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The goal of this work is to extend the Edge Meshless Method (EMM) presenting a new way to build the vector shape functions based on the H(curl) space. These vector shape functions allow the use of ...

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 pe...

When the method of finite spheres is used for the solution of time-harmonic acoustic wave propagation problems in nonhomogeneous media, a mixed (or saddle-point) formulation is obtained in which the unknowns are the pressure fields and the Lagrange multiplier fields defined at the interfaces between the regions with distinct material properties. Then certain inf-sup conditions must be satisfied by the discretized spaces in order for the finite-dimensional problems to be well-posed. We discuss in this paper the analysis and use of these conditions. Since the conditions involve norms of functionals in fractional Sobolev spaces, we derive ‘stronger’ conditions that are simpler in form. These new conditions pave the way for the inf-sup testing, a tool for assessing the stability of the discretized problems.

The classical numerical methods for the simulation of wave propagation phenomena in multiscale systems can demand an unnecessary computational cost. This study proposes a multiclass strategy to be applied to the linear multistep time integration methods in the formalism of the discontinuous Galerkin (DG) space discretisation. The multiclass scheme is applied specifically to linear multistep strong stability preserving method (SSPMS). The potential of this strategy is demonstrated by numerical tests applied to two electromagnetic problems. The results show that the proposed schemes promote a significant improvement compared with the standard SSPMS and the fourth-order Runge-Kutta. Furthermore, in order to obtain a real speed up, this study presents a class parameter that produces a previous knowledge to determine the number of classes.

This paper presents an end-to-end massively parallelized procedure for the solution of boundary value problems on Graphics Processing Units (GPU). The proposal is an integrated strategy that not only entails the calculation of nodal contributions, and the stiffness matrix assembly using the Meshless Local Petrov Galerkin Method (MLPG) but also the iterative solution of the system of algebraic equations in combination with methods from the Conjugate Gradient (CG) family. This end-to-end solution is fully developed using the Compute Unified Device Architecture (CUDA) platform without the need for extra data movement between the device and host after the matrix assembly. This is possible thanks to the parallel nature of the MLPG; each node designates a thread on the device. The introduced solution is wholly executed in the GPU, with minimal auxiliary structures or global synchronization points. The proposed approach was applied to the solution of a simple electromagnetic problem, and a sevenfold speedup was observed.

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...

A frequency selective surface (FSS) composed of a periodic arrangement of meander line inclusions is numerically analysed. The study is presented with respect to the number of meanders and is a gen...

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.

The knowledge of the electromagnetic constitutive properties of materials is crucial in many applications. Free-space methods are widely used for this purpose, despite their inherent practical difficulties. This paper describes an affordable free-space experimental setup for the characterization of flat samples in 1&ndash, 6 GHz in a non-anechoic environment. The extracted properties are obtained from the calibrated Scattering Parameters, using a frequency-by-frequency solution or a multi-frequency reconstruction. For the first, we describe how the Time-Domain Gating can be implemented and used for filtering the signals. For the latter, a weighting factor is introduced to balance the reflection and transmission data, allowing one to have a more favorable configuration. The different role of transmission and reflection measurements on the achievable results is analyzed with regard to experimental uncertainties and different noise scenarios. Results from the two strategies are analyzed and compared. Good agreement between simulation, measurement and literature is obtained. According to the reported results for dielectric materials, there is no need of filtering the data by a Time-Domain Gating in case of the multi-frequency approach. Experimental results for Polymethylmethacrylate (PMMA) and Polytetrafluorethylene (PTFE) samples validate both the setup and the processing.

Reducing the scattering and enhancing the bandwidth (BW) are two desirable aspects in cloak applications. In this paper, we propose their optimization using a simplified objective function, which avoids a costly detailed frequency sweep to get the BW at each iteration. The multi-objective characteristic of our optimization permits us to obtain a set of possible solutions (the Pareto-Front), which represents different compromises between the two objectives. Two examples of dielectric cloaks are presented and discussed.

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 a study of the influence of the geometric shape on the resonance frequency of the artificial magnetic conductor (AMC) by analysis of the electric field distributions on top of the surface metallic patch inside the unit cell. It is known that various parameters such as geometry, dielectric substrate thickness, gap between patches, length and width of patch, size of unit cell, permittivity and permeability strongly affect the resonance frequency. In attempts to elucidate the miniaturization process, as reference, a metallic square patch with a unit cell of size 10 mm × 10 mm was simulated and a resonance frequency of 5.75 GHz was obtained. The device has illuminated by a plane wave with polarization in the y direction. Additionally, different geometries were performed such as triangle, hexagon, circle and cross of Jerusalem. We realized that the field distribution can be used as an physical insight to understand the AMC miniaturization process. In particular, bow-tie geometry provided considerable electrical miniaturization compared with square patch, about 1.5 GHz. The results are supported by finite element method. Our findings suggest that shift at resonant frequency may be interpreted as a variation in the net induced electric polarizability on the surface of the metallic patches.

This paper presents a detailed study of the influence of the geometric shape at the resonance frequency of the AMC through the analysis of the electric field distributions on the surface metal patch inside the unit cell. It is known that various parameters such as geometry, dielectric substrate thickness, gap between patches, length and width of patch, size of unit cell, permittivity and permeability strongly affect the resonance frequency. In attempts to elucidate the miniaturization process, as reference, a square patch with a unit cell of size 10 mm × 10 mm has simulated and a resonance frequency of 5.75 GHz has obtained. The device has illuminated by a plane wave with polarization in the y direction. The following geometric shapes were performed: square, circle, hexagon, meander and bowtie. We realized that the field distribution can be used as an physical insight to understand the operation of the metasurface miniaturization process. In particular, bowtie geometry provided considerable electrical miniaturization compared with square patch, about 1.5 GHz. The results are supported by finite element method, using the commercial software COMSOL Multiphysics. Our findings suggest that net induced electric polarizability at edges of metal patches is the principal cause of shift at resonance frequency. Two bowtie shapes are proposed and has provided considerable electrical miniaturization, about 1.5 GHz, compared with square patch to the same dimension unit cell. Therefore, this letter present and propose a novel methodology to study and search geometries, based on analysis of electric field distribution.

The influence of permittivity and substrate thickness at the resonance frequency of artificial magnetic conductor is investigated. It is known that various parameters such as geometry, dielectric substrate thickness, gap between patches, length and width of patch, size of unit cell, permittivity and permeability strongly affect the resonance frequency. In attempts to elucidate the miniaturization process, as reference, a square patch with a unit cell of size 10 mm × 10 mm has simulated and a resonance frequency of 5.75 GHz has obtained. The device has illuminated by a plane wave with polarization in the y direction. Simulations have been employed to appreciate the behaviour of resonance frequency in function of substrate thickness, and permittivity. The results are supported by finite element method (FEM), using the commercial software COMSOL Multiphysics. Our findings show that there is a decrease at the resonance frequency owing to increase both permittivity and substrate thickness, while an opposite effect has been noted when the gap size between consecutive metals patches is increased. This means that the effect of increasing the dielectric thickness is equivalent to increasing effective permittivity of the system. We believe that the responsible mechanism for this behaviour is the induced electric polarizability on top of metal surface. Therefore, this work suggests that an efficient way to reduce resonance frequency is to look for geometries that maximize net induced electric polarizability and an analysis of electric field distribution could be used in order to design novel structure.

A modified meshless local Petrov-Galerkin for an electromagnetic axisymmetric problem is presented in this paper. The method uses the shape functions generated by the radial point interpolation method with a modified T-scheme to select the support nodes, and also a new and malleable strategy to determine the test domains. The convergence of the method is evaluated using a coaxial cavity problem and it is compared with the finite-element method for two different meshes: one with a good quality mesh and another partially composed to bad quality elements. The total execution time using both methods is also compared.

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.

The focus of this study is on the design of feedback control laws for swarms of robots that are based on models from fluid dynamics. We apply an incompressible fluid model to solve a pattern generation task. Possible applications of an efficient solution to this task are surveillance and the cordoning off of hazardous areas. More specifically, we use the smoothed-particle hydrodynamics (SPH) technique to devise decentralized controllers that force the robots to behave in a similar manner to fluid particles. Our approach deals with static and dynamic obstacles. Considerations such as finite size and nonholonomic constraints are also addressed. In the absence of obstacles, we prove the stability and convergence of controllers that are based on the SPH method. Computer simulations and actual robot experiments are shown to validate the proposed approach.

In this paper the coupling of natural element method with the boundary element method (Hybrid NEM — BEM method) is proposed to solve the electromagnetic scattering problem. A dielectric cylinder is solved by the proposed approach and the results are compared with the analytical solution showing the usefulness and accuracy of the method.

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 reflects results of research related to developing a new methodology for automatic graph drawing based on applying genetic algorithms. The methodology has permitted the elaboration of a hybrid technique that combines the most popular, classical, topology-shape-metric approach to orthogonal drawings on the grid and a genetic algorithm that is directed, in its evolutionary process, at multicriteria decision making in a fuzzy environment. In the traditional use of the topology-shape-metric approach, a single fixed planar embedding is obtained in the planarization step. Thereafter this embedding is subjected to the orthogonalization and compaction steps. However, this sequence does not guarantee that the fixed planar embedding will generate a final drawing of a good quality. Moreover, every topology-shape-metric step is classified as a NP-hard problem, and choices as well as heuristics used in previous stages have a direct impact on subsequent ones. Taking this into account, the developed hybrid technique generates a greater number of planar embeddings by varying the order of edges' insertion when forming the planar embeddings in planarization step. Thus, the problem is formulated as a permutation-based combinatorial optimization problem. The genetic algorithm is applied at the planarization step of the topology-shape-metric. This allows one to generate the population with the corresponding number of planar embeddings. Each planar embedding obtained in the planarization step is submitted to the orthogonalization and compaction. Their results serve for applying the procedures of multicriteria decision making in a fuzzy environment. Thus, in the evolutionary process, the genetic algorithm is able to select individuals, which provide more harmonious solutions (relatively of the solutions obtained with traditional applying the topology-shape-metric approach) from the point of view of the aesthetic criteria that are usually utilized at the three steps of automatic graph drawing. This is convincingly demonstrated by experimental results given in the paper.

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.

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).

PurposeThe purpose of this paper is to solve both eigenvalue and boundary value problems coming from the field of quantum mechanics through the application of meshless methods, particularly the one known as meshless local Petrov‐Galerkin (MLPG).Design/methodology/approachRegarding eigenvalue problems, the authors show how to apply MLPG to the time‐independent Schrödinger equation stated in three dimensions. Through a special procedure, the numerical integration of weak forms is carried out only for internal nodes. The boundary conditions are enforced through a collocation method. The final result is a generalized eigenvalue problem, which is readily solved for the energy levels. An example of boundary value problem is described by the time‐dependent nonlinear Schrödinger equation. The weak forms are again stated only for internal nodes, whereas the same collocation scheme is employed to enforce the boundary conditions. The nonlinearity is dealt with by a predictor‐corrector scheme.FindingsResults show that the combination of MLPG and a collocation scheme works very well. The numerical results are compared to those provided by analytical solutions, exhibiting good agreement.Originality/valueThe flexibility of MLPG is made explicit. There are different ways to obtain the weak forms, and the boundary conditions can be enforced through a number of ways, the collocation scheme being just one of them. The shape functions used to approximate the solution can incorporate modifications that reflect some feature of the problem, like periodic boundary conditions. The value of this work resides in the fact that problems from other areas of electromagnetism can be attacked by the very same ideas herein described.

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.

PurposeThe purpose of this paper is to solve the electromagnetic scattering problem through a new integral‐based approach that uses the moving least squares (MLS) meshless method to generate its shape functions.Design/methodology/approachThe electric field integral equation and its magnetic counterpart (MFIE) are discretized via special shape functions built numerically through the MLS procedure. This approach is applied to the particular problem concerning the scattering of a TM plane wave by an infinite conductor cylinder. An error norm is established in order to verify the quality of the obtained results.FindingsResults show that the discretization process which employs MLS shape functions presents very good precision and fast convergence to the solution, when compared to results provided by another numerical method, the method of moments.Originality/valueMLS shape functions occur in meshless methods intended to solve problems based on differential formulation. This paper shows that these shape functions can also be applied successfully to problems coming from an integral formulation.

Purpose – The purpose of this paper is to investigate the extension of Delaunay refinement algorithms to work directly with a curved geometry in arbitrary dimensional spaces, which is also able to refine geometry pieces of different dimensions altogether.Design/methodology/approach – The extension of Delaunay refinement is based on ideas of the Bowyer‐Watson algorithm and Ruppert algorithm.Findings – The attempt to extend the fundamental ideas of Delaunay refinement to cope with curved geometries led to an algorithm whose performance in practice, regarding speed and mesh quality, is comparable to classical Delaunay refinement for flat geometries. Unfortunately, there are only theoretical guarantees that the refinement itself works under some conditions. No theoretical mesh quality bounds are provided.Research limitations/implications – A mesh refinement algorithm that deals with curved geometries is a key feature for adaptive mesh generators, so that points are inserted properly in the curved pieces inste...

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.

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.

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 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 robot's 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.

A particular meshless method, named meshless local Petrov-Galerkin is investigated. To treat the essential boundary condition problem, an alternative approach is proposed. The basic idea is to merge the best features of two different methods of shape function generation: the moving least squares (MLS) and the radial basis functions with polynomial terms (RBFp). Whereas the MLS has lower computational cost, the RBFp imposes in a direct manner the essential boundary conditions. Thus, dividing the domain into different regions a hybrid method has been developed. Results show that it leads to a good trade-off between computational time and precision.

In this paper, a new robust stability analysis approach is developed for uncertain discrete-time linear time-invariant systems with polytopic or affine parameter-dependent uncertainty models. The proposed approach is based on a combination of a branch-and-bound like strategy with linear matrix inequality (LMI) based analysis formulations. Two sufficient conditions are considered, one for the robust stability of the uncertain system and other one for the contrary situation. If both sufficient conditions fail to characterize the polytope, then it is iteratively subdivided into subpolytopes until some one proves to be unstable or all ones are verified to be robustly stable. The polytope subdivision is implemented by means of a specially developed simplex subdivision algorithm. Exhaustive numerical tests prove the efficiency of the proposed approach when compared with the most recent LMI-based formulations.

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

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

An approach to compute the H 2 - or H infin -guaranteed costs with any prescribed accuracy is presented. The proposed approach can be applied to uncertain state-space models of linear time-invariant systems, where the system matrices depend on uncertain parameters or vary in a polytopic domain of the space of matrices. The developed approach is based on a new implementation of the branch-and-bound algorithm with the upper-bound functions based on linear matrix inequality (LMI) characterisations. The branch operation is based on a new subdivision technique that can be applied to any kind of polytope shape, not restricted to the hyper-rectangle case. When applied alone, the LMI-based analysis formulations can fail to compute the guaranteed costs, or they can present conservative results. Examples are presented to illustrate that the proposed analysis approach overcomes the problems faced with LMI-based formulations with reasonable computational time.

This article presents a simple efficient algorithm for the subdivision of a d -dimensional simplex in k 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 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.

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