Author

# Guido Lombardi

Bio: Guido Lombardi is an academic researcher from Instituto Politécnico Nacional. The author has contributed to research in topics: Integral equation & Singular solution. The author has an hindex of 2, co-authored 9 publications receiving 19 citations.

##### Papers

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28 Oct 2020

12 citations

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10 Jul 1995

TL;DR: The application of the volumetric integral equation (VIE) method to the solution of the problem of scattering from a three-dimensional object buried in a dielectric half-space is outlined and a computational time reduction is obtained.

Abstract: The application of the volumetric integral equation (VIE) method to the solution of the problem of scattering from a three-dimensional object buried in a dielectric half-space is outlined. The VIE method described and applied in this paper is basically an extension of that proposed by Richmond and originally applied to dielectric bodies in free space. The approximate solution of the integral equation for the total electric field is performed by discretizing the dielectric body and reducing the equation itself to a linear system. The computation of the coefficients of this latter system involves the evaluation and multiple integration of the suitable dyadic Green's function. Through some analytical considerations and the use of efficient automatic integrators, a computational time reduction is obtained.

6 citations

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21 Sep 2020

6 citations

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02 Sep 2004TL;DR: In this article, a numerical process to model singular vector physical quantities associated to at least a body (E), with possible local singular behavior of the physical quantities that may assume unlimited values in the singularity region, is described.

Abstract: Numerical process to model singular vector physical quantities associated to at least a body (E), with possible local singular behavior of the physical quantities that may assume unlimited values in the singularity region. According to this invention this process is characterized by the following operations: to scan (10) the geometry of the singularity region and to plot it with a reference frame; to subdivide the singularity region into two dimensional domains, usually curvilinear; and; to describe with reference to these domains the properties of at least a physical quantity directly in the parent domain, deriving the singular curl conforming basis functions and the singular divergence conforming basis functions for meshed domains with (T, TE, TV) triangles and (Q) quadrilaterals, usually curvilinear. Besides this process allows for the definition of particular set of singular basis functions for FEM and MoM applications (figure 1).

5 citations

01 Jan 2003

TL;DR: Graglia et al. as mentioned in this paper presented higher-order singular curland divergenceconforming bases on curved triangular and quadrilateral elements, directly defined in their parent space, which can be used for any order.

Abstract: Curl-conforming functions are useful in the FEM solution of the transverse vector Helmholtz equation, whereas divergence-conforming functions are used in the Moments Method solution of surface integral equations. This work improves on the results of a previous work (R.D. Graglia, G. Lombardi, 2002 IEEE AP-S Symp. Digest, vol. I, pp. 62-65) and presents higher-order singular curland divergenceconforming bases on curved triangular and quadrilateral elements, directly defined in their parent space. The method used to construct such bases is simple and general, and can be used for any order. Several issues are addressed including completeness of the bases and number of degrees of freedom. Our bases incorporate the edge condition and are able to approximate the unknown field components in the neighborhood of the edge of a wedge for any order of the singularity coefficient ν, that is supposed given and known a priori. The wedge can be penetrable in the curl-conforming case, while it is supposed metallic in the divergence conforming case. For metal wedges of aperture angle α, one has ν = π/(2π − α). Our curl (divergence) conforming singular functions are compatible with standard p-th order vector functions in adjacent elements (R.D. Graglia, D.R. Wilton and A.F. Peterson, IEEE Trans. Antennas Propagat., vol. 45, no. 3, pp. 329–342, 1997), and guarantee tangential (normal) continuity along the edges of the elements allowing for the discontinuity of normal (tangential) components, adequate modelling of the curl (divergence), and removal of spurious modes (solutions). The Galerkin form of FEM to study with curl-conforming elements a homogeneous circular waveguide of unit radius with a baffle extending to its center has been implemented. The figure reports the relative errors on k2 z for the lowest order TE mode, that at the edge vertex supports singular fields with ν = 1/2.

2 citations

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TL;DR: In this paper, a singular high-order vector base for curved triangular and quadrilateral elements is proposed, which guarantees tangential continuity along the edges of the elements allowing for the discontinuity of normal (tangential) components, adequate modeling of the curl (divergence), and removal of spurious modes (solutions).

Abstract: This paper presents new singular curl- and divergence-conforming vector bases that incorporate the edge conditions. Singular bases complete to arbitrarily high order are described in a unified and consistent manner for curved triangular and quadrilateral elements. The higher order basis functions are obtained as the product of lowest order functions and Silvester-Lagrange interpolatory polynomials with specially arranged arrays of interpolation points. The completeness properties are discussed and these bases are proved to be fully compatible with the standard, high-order regular vector bases used in adjacent elements. The curl (divergence) conforming singular bases guarantee tangential (normal) continuity along the edges of the elements allowing for the discontinuity of normal (tangential) components, adequate modeling of the curl (divergence), and removal of spurious modes (solutions). These singular high-order bases should provide more accurate and efficient numerical solutions of both surface integral and differential problems. Sample numerical results confirm the faster convergence of these bases on wedge problems.

89 citations

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03 Jun 2014

TL;DR: In this article, a 3D spatial model of the diffracting structure is provided and the computed spectral information for the model is compared with the measured spectral information of the structure.

Abstract: Provided are scatterometry techniques for evaluating a 3D diffracting structure. In one embodiment, a method involves providing a 3D spatial model of the diffracting structure and discretizing the model into a 3D spatial mesh. The method includes approximating 3D fields for each element of the 3D mesh using 3D spatial basis functions and generating a matrix including coefficients of the 3D spatial basis functions approximating the fields. The coefficients of the 3D spatial basis functions are computed and used in computing spectral information for the model. The computed spectral information for the model is compared with measured spectral information for the diffracting structure. If the model is a good model fit, the method involves determining a physical characteristic of the diffracting structure based on the model of the diffracting structure.

22 citations

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13 Feb 2013

TL;DR: In this article, the authors proposed a 3D electromagnetic field simulation method based on a periodic structure of a non-matching grid, which has the advantages that under the condition that the grid is not limited at all, the high-frequency characteristic of the periodic structure can be accurately and quickly calculated.

Abstract: The invention relates to a three-dimensional electromagnetic field simulation method based on a periodic structure of a non-matching grid. The three-dimensional electromagnetic field simulation method comprises the following steps of: selecting a specific microwave pipe high-frequency circuit with a periodic characteristic; modeling by capturing a structure with a periodic length from the high-frequency circuit selected in the step A, and building a geometric structure model corresponding to the high-frequency structure with the periodic length; determining a main face and a slave face according to the periodicity of the geometric structure model, performing grid division on the built geometric structure model, and transforming the continuous geometric structure space into a discrete grid space; and generating a combined face grid according to a master face grid and a slave face grid in a simulation region. The three-dimensional electromagnetic field simulation method has the advantages that under the condition that the grid is not limited at all, the high-frequency characteristic of the periodic structure can be accurately and quickly calculated.

9 citations

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TL;DR: In this paper, the authors present the modern state of the WienerHopf factorization method and its generalizations, and the main constructive results for matrix WFH problems are presented, approximate methods a...

Abstract: This paper reviews the modern state of the WienerHopf factorization method and its generalizations. The main constructive results for matrix WienerHopf problems are presented, approximate methods a...

6 citations

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TL;DR: A numerical simulator based on the discrete dipole approximation was developed, validated, and subsequently used to compute scattering from root structures modeled by an ensemble of buried cylinders that quantifies the potential for false alarms and increased clutter due to buried roots.

Abstract: It is widely acknowledged that tree roots and other forms of buried biomass can have an adverse effect on the performance of ground-penetrating radars (GPRs). In this paper, we present analyses that examine that effect for ground-contacting GPR systems. A test site containing extensive root infiltration at Eglin Air Force Base, Florida, was excavated, and the root structure and soil were thoroughly characterized. A numerical simulator based on the discrete dipole approximation, which is an integral-equation-based method, was developed, validated, and subsequently used to compute scattering from root structures modeled by an ensemble of buried cylinders. An examination of the results is presented that quantifies the potential for false alarms and increased clutter due to buried roots.

6 citations