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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]

In this paper, we solve the \mathcal E and \mathcal B mixed finite element time domain formulation using the alternating-direction implicit (ADI) scheme in time. To save computational cost, the algorithm is improved using a recursive sparsification procedure that approximates the inverse matrix needed to calculate the electric field. Although the method is unconditionally stable, we show that the numerical performance of the algorithm is strongly related to the time step. Numerical results demonstrated that for the same accuracy our approach is much faster than the ADI with Cholesky factorization. [ABSTRACT FROM PUBLISHER]

This paper addresses the generalized finite-element method enriched by plane waves for the 2-D Helmholtz equation. The enrichment function is modified to reduce the effect of numerical dispersion from coarse meshes and to make it possible to treat essential boundary conditions in a straightforward way. Two numerical examples, the free space propagation problem and the plane wave scattering by a cylinder, demonstrate the effectiveness of the new enrichment function. [ABSTRACT FROM PUBLISHER]

ABSTRACT In Part I (W. G. Facco et al., Microwave and Optical Technology Letters 54 (2012) 2709-2716), we introduced the q-version of the nonconforming generalized finite element method (NC-GFEM) for the Helmholtz equation where the interface between the media can be handled as piecewise linear segments. Here we continue the development of the NC-GFEM for Helmholtz where the interface between the media can be handled as piecewise curvilinear. We address: (a) a new scheme of integration to evaluate the integral along the interfaces and (b) the mortar element method (MEM) as a substitute for the Lagrange multipliers. The MEM has the advantage of generating sparse and positive definite systems. Various numerical aspects affecting the NC-GFEM efficiency are analyzed by solving a two-dimensional scattering problem. The convergence of the method is also presented as a function of the number of plane wave directions. © 2014 Wiley Periodicals, Inc. Microwave Opt Technol Lett 56:1913-1919, 2014 [ABSTRACT FROM AUTHOR]

To solve wave propagation problems over large domains composed by different media, many authors use the generalized finite element method (GFEM) with a geometrically conforming partition and plane wave enrichment.Such analysis is often accomplished by decomposing the entire domain into several subdomains and performing the analysis individually on each one. Then, the global analysis can be realized by using Lagrange multipliers to ensure the interface constraints. In this article, the GFEM with plane wave enrichment is extended to nonconforming discrete cases where the interface between the media can be handled as piecewise linear segments. Results for problems for which the analytical solution is known are presented to demonstrate the efficiency of the proposed technique. The convergence of the method is also presented as a function of the number of plane wave directions. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 54:2709-2716, 2012; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.27166 [ABSTRACT FROM AUTHOR]

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). [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM PUBLISHER]

This paper describes an approach to solve the thermal-electromagnetic problem inside a single mode applicator loaded with a ceramic sample. The FEM is combined with analytical techniques to solve the electromagnetic problem. We obtain a fast, simple and accurate method that allows performance investigation of the single mode cavity during the whole heating process. A key feature of the method is to permit iris aperture and short position to vary during the heating. The dependence upon temperature of the complex permittivity of the load is included in the model. The simulation of a thin cylinder ceramic shows that the approach proposed is capable to provide accurate results with low computational cost. [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. [ABSTRACT FROM AUTHOR]