables are sufficiently separated one from another and from other wired systems and metallic structures. All these simplifications hamper the succesful application of the analytical (traditional) in typical industrial installation methods, such as cable systems in trays or pipes. In this context, this paper presents a methodology based on finite element analysis to overcome these limitations. This methodology, which was implemented in the FEMM software (free), was also used to investigate the influence of proximity effects on the parameters associated with three different installation methods often found in industrial facilities: cables above the earth surface, cables in an enclosing pipe and cables in a tray. The results indicate the importance of considering proximity effects in the calculation of cable parameters in practical conditions, especially for high-frequency studies.

This paper presents the face-based gradient smoothing point interpolation method (FS-PIM), a numerical method derived from the PIM that solves 3-D boundary value problems. FS-PIM is supported by the theory of G-space, weakened-weak formulations and the gradient smoothing operation. The method is applied in the analysis of electrostatic problems. The obtained results show that both convergence rate and accuracy of the approximation generated by FS-PIM are better than the ones presented by the finite element method, indicating that the technique is suitable for electromagnetic applications.

This paper deals with one member of the class of meshless methods, namely the Meshless Local Petrov-Galerkin (MLPG) method, and explores its application to boundary-value problems arising in the analysis of two-dimensional electromagnetic wave propagation and scattering. This method shows some similitude with the widespread finite element method (FEM), like the discretization of weak forms and sparse global matrices. MLPG and FEM differ in what regards the construction of an unstructured mesh. In MLPG, there is no mesh, just a cloud of nodes without connection to each other spread throughout the domain. The suppression of the mesh is counterbalanced by the use of special shape functions, constructed numerically. This paper illustrates how to apply MLPG to wave scattering problems through a number of cases, in which the results are compared either to analytical solutions or to those provided by other numerical methods.

This paper illustrates how to determine the bandgap structure of photonic crystals through MLPG. This method is akin to the Finite Element Method (FEM), as it also deals with the discretization of weak forms and produces sparse global matrices. The major difference is the complete absence of any kind of mesh. We concentrate in a particular version of it, the MLPG4, also known as Local Boundary Integral Equation Method (LBIE). Since the boundary conditions governing the electromagnetic field are periodic in a unit cell, we develop a special scheme to embed this feature on the shape functions used in the discretization process. As a result, boundary conditions do not need to be imposed on the unit cell. Index Terms—Electromagnetic wave propagation, finite element methods, integral equations, photonic crystals.

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.

Meshless Methods, also called Meshfree Methods, are a class of numerical methods to solve partial differential equations. The main characteristic of these methods is that they do not need a mesh like the one used in the Finite Element Method. In this sense meshless methods are very useful for modeling moving structures, such as electric machines, without a remeshing process. In this work the Element-Free Galerkin Method is used to simulate a three phase induction motor model including, for the first time, the field circuit coupling transient equations and the rotor movement.

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.

This paper presents a parallel algorithm to improve the quality of surface meshes representing models obtained from surface reconstruction, as well as models generated by the application of the Boolean and assembly operations to predefined primitives, such as spheres and blocks. The smooth surface approximation is generated in parallel, the faces are distributed evenly among the processors. Then, the surface mesh is divided into sections, which are refined first, and intersections for remeshing at the end.

In this paper, we apply a meshless method based on local boundary integral equations (LBIEs) to solve electromagnetic problems. The discretization process is carried out through the use of special basis functions that, unlike the Finite Element Method, are not confined to an element and do not require the support of an underlying mesh. The approach herein developed can be applied to general three-dimensional scalar boundary value problems arising in electromagnetism.

In this work, we apply a meshless-based method to a set of integral equations arising in electromagnetic wave propagation and scattering. The objective is not only to solve these equations through a meshless-based method, but also to find a way to build shape functions that could work for any cross-sectional geometry. We have found that the Moving Least Squares (MLS) approximation is not able to provide useful shape functions in every situation. This technique relies on matrix inversions and, according to the geometry, singular matrices can occur. In order to avoid this problem, we have taken the Improved Moving Least Squares (IMLS) approximation, that does not depend upon matrix inversions and then applied it to a number of cross-sectional geometries.

PurposeThe purpose of this paper is to introduce a new methodology to implement periodic and anti‐periodic boundary conditions in the element free Galerkin method (EFGM).Design/methodology/approachThis paper makes use of the interpolating moving least squares (IMLS) in the EFGM to implement periodic and anti‐periodic boundary conditions. This fact allows imposing periodic and anti‐periodic boundary conditions in a way similar to the one used by the finite element method.FindingsEFGM generally uses the moving least squares to obtain its shape functions. So, these functions do not possess the Kronecker delta property. As a consequence, the imposition of essential, as well as periodic and anti‐periodic boundary conditions needs other techniques to do it. When EFGM makes use of IMLS the shape functions satisfy the Kronecker delta property. As consequence the periodic boundary conditions implementation can be done in a direct way, similar to the FEM.Originality/valueIMLS provides a new way of periodic boundary conditions implementation in EFGM. This kind of implementation provides an easy and direct way in comparison to usual existing methods. With this technique EFGM can now easily take advantage of electrical machines symmetry.

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

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

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

This paper presents the meshless moving least square reproducing kernel method, originating from mechanics, which is applied for the first time to the solution of electromagnetic problems. Two-dimensional static problems are studied and simulation results show good agreement with analytical and other numerical solutions.

This paper presents a data structure for a 3-D preprocessor of an electromagnetic field computation program using object-oriented programming. An object-oriented database was organized to store all the necessary data to build an electromagnetic problem and generate its mesh, giving better flexibility and allowing a high improvement in organization.

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++.

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. >

This work describes a meshless method to obtain the electromagnetic characteristics of a monopole placed over a perfectly electric ground plane. The Meshless Local Petrov-Galerkin is used with shape functions generated by Moving Least Squares. Boundary conditions are imposed by a collocation method that does not require any numerical integration. The proposed axisymmetric analysis has a simple implementation and reduced computational effort. The results are in agreement with theoretical data and simulations found in the literature.

This paper presents an effective and efficient parallel algorithm to improve the quality of surface meshes representing models generated by the application of the Boolean and assembly operations to predefined primitives, such as spheres and blocks, as well as models obtained from surface reconstruction.

In this work we apply a meshless method based on Local Boundary Integral Equations (LBIE) to find the solution to boundary value problems. We discretize the weak form through the use of special basis functions that, unlike the Finite Element Method (FEM), are not confined to an element and do not need the support of an underlying mesh. The approach developed can be applied to general 3D scalar boundary value problems that arise in areas such as electrostatics and acoustic scattering, among others.

This work presents a method which enables coupling between equations of electric circuits and a magnetic field for a time domain model making use of a meshless method. A three-phase induction machine is used as example and its field-circuit transient coupling equations are presented. With the Element-Free Galerkin Method (EFGM) the final system of equations is obtained and flux and currents are evaluated.

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).

This article describes a framework for meshless methods using the generic programming paradigm. The framework is developed in C++ language with support of template mechanism. The idea is to build a set of extensible tools so that the framework is able to instantiate the main meshless methods such as Element Free Galerkin Method (EFG), Meshless Local Petrov Galerkin Method (MLPG), Point Interpolation Methods (PIM) and others.

In this paper we apply a meshless method to the classical electromagnetic scattering integral field equations. These equations are discretized via two different schemes related to the construction of shape functions: the Moving Least Squares (MLS) and the Improved Moving Least Squares (IMLS) approximations. We then establish a comparison between these two approximations in what concerns to their applicability and rates of convergence.

In this work, we solve the scattering problem of a plane wave by a dielectric cylinder through the Unimoment Method, where a new approach was taken when solving the interior problem: a meshless method based on local boundary integral equations (LBIE). Traditionally, the interior problem is attacked through the Finite Element Method, because one gets sparse matrices. But as in FEM, a meshless LBIE approach also provides sparse matrices, without the drawback of constructing a grid. We develop the formalism and illustrate the application of the aforementioned method to the scattering by a dielectric circular cylinder, a problem which is known to possess analytical solution.

Computational simulations involving problems of Power Quality, Electromagnetic Transients and Electromagnetic Compatibility, among others, require the application of time-domain cable models appropriate for high-frequency studies, able to represent the cable parameter variation in relation to frequency. Most of the models that satisfy this condition require, to be elaborated, input data regarding the cable resistance and inductance for different frequencies. Since the measurement of such parameters is oftentimes not feasible, the possibility of their determination from analytical or computational methods is highly desirable. Routines of the type “Cable/Line Constants”, commonly featured in commercial simulators, are widely used for this purpose; nevertheless, they present limitations that lead to inaccuracy and restrictions in their applicability. In this context, a methodology for cable parameter determination, based on Finite Element Analysis (FEA), is presented, which overcomes these problems and thus arises as a very attractive tool for cable/line modeling.

This paper addresses the simulation of fluids and charged particles in electrostatic fields. We couple smoothed particle hydrodynamics and finite elements. Our approach is demonstrated in a problem of pattern generation with robots

A GPU-adapted Finite Element Method (A-FEM) implementation without using a mesh coloring strategy to avoid race conditions is presented. All the elements are simultaneously processed, and the local data is computed and consolidated into the device memory in a new adapted Coordinate Format data structure (a-COO). The comparison between the proposed solution and two GPU Element-by-Element Finite Element Method (EbE-FEM) approaches shows promising results since it is no longer necessary the mesh coloring step. This new approach is well suited for problems that need re-meshing and consequently would need re-coloring, e.g., adaptive mesh refinement.