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  • Nonconforming discretization of the electric-field integral equation for closed perfectly conducting objects

     Ubeda Farre, Eduardo; Rius Casals, Juan-manuel; Heldring, Alexander
    IEEE transactions on antennas and propagation
    Vol. 62, num. 8, p. 4171-4186
    DOI: 10.1109/TAP.2014.2325954
    Date of publication: 2014-08-01
    Journal article

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    Galerkin implementations of the method of moments (MoM) of the electric-field integral equation (EFIE) have been traditionally carried out with divergence-conforming sets. The normal-continuity constraint across edges gives rise to cumbersome implementations around junctions for composite objects and to less accurate implementations of the combined field integral equation (CFIE) for closed sharp-edged conductors. We present a new MoM-discretization of the EFIE for closed conductors based on the nonconforming monopolar-RWG set, with no continuity across edges. This new approach, which we call "even-surface odd-volumetric monopolar-RWG discretization of the EFIE", makes use of a hierarchical rearrangement of the monopolar-RWG current space in terms of the diver-gence-conforming RWG set and the new nonconforming "odd monopolar-RWG" set. In the matrix element generation, we carry out a volumetric testing over a set of tetrahedral elements attached to the surface triangulation inside the object in order to make the hyper-singular Kernel contributions numerically manageable. We show for several closed sharp-edged objects that the proposed EFIE-implementation shows improved accuracy with respect to the RWG-discretization and the recently proposed volumetric monopolar-RWG discretization of the EFIE. Also, the new formulation becomes free from the electric-field low-frequency breakdown after rearranging the monopolar-RWG basis functions in terms of the solenoidal, Loop, and the nonsolenoidal, Star and "odd monopolar-RWG", components.

    Galerkin implementations of the method of moments (MoM) of the electric-field integral equation (EFIE) have been traditionally carried out with divergence-conforming sets. The normal-continuity constraint across edges gives rise to cumbersome implementations around junctions for composite objects and to less accurate implementations of the combined field integral equation (CFIE) for closed sharp-edged conductors. We present a new MoM-discretization of the EFIE for closed conductors based on the nonconforming monopolar-RWG set, with no continuity across edges. This new approach, which we call

  • On the convergence of the ACA algorithm for radiation and scattering problems

     Heldring, Alexander; Ubeda Farre, Eduardo; Rius Casals, Juan-manuel
    IEEE transactions on antennas and propagation
    Vol. 62, num. 7, p. 3806-3809
    DOI: 10.1109/TAP.2014.2316293
    Date of publication: 2014-07-01
    Journal article

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    The adaptive cross approximation (ACA) algorithm, when used to accelerate the numerical solution of integral equations for radiation and scattering problems, sometimes suffers from inaccuracies. These inaccuracies occur when the ACA convergence criterion, which is based on an approximation of the residual relative error, is prematurely satisfied. This paper identifies the two sources of this problem and proposes adaptations of the algorithm that remedy them.

  • Volumetric testing with wedges for a nonconforming discretization of the Electric-Field Integral Equation

     Ubeda Farre, Eduardo; Rius Casals, Juan-manuel; Heldring, Alexander
    IEEE International Symposium on Antennas and Propagation
    p. 2192-2193
    DOI: 10.1109/APS.2014.6905423
    Presentation's date: 2014-07
    Presentation of work at congresses

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    The discretization in Method of Moments (MoM) of the Electric-Field Integral Equation (EFIE) is traditionally carried out with divergence-conforming sets of basis functions, like the RWG set. This enforces the normal continuity of the current across the edges arising from the discretization and makes the quasi-singular Kernel contributions numerically manageable. However, these MoM-implementations of the EFIE show little flexibility when handling nonconformal meshes, normally arising from from the juxtaposition or interconnection of independent meshes in the modular design of composite objects. A nonconforming discretization of the EFIE is possible if the testing procedure is carried out over volumetric elements attached to the surface triangulation, inside the body. In this paper, we present a new nonconforming discretization of the EFIE, where wedges attached to the source triangles are used as testing volumetric elements.

  • Nonconforming discretization of the Magnetic-Field Integral Equation with volumetric testing

     Ubeda Farre, Eduardo; Rius Casals, Juan-manuel; Heldring, Alexander
    IEEE International Symposium on Antennas and Propagation
    p. 2194-2195
    DOI: 10.1109/APS.2014.6905424
    Presentation's date: 2014-07
    Presentation of work at congresses

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    The RWG-discretization in Method of Moments (MoM) of the Magnetic-Field and Electric-Field Integral Equations (MFIE, EFIE) show evident discrepancy in the computed RCS, especially for small objects with edges and corners. The nonconforming monopolar-RWG discretization of the MFIE exhibits a smaller a deviation with respect to the EFIE. The Combined-Field Integral Equation (CFIE), which arises from the combination of the EFIE and the MFIE, is very often implemented with the RWG basis functions, whereby some accuracy with respect to EFIE is lost too. In this paper, we present a new nonconforming monopolar-RWG discretization of the MFIE, based on testing the magnetic field over small tetrahedral elements attached to the surface, inside the body under analysis. This formulation is compatible with a successful nonconforming discretization of the EFIE with the monopolar-RWG expansion of the current and volumetric testing. This allows the development of a nonconforming discretization of the CFIE.

  • New graphical processing technique for fast shadowing computation in PO surface integral

     Rius Casals, Juan-manuel; Carbo Meseguer, Alexis; Bjerkemo, Jakob; Ubeda Farre, Eduardo; Heldring, Alexander; Mallorqui Franquet, Jordi Joan; Broquetas Ibars, Antoni
    IEEE transactions on antennas and propagation
    Vol. 62, num. 5, p. 2587-2595
    DOI: 10.1109/TAP.2014.2307321
    Date of publication: 2014-05-01
    Journal article

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    This paper presents a new graphical processing technique for fast computation of PO surface integral. In contrast with the original graphical processing approach introduced by the authors in 1993, the new one combines a novel shadowing computation algorithm together with the conventional facet-based Gordon's formula, instead of the pixel-based Asvestas' approximation. The resulting hybrid approach needs more CPU power for very complex radar targets, but is free from the pixel discretization noise inherent to graphical processing. It has the same accuracy as conventional Physical Optics computation, but shadowed facets detection is more than 10 times faster than with the most efficient alternative algorithms of O(N log N) computational cost. © 2014 IEEE.

  • Iterative method of moments solution of problems involving electrically large and concave geometries

     Heldring, Alexander; Rius Casals, Juan-manuel; Ubeda Farre, Eduardo
    International Conference on Electromagnetics in Advanced Applications
    p. 266-269
    DOI: 10.1109/ICEAA.2013.6632235
    Presentation's date: 2013-09-09
    Presentation of work at congresses

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    This paper presents a study of the scaling with frequency (computational complexity) of preconditioned iterative solution, using the Multilevel Fast Multipole Method, of a class of radiation and scattering problems that exhibits particularly slow convergence: problems involving electrically large, open and concave geometries. A comparison is presented between a well-known state of the art preconditioner (ILU) and a recently introduced preconditioning method, the Multiscale Compressed Block Decomposition.

  • Volumetric testing for a nonconforming discretization in method of moments of the electric-field surface integral equation

     Ubeda Farre, Eduardo; Rius Casals, Juan-manuel; Heldring, Alexander
    International Conference on Electromagnetics in Advanced Applications
    p. 121-124
    DOI: 10.1109/ICEAA.2013.6632202
    Presentation's date: 2013-09
    Presentation of work at congresses

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    Implementations in Method of Moments of the Electric-Field Integral Equation (EFIE) are traditionally carried out with divergence-conforming sets, with normal continuity of the current across edges. This gives rise to awkward implementations around junctions in composite dielectric objects. Also, RWG-implementations of the Combined-Field Integral Equation for sharp-edged objects suffer from some loss of accuracy. In this paper, we present a new nonconforming discretization of the EFIE, with no continuity requirements across edges. In the generation of the impedance elements, we employ a volumetric testing over a set of tetrahedral elements attached to the meshed surface to let the hyper-singular Kernel contributions numerically manageable. We show that the decomposition of the current into normally-continuous and discontinuous contributions leads to enhanced accuracy in the computed RCS.

  • Discretization of the EFIE in Method of Moments without continuity of the normal current component across edges

     Ubeda Farre, Eduardo; Rius Casals, Juan-manuel; Heldring, Alexander
    IEEE International Symposium on Antennas and Propagation
    p. 448-449
    DOI: 10.1109/APS.2013.6710885
    Presentation's date: 2013-07-08
    Presentation of work at congresses

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    The discretization in Method of Moments (MoM) of the Electric-Field Integral Equation (EFIE) is traditionally carried out by preserving the continuity of the normal component in the expansion of the current across the edges arising from the discretization. This allows the cancellation of the hyper-singular Kernel contributions arising from the discretization of the EFIE. Divergence-conforming sets, like the RWG set, appear then as suitable choices to generate successful MoM-EFIE implementations. In this paper, we present a novel MoM- discretization of the EFIE with the non-conforming monopolar- RWG basis functions, with jump discontinuities in the expanded normal component of the current. We show with RCS results that the new EFIE implementation shows good agreement with the traditional normal-continuous RWG-implementation.

  • Preconditioning the Electric Field Integral Equation with the MS-CBD method

     Heldring, Alexander; Ubeda Farre, Eduardo; Rius Casals, Juan-manuel
    Iberian Meeting on Computational Electromagnetics
    Presentation's date: 2013-05-14
    Presentation of work at congresses

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    A novel preconditioning scheme for Method of Moment computations is proposed. It consists of an adapted version of an accelerated direct solution method, the Multiscale Compressed Block Decomposition. It is of particular interest for accelerating the convergence of the iterative solution of open problems that are electrically large and exhibit strong concavity. For such problems, when solved with the Multilevel Fast Multipole Algorithm, the convergence is the main efficiency bottleneck. The novel scheme is compared with the de facto standard preconditioner ILU for a representative problem and shown to be considerably more efficient

  • Fast shadowing computation in physical optics surface

     Rius Casals, Juan-manuel; Carbo, Alex; Ubeda Farre, Eduardo; Heldring, Alexander
    Iberian Meeting on Computational Electromagnetics
    Presentation's date: 2013-05-14
    Presentation of work at congresses

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    GRECO code has been updated by replacing the graphical processing technique for computation of Physical Optics surface integral by a hybrid CPU-graphical processing approach. The resulting code needs more CPU power for complex radar targets, but is free from the pixel discretization noise inherent to graphical processing. It has the same accuracy as conventional Physical Optics computation, but is an order of magnitude faster than the most efficient implementations with NlogN shadowed facets detection

    GRECO code has been updated by replacing the graphical processing technique for computation of Physical Optics surface integral by a hybrid CPU-graphical processing approach. The resulting code needs more CPU power for complex radar targets, but is free from the pixel discretization noise inherent to graphical processing. It has the same accuracy as conventional Physical Optics computation, but is an order of magnitude faster than the most efficient implementations with NlogN shadowed facets detection.

  • GRECO Code Rejuvenated: hybrid CPU-graphical processing

     Rius Casals, Juan-manuel; Carbo, Alex; Ubeda Farre, Eduardo; Heldring, Alexander
    European Conference on Antennas and Propagation
    p. 2348-2351
    Presentation's date: 2013-04-10
    Presentation of work at congresses

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    GRECO code has been updated by replacing the graphical processing technique for computation of Physical Optics surface integral by a hybrid CPU-graphical processing approach. The resulting code needs more CPU power for complex radar targets, but is free from the pixel discretization noise inherent to graphical processing. It has the same accuracy as conventional Physical Optics computation, but is an order of magnitude faster than the most efficient implementations with NlogN shadowed facets detection.

  • The multiscale compressed block decomposition as a preconditioner for method of moments computations

     Heldring, Alexander; Ubeda Farre, Eduardo; Rius Casals, Juan-manuel
    European Conference on Antennas and Propagation
    p. 390-393
    Presentation's date: 2013-04-08
    Presentation of work at congresses

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    A new preconditioner for Method of Moments computations is presented. It is based on a direct solver, the Multiscale Compressed Block Decomposition method, which has been adapted to reduce storage requirements and setup time. Numerical experiments show considerable improvement in overall efficiency in comparison with common preconditioners such as Incomplete LU decomposition, in particular for problems involving electrically large, open geometries.

    A new preconditioner for Method of Moments computations is presented. It is based on a direct solver, the Multiscale Compressed Block Decomposition method, which has been adapted to reduce storage requirements and setup time. Numerical experiments show considerable improvement in overall efficiency in comparison with common preconditioners such as Incomplete LU decomposition, in particular for problems involving electrically large, open geometries.

  • Stable discretization of the electric-magnetic field integral equation with the taylor-orthogonal basis functions

     Ubeda Farre, Eduardo; Tamayo Palau, José María; Rius Casals, Juan-manuel; Heldring, Alexander
    IEEE transactions on antennas and propagation
    Vol. 61, num. 3, p. 1484-1490
    DOI: 10.1109/TAP.2012.2227925
    Date of publication: 2013-03
    Journal article

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    We present two new facet-oriented discretizations in method of moments (MoM) of the electric-magnetic field integral equation (EMFIE) with the recently proposed Taylor-orthogonal (TO) and divergence-Taylor-orthogonal (div-TO) basis functions. These new schemes, which we call stable, unlike the recently published divergence TO discretization of the EMFIE, which we call standard, result in impedance matrices with stable condition number in the very low frequency regime. More importantly, we show for sharp-edged objects of moderately small dimensions that the computed RCS with the stable EMFIE schemes show improved accuracy with respect to the standard EMFIE scheme. The computed RCS for the sharp-edged objects tested becomes much closer to the RCS computed with the RWG discretization of the electric-field integral equation (EFIE), which is well-known to provide good RCS accuracy in these cases. To provide best assessment on the relative performance of the several implementations, we have cancelled the main numerical sources of error in the RCS computation: (i) we implement the EMFIE so that the non-null static quasi-solenoidal current does not contribute in the far-field computation; (ii) we compute with machine-precision the strongly singular Kernel-contributions in the impedance elements with the direct evaluation method.

    We present two new facet-oriented discretizations in method of moments (MoM) of the electric-magnetic field integral equation (EMFIE) with the recently proposed Taylor-orthogonal (TO) and divergence-Taylor-orthogonal (div-TO) basis functions. These new schemes, which we call stable, unlike the recently published divergence TO discretization of the EMFIE, which we call standard, result in impedance matrices with stable condition number in the very low frequency regime. More importantly, we show for sharp-edged objects of moderately small dimensions that the computed RCS with the stable EMFIE schemes show improved accuracy with respect to the standard EMFIE scheme. The computed RCS for the sharp-edged objects tested becomes much closer to the RCS computed with the RWG discretization of the electric-field integral equation (EFIE), which is well-known to provide good RCS accuracy in these cases. To provide best assessment on the relative performance of the several implementations, we have cancelled the main numerical sources of error in the RCS computation: (i) we implement the EMFIE so that the non-null static quasi-solenoidal current does not contribute in the far- field computation; (ii) we compute with machine-precision the strongly singular Kernel-contributions in the impedance elements with the direct evaluation method.

  • Accelerated direct solution of the method-of-moments linear system

     Heldring, Alexander; Tamayo Palau, José María; Ubeda Farre, Eduardo; Rius Casals, Juan-manuel
    Proceedings of the IEEE
    Vol. 101, num. 2, p. 364-371
    DOI: 10.1109/JPROC.2012.2193369
    Date of publication: 2013-02
    Journal article

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    This paper addresses the direct (noniterative) solution of the method-of-moments (MoM) linear system, accelerated through block-wise compression of the MoM impedance matrix. Efficient matrix block compression is achieved using the adaptive cross-approximation (ACA) algorithm and the truncated singular value decomposition (SVD) postcompression. Subsequently, a matrix decomposition is applied that preserves the compression and allows for fast solution by backsubstitution. Although not as fast as some iterative methods for very large problems, accelerated direct solution has several desirable features, including: few problem-dependent parameters; fixed time solution avoiding convergence problems; and high efficiency for multiple excitation problems [e.g., monostatic radar cross section (RCS)]. Emphasis in this paper is on the multiscale compressed block decomposition (MS-CBD) algorithm, introduced by Heldring , which is numerically compared to alternative fast direct methods. A new concise proof is given for the N2 computational complexity of the MS-CBD. Some numerical results are presented, in particular, a monostatic RCS computation involving 1 043 577 unknowns and 1000 incident field directions, and an application of the MS-CBD to the volume integral equation (VIE) for inhomogeneous dielectrics.

  • Sparsified adaptive cross approximation algorithm for accelerated method of moments computations

     Heldring, Alexander; Tamayo Palau, José María; Simon, Carine; Ubeda Farre, Eduardo; Rius Casals, Juan-manuel
    IEEE transactions on antennas and propagation
    Vol. 61, num. 1, p. 240-246
    DOI: 10.1109/TAP.2012.2215292
    Date of publication: 2013-01
    Journal article

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    This paper presents a modification of the adaptive cross approximation (ACA) algorithm for accelerated solution of the Method of Moments linear system for electrically large radiation and scattering problems. As with ACA, subblocks of the impedance matrix that represent the interaction between well separated subdomains are substituted by ¿compressed¿ approximations allowing for reduced storage and accelerated iterative solution. The modified algorithm approximates the original subblocks with products of sparse matrices, constructed with the aid of the ACA algorithm and of a sub-sampling of the original basis functions belonging to either subdomain. Because of the sampling, an additional error is introduced with respect to ACA, but this error is controllable. Just like ordinary ACA, sparsified ACA is kernel-independent and needs no problem-specific information, except for the topology of the basis functions. As a numerical example, RCS computations of the NASA almond are presented, showing an important gain in efficiency. Furthermore, the numerical experiment reveals a computational complexity close to N logN for sparsified ACA for a target electrical size of up to 50 wavelengths.

    This paper presents a modification of the adaptive cross approximation (ACA) algorithm for accelerated solution of the Method of Moments linear system for electrically large radiation and scattering problems. As with ACA, subblocks of the impedance matrix that represent the interaction between well separated subdomains are substituted by “compressed” approximations allowing for reduced storage and accelerated iterative solution. The modified algorithm approximates the original subblocks with products of sparse matrices, constructed with the aid of the ACA algorithm and of a sub-sampling of the original basis functions belonging to either subdomain. Because of the sampling, an additional error is introduced with respect to ACA, but this error is controllable. Just like ordinary ACA, sparsified ACA is kernel-independent and needs no problem-specific information, except for the topology of the basis functions. As a numerical example, RCS computations of the NASA almond are presented, showing an important gain in efficiency. Furthermore, the numerical experiment reveals a computational complexity close to N logN for sparsified ACA for a target electrical size of up to 50 wavelengths.

  • Stable discretization of the electric-magnetic field integral equation with the divergence Taylor-Orthogonal basis functions

     Ubeda Farre, Eduardo; Tamayo Palau, Jose Maria; Rius Casals, Juan-manuel
    IEEE International Symposium on Antennas and Propagation
    DOI: 10.1109/APS.2012.6348616
    Presentation's date: 2012-07-12
    Presentation of work at congresses

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  • Discretization of surface integral equations using conforming and non-conforming basis functions

     Ubeda Farre, Eduardo; Ylä-Oijala, Pasi; Tamayo Palau, Jose Maria; Kiminki, Sami P.; Rius Casals, Juan-manuel; Järvenpää, Seppo
    IEEE International Symposium on Antennas and Propagation
    Presentation's date: 2012-07-11
    Presentation of work at congresses

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  • Discretization of the electric-magnetic field integral equation with the divergence Taylor-Orthogonal basis functions free from the magnetic-field and the electric-field low-frequency breakdowns

     Ubeda Farre, Eduardo; Tamayo Palau, Jose Maria; Rius Casals, Juan-manuel
    European Conference on Antennas and Propagation
    p. 707-711
    DOI: 10.1109/EuCAP.2012.6206631
    Presentation's date: 2012
    Presentation of work at congresses

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  • Sparsified ACA for accelerated iterative solution of the MoM linear system

     Heldring, Alexander; Rius Casals, Juan-manuel; Ubeda Farre, Eduardo; Tamayo Palau, Jose Maria
    Iberian Meeting on Computational Electromagnetics
    p. 13-15
    Presentation's date: 2011-11-02
    Presentation of work at congresses

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    A new algorithm, the Sparsified Adaptive Cross Approximation (SPACA) is presented for fast iterative solution of the Method of Moments linear system. Like ordinary ACA, it is a completely kernel-independent method, but it is faster and yields a higher compression rate than ordinary ACA, without compromising the accuracy. As an example, the RCS of a perfectly conducting sphere is computed using up to 786,432 basis functions. It is shown that SPACA exhibits close to NlogN complexity for this problem.

    Postprint (author’s final draft)

  • Divergence-conforming discretization of second-kind integral equations for the RCS computation in the Rayleigh frequency region

     Ubeda Farre, Eduardo; Rius Casals, Juan-manuel
    Radio science
    Vol. 46, num. 5, p. 1-10
    DOI: 10.1029/2010RS004550
    Date of publication: 2011-09-15
    Journal article

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  • Divergence-Taylor-Orthogonal basis functions for the discretization of second-kind surface integral equations in the Method of Moments

     Ubeda Farre, Eduardo; Tamayo Palau, Jose Maria; Rius Casals, Juan-manuel
    Computational Electromagnetics International Workshop
    p. 8-12
    DOI: 10.1109/CEM.2011.6047318
    Presentation's date: 2011-08-11
    Presentation of work at congresses

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  • Facet-Oriented Discretization of the Electric-Magnetic Field Integral Equation for the accurate scattering analysis of perfectly conducting sharp-edged objects

     Tamayo Palau, Jose Maria; Ubeda Farre, Eduardo; Rius Casals, Juan-manuel
    IEEE International Symposium on Antennas and Propagation
    p. 194-196
    DOI: 10.1109/APS.2011.5996675
    Presentation's date: 2011-07-04
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  • Zeroth-Order Complete Discretizations of Integral-Equation formulations involving conducting or dielectric objects at very low frequencies

     Ubeda Farre, Eduardo; Tamayo Palau, José María; Rius Casals, Juan-manuel; Heldring, Alexander
    IEEE transactions on antennas and propagation
    Vol. 59, num. 7, p. 2735-2741
    DOI: 10.1109/TAP.2011.2152316
    Date of publication: 2011-05-10
    Journal article

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  • Discretization of the Electric-Magnetic field integral equation with the Divergence-Taylor-Orthogonal basis functions

     Ubeda Farre, Eduardo; Tamayo Palau, Jose Maria; Rius Casals, Juan-manuel
    European Conference on Antennas and Propagation
    p. 2613-2617
    Presentation's date: 2011-04-11
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  • Multiscale compressed block decomposition for fast direct solution of method of moments linear system

     Heldring, Alexander; Rius Casals, Juan-manuel; Tamayo Palau, Jose Maria; Parrón, Josep; Ubeda Farre, Eduardo
    IEEE transactions on antennas and propagation
    Vol. 59, num. 2, p. 526-536
    DOI: 10.1109/TAP.2010.2096385
    Date of publication: 2011-02
    Journal article

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    The multiscale compressed block decomposition algorithm (MS-CBD) is presented for highly accelerated direct (non iterative) solution of electromagnetic scattering and radiation problems with the method of moments (MoM). The algorithm is demonstrated to exhibit N2 computational complexity and storage requirements scaling with N 3.5, for electrically large objects. Several numerical examples illustrate the efficiency of the method, in particular for problems with multiple excitation vectors. The largest problem presented in this paper is the monostatic RCS of the NASA almond at 50 GHz, for one thousand incidence angles, discretized using 442,089 RWG basisf unctions. Being entirely algebraic, MS-CBD is independent of the Greens function of the problem.

  • Taylor-orthogonal basis functions for the discretization in method of moments of second kind integral equations in the scattering analysis of perfectly conducting or dielectric objects  Open access

     Ubeda Farre, Eduardo; Tamayo Palau, José María; Rius Casals, Juan-manuel
    Progress in electromagnetics research (PIER)
    Vol. 119, p. 85-105
    DOI: 10.2528/PIER11051715
    Date of publication: 2011
    Journal article

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    We present new implementations in Method of Moments of two types of second kind integral equations: (i) the recently proposed Electric-Magnetic Field Integral Equation (EMFIE), for perfectly conducting objects, and (ii) the Müller formulation, for homogeneous or piecewise homogeneous dielectric objects. We adopt the Taylor-orthogonal basis functions, a recently presented set of facet-oriented basis functions, which, as we show in this paper, arise from the Taylor's expansion of the current at the centroid of the discretization triangles. We show that the Taylor-orthogonal discretization of the EMFIE mitigates the discrepancy in the computed Radar Cross Section observed in conventional divergence-conforming implementations for moderately small, perfectly conducting, sharp-edged objects. Furthermore, we show that the Taylor-discretization of the Müller-formulation represents a valid option for the analysis of sharp-edged homogenous dielectrics, especially with low dielectric contrasts, when compared with other RWG-discretized implementations for dielectrics. Since the divergence-Taylor Orthogonal basis functions are facet-oriented, they appear better suited than other, edge-oriented, discretization schemes for the analysis of piecewise homogenous objects since they simplify notably the discretization at the junctions arising from the intersection of several dielectric regions.

  • Simulation of shipborne small HF antennas with RWG discretization and fast solver

     Rius Casals, Juan-manuel; Jofre Roca, Luis; Tamayo Palau, Jose Maria; Heldring, Alexander; Ubeda Farre, Eduardo
    IEEE International Conference on Wireless Information Technology and Systems
    DOI: 10.1109/ICWITS.2010.5611892
    Presentation's date: 2010-09-01
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    In this paper, an alternative approach has been used to analyze an electrically small antenna (1.2m in the 2-30 MHz band) in a large ship (238m length) using a generic EFIE simulation code with Rao, Wilton and Glisson (RWG) basis functions, with the minimum necessary modifications to tackle the lowfrequency and multiscale issues that lead to a very poorly conditioned linear system.

  • New electric-magnetic field integral equation for the scattering analysis of perfectly conducting sharp-edged objects at very low or extremely low frequencies

     Ubeda Farre, Eduardo; Rius Casals, Juan-manuel
    IEEE International Symposium on Antennas and Propagation
    DOI: 10.1109/APS.2010.5561038
    Presentation's date: 2010-07-14
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  • Very accurate computation of the impedance elements on the discretization of the magnetic field integral equation with the orthogonal basis functions  Open access

     Tamayo Palau, Jose Maria; Ubeda Farre, Eduardo; Polimeridis, Athanasios G.; Rius Casals, Juan-manuel; Mosig, Juan Ramón
    Iberian Meeting on Computational Electromagnetics
    p. 48-52
    Presentation's date: 2010-05-19
    Presentation of work at congresses

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    We show a novel integrating technique, the direct evaluation method, that provides maximum accuracy in the computation of the MFIE-interactions between neighboring noncoplanar basis functions sharing an edge or a vertex of the discretization. Unlike the previous techniques, this strategy requires no extraction of quasi-singular terms from the Kernel and accounts for both inner- and outer-integrals. We show that the recently proposed discretization of the MFIE with orthogonal facet-oriented basis functions provide best accuracy in the RCS computation of objects with small electrical dimensions when compared with other conventional basis functions sets.

  • Accelerated direct solution of the MoM-VIE for dielectric scatterers  Open access

     Heldring, Alexander; Tamayo Palau, Jose Maria; Rius Casals, Juan-manuel; Ubeda Farre, Eduardo
    Iberian Meeting on Computational Electromagnetics
    p. 25-29
    Presentation's date: 2010-05-19
    Presentation of work at congresses

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    The Multiscale Compressed Block Decomposition algorithm (MS-CBD), a direct (non-iterative) linear solver, is applied to accelerate the solution of the MoM-VIE formulation for dielectric scatterers. Numerical solutions are presented for problems with several hundreds of thousands of unknowns. Asymptotically (with respect to the electrical size of the problem), the solution time scales with the number of unknowns squared. The numerical examples confirm this theoretical value.

  • Software framework for integration of method of moments kernels with direct or iterative fast solvers

     Rius Casals, Juan-manuel; Herrero, J. A.; Tamayo Palau, Jose Maria; Heldring, Alexander; Ubeda Farre, Eduardo; Parrón, Josep; López-Peña, Sergio; Polimeridis, Athanasios G.; Mosig, Juan Ramón; Espinosa, Hugo; Boag, Amir
    European Conference on Antennas and Propagation
    p. 1-2
    Presentation's date: 2010-04-15
    Presentation of work at congresses

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  • Orthogonal basis functions for the discretization of the Magnetic-field Integral Equation in the low frequency regime

     Ubeda Farre, Eduardo; Tamayo Palau, Jose Maria; Rius Casals, Juan-manuel
    European Conference on Antennas and Propagation
    p. 1-4
    Presentation's date: 2010-04-15
    Presentation of work at congresses

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  • TECNOLOGIA Y NUEVAS TECNICAS DE DISEÑO PARA INTEGRACION EN CHIP DE CABECERAS DE MICROONDAS

     Mateu Mateu, Jordi; Ubeda Farre, Eduardo; González Arbesú, José María; Heldring, Alexander; Collado Gomez, Juan Carlos
    Competitive project

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  • Framework for integration of fast solvers in method of moments kernels

     Rius Casals, Juan-manuel; Tamayo Palau, Jose Maria; Heldring, Alexander; Parrón, Josep; Ubeda Farre, Eduardo
    LEMA-EPFL Workshop on Integral Techniques for Electromagnetics
    Presentation's date: 2009-09-08
    Presentation of work at congresses

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  • Zeroth-order divergence-complete discretizations of the EFIE at very low frequencies  Open access

     Ubeda Farre, Eduardo; Tamayo Palau, Jose Maria; Rius Casals, Juan-manuel
    Computational Electromagnetics Workshop
    p. 1-4
    Presentation's date: 2009-07-20
    Presentation of work at congresses

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    We present the Self-Loop basis functions, an edge-oriented divergence-conforming set with zero charge density. These basis functions allow a rearrangement of the Linear-linear basis functions set to overcome the low-frequency breakdown of the Electric-field Integral Equation.

  • Novel self-loop basis functions for the stability of the Linear-linear discretization of the Electric Field Integral Equation at very low frequencies  Open access

     Tamayo Palau, Jose Maria; Ubeda Farre, Eduardo; Rius Casals, Juan-manuel
    IEEE International Symposium on Antennas and Propagation
    p. 2619-2622
    DOI: 10.1109/APS.2009.5172153
    Presentation's date: 2009-06
    Presentation of work at congresses

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    A self-loop basis functions is presented, a new set of solenoidal basis functions, which, together with the loop-star basis functions, define a rearrangement of the LL-discretization in method of moments of the EFIE that results in a stable impedance matrix at very low frequencies.

  • Fast iterative solution of integral equations with method of moments and matrix decomposition algorithm - Singular value decomposition

     Rius Casals, Juan-manuel; Parron, J; Heldring, Alexander; Ubeda Farre, Eduardo; Tamayo Palau, Jose Maria
    IEEE transactions on antennas and propagation
    Vol. 56, num. 8, p. 2314-2324
    DOI: 10.1109/TAP.2008.926762
    Date of publication: 2008-09
    Journal article

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  • Comments on ¿The Use of Curl-Conforming Basis Functions for the Magnetic-Field Integral Equation¿

     Ubeda Farre, Eduardo; Rius Casals, Juan-manuel
    IEEE transactions on antennas and propagation
    Vol. 56, num. 7, p. 2142
    DOI: 10.1109/TAP.2008.924781 10.1109/TAP.2008.924777
    Date of publication: 2008-07
    Journal article

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  • RCS convergence versus the number of unknowns and very low frequency behavior of the Galerkin MFIE discretizations of sharp-edged objects with monopolar RWG and nxRWG basis functions

     Ubeda Farre, Eduardo; Rius Casals, Juan-manuel
    IEEE International Antennas and Propagation Symposium
    Presentation of work at congresses

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  • Survey on the RCS convergence for discretizations in Method of Moments of Integral Equations with planar rectangular basis functions

     Ubeda Farre, Eduardo; Rius Casals, Juan-manuel
    IEEE International Antennas and Propagation Symposium
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  • Multiscale CBD for Fast Direct Solution of MoM Linear System

     Heldring, Alexander; Tamayo Palau, Jose Maria; Rius Casals, Juan-manuel; Parrón, J; Ubeda Farre, Eduardo
    IEEE International Antennas and Propagation Symposium
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  • Progress in MoM Solution of Electromagnetic Scattering and Radiation at UPC AntennaLab

     Heldring, Alexander; Tamayo Palau, Jose Maria; Ubeda Farre, Eduardo; Rius Casals, Juan-manuel
    VI Encuentro Ibérico de Electromagnetismo Computacional
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  • Fast Direct Solution of MoM linear system

     Heldring, Alexander; Tamayo Palau, Jose Maria; Ubeda Farre, Eduardo; Rius Casals, Juan-manuel
    IEEE transactions on antennas and propagation
    Vol. 55, num. 11, p. 3220-3228
    Date of publication: 2007-11
    Journal article

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  • Accurate computation of the impedance elements of the magnetic-field integral equation with RWG basis functions through field-domain and source-domain integral swapping

     Ubeda Farre, Eduardo; Heldring, Alexander; Rius Casals, Juan-manuel
    Microwave and optical technology letters
    Vol. 49, num. 3, p. 709-712
    Date of publication: 2007-03
    Journal article

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  • Advances in Numerical Electromagnetics at UPC AntennaLab

     Ubeda Farre, Eduardo; Heldring, Alexander; Rius Casals, Juan-manuel; Espinosa, H; Tamayo Palau, Jose Maria; Parron, J
    Computational Electromagnetics Workshop
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  • Advances in Numerical Electromagnetics at UPC and UAB

     Heldring, Alexander; Ubeda Farre, Eduardo; Rius Casals, Juan-manuel; Espinosa, H; Tamayo Palau, Jose Maria; Parrón, J
    V Encuentro Ibérico de Electromagnetismo Computacional
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  • Better RCS-Performance of the MFIE Discretization with Monopolar RWG and Monopolar Linear-Linear Basis Functions than with their Dipolar Counterparts

     Ubeda Farre, Eduardo; Rius Casals, Juan-manuel
    IEEE International Antennas and Propagation Symposium
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  • Efficient computation of the effect of wire ends in thin wire analysis  Open access

     Heldring, Alexander; Ubeda Farre, Eduardo; Rius Casals, Juan-manuel
    IEEE transactions on antennas and propagation
    Vol. 54, num. 10, p. 3034-3037
    Date of publication: 2006-10
    Journal article

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    Computationally efficient algorithms are presented for the computation of the effect of flat wire ends (end caps) in the common thin wire model. A uniform charge distribution over the surface of the end cap is assumed, and the full or exact kernel of the electric field integral equation formulation for cylindrical wires is used. The algorithms have been implemented in a highly efficient, low order, full kernel method of moments code for the analysis of relatively thick wire antennas and scatterers. The extra computational cost of including the end cap effect is small. The code has been applied to the analysis of a thick linear dipole and the results correspond very well with those of a recently published study using a much more computationally expensive implementation of the magnetic field integral equation with high order discretization methods.

  • Miniaturización y mejora de cabeceras de radiofrecuencia mediante el uso de nuevos materiales y metamateriales

     Collado Gomez, Juan Carlos; Heldring, Alexander; Santos Blanco, María Concepción; O'callaghan Castella, Juan Manuel; Ubeda Farre, Eduardo; González Arbesú, José María; Mateu Mateu, Jordi
    Competitive project

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