Meshfree analysis of electromagnetic wave scattering from conducting targets: Formulation and computations

Analysis of Homogeneous Waveguides via the Meshless Radial Basis Function-Generated-Finite-Difference Method

“…where are the values of at the stencil points, are the weights and is the stencil size ( ). In (2), and The calculation of begins by considering an interpolant of the form [5], [6] ( To obtain and , the interpolant ( 3) is enforced to be exact at the nodes of the stencil with the additional constrains for the polynomials: (4) This results in the following block linear system (5) where is a symmetric RBF interpolation matrix with elements is a matrix with and, and are vectors given by and Applying the differential operator to the interpolant in (3) and evaluating at we get (6) where Solving (5) for , substituting the result into (6) and comparing with (2), the following linear system is obtained (7) where contains the sought weights and the coefficients in are discarded after solving.…”

“…During the last decades, meshless methods have been suc cessfully applied in many branches of science and engineering. However they still remain relatively less developed within the Computational Electromagnetics field [2] [4].…”

The method of finite spheres in acoustic wave propagation through nonhomogeneous media: Inf-sup stability conditions

“…The method has also been used in the AMORE scheme of analysis [7] and it is the basis for the development of the 'overlapping finite elements' [8]. First proposed as a tool for the analysis of solids, the MFS has also successfully been applied to electromagnetic wave scattering problems [9]. Building on these results, we conducted a study [10] in which we used the MFS to solve time-harmonic acoustic wave propagation problems in nonhomogeneous media [11].…”

A Nonlocal Operator Method for Partial Differential Equations with Application to Electromagnetic Waveguide Problem

“…For the analysis of complex structures in engineering, mesh generation remains a laborious and time-consuming process, which often requires human interaction with meshing program and corrections for local mesh. To alleviate the mesh entanglement, socalled meshless or meshfree methods have been proposed during the 1990s [Viana and Mesquita (1999); Xuan, Zeng, Shanker et al (2004); Razmjoo, Movahhedi and Hakimi (2011); Nicomedes, Bathe, Moreira et al (2017)]. Meshless methods have been afterwards developed, enriched and applied to analyze a wide variety of problems in engineering including electromagnetic problems.…”