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Sant'Ambrogio di Torino, Italy

Vipiana F.,Antenna and EMC Laboratory LACE | Francavilla M.A.,Polytechnic University of Turin | Vecchi G.,Polytechnic University of Turin
IEEE Transactions on Antennas and Propagation | Year: 2010

We propose a method to significantly improve the spectral properties of the EFIE MoM matrix for broad-band analysis of structures with fine details, non-uniform meshes, and large overall sizes. A multilevel approach allows to overlay fine meshes and quasi-Nyquist sampled meshes; the fine-mesh conditioning is solved via hierarchical basis functions, and the quasi-Nyquist sampled part is treated by an algebraic incomplete LU preconditioner. Numerical results show the effectiveness of the approach for several realistic structures with overall sizes of ten/twenty wavelengths and levels of detail from very moderate to extending over the whole structure. © 2006 IEEE.


Polimeridis A.G.,Massachusetts Institute of Technology | Vipiana F.,Polytechnic University of Turin | Vipiana F.,Antenna and EMC Laboratory LACE | Mosig J.R.,Ecole Polytechnique Federale de Lausanne | Wilton D.R.,Massachusetts Institute of Technology
IEEE Transactions on Antennas and Propagation | Year: 2013

Fully numerical schemes are presented for high precision computations of the four-dimensional integrals arising in Galerkin surface integral equation formulations. More specifically, the focal point of this paper is the singular integrals for coincident, edge adjacent and vertex adjacent planar and curvilinear triangular elements. The proposed method, dubbed as DIRECTFN, utilizes a series of variable transformations, able to cancel both weak (1/R) and strong (1/R2) singularities. In addition, appropriate interchanges in the order of the associated one-dimensional integrations result in further regularization of the overall integrals. The final integrands are analytic functions with respect to all variables involved and, hence, the integrals can be efficiently evaluated by means of simple Gaussian integration. The accuracy and convergence properties of the new schemes are demonstrated by evaluating representative weakly singular and strongly singular integrals over planar and quadratic curvilinear elements. © 2013 IEEE.


Vipiana F.,Polytechnic University of Turin | Vipiana F.,Antenna and EMC Laboratory LACE | Wilton D.R.,University of Houston
IEEE Transactions on Antennas and Propagation | Year: 2013

In this paper, we present a purely numerical procedure to evaluate strongly near-singular integrals involving the gradient of Helmholtz-type potentials for observation points at finite, arbitrarily small distances from the source domain. In the proposed approach the source domain is subdivided into a disc plus truncated subtriangles, and proper variable transformations are applied in each integration domain to exactly cancel the kernel singularity. A novel feature of the proposed angular transform is that required discrete values of the inverse transform, which is transcendental, are determined via a root-finding procedure; the same idea can also be applied to other transforms that arise in singularity cancellation methods. The resulting integral may then evaluated via a low order Gauss-Legendre quadrature scheme. © 2012 IEEE.


Vipiana F.,Antenna and EMC Laboratory LACE | Vecchi G.,Polytechnic University of Turin | Wilton D.R.,University of Houston
IEEE Transactions on Antennas and Propagation | Year: 2010

We present a multi-resolution (MR) basis for the method of moments (MoM) analysis of the electric field integral equation (EFIE) for fully arbitrary 3-D conductors composed of wires connected to surfaces. Representation of the unknown current with the MR basis results in a physics-based preconditioner, especially for geometrically complex and/or finely meshed structures, and/or low frequency problems. The proposed MR basis is constructed as a linear combination of the basis functions usually employed in the MoM-based codes, namely the piecewise linear (PWL) functions for wires modelled via line segments, the Rao-Wilton-Glisson (RWG) functions for surfaces modelled with triangles, and junction basis functions for modelling their connections. The key challenge and the novelty of the present work is the construction of multi-resolution basis functions defined on arbitrary cells formed by triangles and line segments modelling surfaces, wires and junctions that coherently include all three types of conventional basis functions. Application of the MR basis results in a basis change, algorithmically equivalent to a purely multiplicative algebraic preconditioner of the EFIE, that can be easily interfaced with pre-existing MoM codes. © 2006 IEEE.


Bertuch T.,Fraunhofer Institute for High Frequency Physics and Radar Techniques | Vipiana F.,Antenna and EMC Laboratory LACE | Vecchi G.,Polytechnic University of Turin
IEEE Transactions on Antennas and Propagation | Year: 2012

We present an approach for the method of moments (MoM) analysis of antennas of arbitrary shape printed on a cylindrical substrate. We propose several key components of a code to perform this analysis, with the explicit goal of adapting MoM codes devised for planar stratified structures. For that purpose, the background medium Green's function is expressed in the mixed-potential (MP) format to allow for efficient numerical integration; the spectral dyadic Green's function is first recast in the spectral counterpart of the spatial mixed-potential form. The convergence of the spectral-to-spatial transform is accelerated by extraction of spectral asymptotic functions and exploitation of the azimuthal periodicity. Several important issues of implementation, numerical stability, and accuracy are addressed with a view to incorporate the spatial MP Green's function into the MoM analysis of printed structures of arbitrary shape using RWG basis functions. The numerical results are in good agreement with those obtained by other methods and with measured data. © 2006 IEEE.

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