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Papers by Roberto Graglia

Institution of Engineering and Technology eBooks, Mar 15, 2016

In science and engineering, one is often required to provide the value fi reached by the quantity... more In science and engineering, one is often required to provide the value fi reached by the quantity f (s) at si out of the knowledge of n samples fk =f (sk) obtained for k = 1,2,... , n, with sk≠si for all k. This is an interpolation problem if si is located within the same range defined by the n isolated points sk and an extrapolation problem whenever si is outside of this range. The interpolation problem is a particular case of the more general curve fitting (or approximation) problem where the function f(s) re-constructed out of the discrete set of known data points goes exactly through these data points. The task of interpolating a function is closely related to the problem of representing an unknown function f(s) within a numerical solution procedure.

IEEE Transactions on Antennas and Propagation, Jul 1, 2012

New curl-conforming hierarchical vector basis functions are developed for quadrilateral and hexah... more New curl-conforming hierarchical vector basis functions are developed for quadrilateral and hexahedral cells. These bases are constructed from orthogonal polynomials and are shown to maintain superior linear independence as their polynomial order is increased. The procedure for constructing these basis functions is described and general expressions are provided for an arbitrary order.

IEEE journal on multiscale and multiphysics computational techniques, 2016

Scalar and vector basis functions have been developed that permit accurate modeling of singularit... more Scalar and vector basis functions have been developed that permit accurate modeling of singularities in electromagnetic fields at geometric edges and corners. This review attempts to organize the different types of functions, to summarize what philosophies have been used in their development, and help identify future work needed in this area.

Institution of Engineering and Technology eBooks, Mar 15, 2016

To demonstrate the use of vector bases developed in preceding chapters, here we consider their us... more To demonstrate the use of vector bases developed in preceding chapters, here we consider their use in numerical solutions of the electric field integral equation (EFIE) for scattering from three-dimensional perfectly conducting objects, and the vector Helmholtz equation for modeling fields within three-dimensional cavities. The EFIE operator involves a divergence of the surface current density, and therefore the MoM or boundary element procedure will be illustrated in conjunction with divergence-conforming basis functions. Since the vector Helmholtz operator involves the curl operator, it will be treated using the finite element method in conjunction with curl-conforming bases. Select numerical results are presented for illustration, and the treatment of curved cells is described. Some of the following has been adapted from [1].

The multilevel nonuniform-grid (MLNG) algorithm, which belongs to the class of "fast" a... more The multilevel nonuniform-grid (MLNG) algorithm, which belongs to the class of "fast" algorithms, is adapted for solving three-dimensional electromagnetic scattering problems. This makes it possible to extend the range of rigorous simulation to significantly higher frequencies and scatterer's sizes than those available for “conventional” methods.

2021 International Conference on Electromagnetics in Advanced Applications (ICEAA), 2021

Singular edge and corner basis functions are incorporated into an integral equation numerical for... more Singular edge and corner basis functions are incorporated into an integral equation numerical formulation for the charge density on parallel-plate capacitors. The underlying representation for charge density is either piecewise constant, linear, or quadratic and provided by conventional representation. The singular edge basis functions are shown to play a significant role in accelerating the convergence of the numerical solutions. When used in conjunction with linear or quadratic underlying representations, the singular corner basis functions have a relatively minor effect on the numerical results.

2022 International Conference on Electromagnetics in Advanced Applications (ICEAA)

1987 IEEE International Symposium on Electromagnetic Compatibility, 1987

Voltages and currents induced in a multiconductor line by a, nuclear electromagnetic pulse (NEMP)... more Voltages and currents induced in a multiconductor line by a, nuclear electromagnetic pulse (NEMP) are determined. The finite conductivity of the terrain is taken into, account by introducing a new theory leading to the definition of the complex images of the wires. End voltages and currents at the loads are obtained through the transmission line formalism. These expressions are then cast in a rather enlightening form, well suited for the transient analysis. The solution proposed, with additional assumptions, leads to closed form results, which are also useful to test numerical codes.

IEEE Journal on Multiscale and Multiphysics Computational Techniques

Successful three-dimensional finite element codes for Maxwell's equations must include and deal w... more Successful three-dimensional finite element codes for Maxwell's equations must include and deal with all four types of geometrical shapes: tetrahedra, bricks, prisms, and quadrangularbased pyramids. However, pyramidal elements have so far been used very rarely because the basis functions associated with them have complicated expression, are complex in derivation, and have never been comprehensively validated. We recently published a simpler procedure for constructing higher-order vector bases for pyramid elements, so here we fill a gap by discussing a whole set of test case results that not only validate our new curl-conforming bases for pyramids, but which enable validation of other codes that use pyramidal elements for finite element method applications. The solutions of the various test cases are obtained using either higher order elements or multipyramidal meshes or both. Furthermore, the results are always compared with the solutions obtained with classical tetrahedral meshes using higher order bases. This allows us to verify that purely pyramidal meshes and elements give numerical results of comparable accuracy to those obtained with multitetrahedral meshes that use elements of the same order, essentially requiring the same number of degrees of freedom. The various results provided here also show that higher order vector bases always guarantee a superior convergence of the numerical results as the number of degrees of freedom increases. Index Terms-Electromagnetic fields, finite-element methods, higher order vector elements, pyramidal elements, numerical analysis.

Abstract The scattering of a plane electromagnetic wave by a disk-sphere metallic target is studi... more Abstract The scattering of a plane electromagnetic wave by a disk-sphere metallic target is studied via several approaches: separation of variables, method of moments, high-frequency techniques, and measurements in anechoic chamber. The results obtained by the different methods are compared and discussed.

New families of hierarchical curl and divergence-conforming vector bases for the most commonly us... more New families of hierarchical curl and divergence-conforming vector bases for the most commonly used two — and three-dimensional cells are directly constructed from orthogonal scalar polynomials to enhance their linear independence, which is a simpler process than an orthogonalization applied to the final vector functions. These functions span the mixed-order (or reduced) spaces of Nédélec and can be used to deal with structures meshed by a mixture of cells of different geometry.

Priority Data: TO2003A000675 05.09.2003 IT Pub. No.: WO/2005/024674 International Application No.... more Priority Data: TO2003A000675 05.09.2003 IT Pub. No.: WO/2005/024674 International Application No.: PCT/IB2004/002856 Publication Date: 17.03.2005 International Filing Date: 02.09.2004 http://www.wipo.int/pctdb/en/wo.jsp?WO=2005024674

Institution of Engineering and Technology eBooks, Mar 15, 2016

In science and engineering, one is often required to provide the value fi reached by the quantity... more In science and engineering, one is often required to provide the value fi reached by the quantity f (s) at si out of the knowledge of n samples fk =f (sk) obtained for k = 1,2,... , n, with sk≠si for all k. This is an interpolation problem if si is located within the same range defined by the n isolated points sk and an extrapolation problem whenever si is outside of this range. The interpolation problem is a particular case of the more general curve fitting (or approximation) problem where the function f(s) re-constructed out of the discrete set of known data points goes exactly through these data points. The task of interpolating a function is closely related to the problem of representing an unknown function f(s) within a numerical solution procedure.

IEEE Transactions on Antennas and Propagation, Jul 1, 2012

New curl-conforming hierarchical vector basis functions are developed for quadrilateral and hexah... more New curl-conforming hierarchical vector basis functions are developed for quadrilateral and hexahedral cells. These bases are constructed from orthogonal polynomials and are shown to maintain superior linear independence as their polynomial order is increased. The procedure for constructing these basis functions is described and general expressions are provided for an arbitrary order.

IEEE journal on multiscale and multiphysics computational techniques, 2016

Scalar and vector basis functions have been developed that permit accurate modeling of singularit... more Scalar and vector basis functions have been developed that permit accurate modeling of singularities in electromagnetic fields at geometric edges and corners. This review attempts to organize the different types of functions, to summarize what philosophies have been used in their development, and help identify future work needed in this area.

Institution of Engineering and Technology eBooks, Mar 15, 2016

To demonstrate the use of vector bases developed in preceding chapters, here we consider their us... more To demonstrate the use of vector bases developed in preceding chapters, here we consider their use in numerical solutions of the electric field integral equation (EFIE) for scattering from three-dimensional perfectly conducting objects, and the vector Helmholtz equation for modeling fields within three-dimensional cavities. The EFIE operator involves a divergence of the surface current density, and therefore the MoM or boundary element procedure will be illustrated in conjunction with divergence-conforming basis functions. Since the vector Helmholtz operator involves the curl operator, it will be treated using the finite element method in conjunction with curl-conforming bases. Select numerical results are presented for illustration, and the treatment of curved cells is described. Some of the following has been adapted from [1].

The multilevel nonuniform-grid (MLNG) algorithm, which belongs to the class of "fast" a... more The multilevel nonuniform-grid (MLNG) algorithm, which belongs to the class of "fast" algorithms, is adapted for solving three-dimensional electromagnetic scattering problems. This makes it possible to extend the range of rigorous simulation to significantly higher frequencies and scatterer's sizes than those available for “conventional” methods.

2021 International Conference on Electromagnetics in Advanced Applications (ICEAA), 2021

Singular edge and corner basis functions are incorporated into an integral equation numerical for... more Singular edge and corner basis functions are incorporated into an integral equation numerical formulation for the charge density on parallel-plate capacitors. The underlying representation for charge density is either piecewise constant, linear, or quadratic and provided by conventional representation. The singular edge basis functions are shown to play a significant role in accelerating the convergence of the numerical solutions. When used in conjunction with linear or quadratic underlying representations, the singular corner basis functions have a relatively minor effect on the numerical results.

2022 International Conference on Electromagnetics in Advanced Applications (ICEAA)

1987 IEEE International Symposium on Electromagnetic Compatibility, 1987

Voltages and currents induced in a multiconductor line by a, nuclear electromagnetic pulse (NEMP)... more Voltages and currents induced in a multiconductor line by a, nuclear electromagnetic pulse (NEMP) are determined. The finite conductivity of the terrain is taken into, account by introducing a new theory leading to the definition of the complex images of the wires. End voltages and currents at the loads are obtained through the transmission line formalism. These expressions are then cast in a rather enlightening form, well suited for the transient analysis. The solution proposed, with additional assumptions, leads to closed form results, which are also useful to test numerical codes.

IEEE Journal on Multiscale and Multiphysics Computational Techniques

Successful three-dimensional finite element codes for Maxwell's equations must include and deal w... more Successful three-dimensional finite element codes for Maxwell's equations must include and deal with all four types of geometrical shapes: tetrahedra, bricks, prisms, and quadrangularbased pyramids. However, pyramidal elements have so far been used very rarely because the basis functions associated with them have complicated expression, are complex in derivation, and have never been comprehensively validated. We recently published a simpler procedure for constructing higher-order vector bases for pyramid elements, so here we fill a gap by discussing a whole set of test case results that not only validate our new curl-conforming bases for pyramids, but which enable validation of other codes that use pyramidal elements for finite element method applications. The solutions of the various test cases are obtained using either higher order elements or multipyramidal meshes or both. Furthermore, the results are always compared with the solutions obtained with classical tetrahedral meshes using higher order bases. This allows us to verify that purely pyramidal meshes and elements give numerical results of comparable accuracy to those obtained with multitetrahedral meshes that use elements of the same order, essentially requiring the same number of degrees of freedom. The various results provided here also show that higher order vector bases always guarantee a superior convergence of the numerical results as the number of degrees of freedom increases. Index Terms-Electromagnetic fields, finite-element methods, higher order vector elements, pyramidal elements, numerical analysis.

Abstract The scattering of a plane electromagnetic wave by a disk-sphere metallic target is studi... more Abstract The scattering of a plane electromagnetic wave by a disk-sphere metallic target is studied via several approaches: separation of variables, method of moments, high-frequency techniques, and measurements in anechoic chamber. The results obtained by the different methods are compared and discussed.

New families of hierarchical curl and divergence-conforming vector bases for the most commonly us... more New families of hierarchical curl and divergence-conforming vector bases for the most commonly used two — and three-dimensional cells are directly constructed from orthogonal scalar polynomials to enhance their linear independence, which is a simpler process than an orthogonalization applied to the final vector functions. These functions span the mixed-order (or reduced) spaces of Nédélec and can be used to deal with structures meshed by a mixture of cells of different geometry.

Priority Data: TO2003A000675 05.09.2003 IT Pub. No.: WO/2005/024674 International Application No.... more Priority Data: TO2003A000675 05.09.2003 IT Pub. No.: WO/2005/024674 International Application No.: PCT/IB2004/002856 Publication Date: 17.03.2005 International Filing Date: 02.09.2004 http://www.wipo.int/pctdb/en/wo.jsp?WO=2005024674