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 ANTENNALAB  Antennas and Wireless Systems Laboratory
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 Castelldefels School of Telecommunications and Aerospace Engineering (EETAC)
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New graphical processing technique for fast shadowing computation in PO surface integral
Rius Casals, Juanmanuel; 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. 25872595
DOI: 10.1109/TAP.2014.2307321
Date of publication: 20140501
Journal article
Read the abstract View Share Reference managersThis 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 facetbased Gordon's formula, instead of the pixelbased 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.
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 facetbased Gordon's formula, instead of the pixelbased 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. 
Nonconforming discretization of the electricfield integral equation for closed perfectly conducting objects
Ubeda Farre, Eduardo; Rius Casals, Juanmanuel; Heldring, Alexander
IEEE transactions on antennas and propagation
Vol. 62, num. 8, p. 41714186
DOI: 10.1109/TAP.2014.2325954
Date of publication: 20140801
Journal article
Read the abstract View Share Reference managersGalerkin implementations of the method of moments (MoM) of the electricfield integral equation (EFIE) have been traditionally carried out with divergenceconforming sets. The normalcontinuity 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 sharpedged conductors. We present a new MoMdiscretization of the EFIE for closed conductors based on the nonconforming monopolarRWG set, with no continuity across edges. This new approach, which we call "evensurface oddvolumetric monopolarRWG discretization of the EFIE", makes use of a hierarchical rearrangement of the monopolarRWG current space in terms of the divergenceconforming RWG set and the new nonconforming "odd monopolarRWG" 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 hypersingular Kernel contributions numerically manageable. We show for several closed sharpedged objects that the proposed EFIEimplementation shows improved accuracy with respect to the RWGdiscretization and the recently proposed volumetric monopolarRWG discretization of the EFIE. Also, the new formulation becomes free from the electricfield lowfrequency breakdown after rearranging the monopolarRWG basis functions in terms of the solenoidal, Loop, and the nonsolenoidal, Star and "odd monopolarRWG", components.
Galerkin implementations of the method of moments (MoM) of the electricfield integral equation (EFIE) have been traditionally carried out with divergenceconforming sets. The normalcontinuity 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 sharpedged conductors. We present a new MoMdiscretization of the EFIE for closed conductors based on the nonconforming monopolarRWG set, with no continuity across edges. This new approach, which we call 
Stable discretization of the electricmagnetic field integral equation with the taylororthogonal basis functions
Ubeda Farre, Eduardo; Tamayo Palau, José María; Rius Casals, Juanmanuel; Heldring, Alexander
IEEE transactions on antennas and propagation
Vol. 61, num. 3, p. 14841490
DOI: 10.1109/TAP.2012.2227925
Date of publication: 201303
Journal article
Read the abstract View Share Reference managersWe present two new facetoriented discretizations in method of moments (MoM) of the electricmagnetic field integral equation (EMFIE) with the recently proposed Taylororthogonal (TO) and divergenceTaylororthogonal (divTO) 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 sharpedged 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 sharpedged objects tested becomes much closer to the RCS computed with the RWG discretization of the electricfield integral equation (EFIE), which is wellknown 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 nonnull static quasisolenoidal current does not contribute in the farfield computation; (ii) we compute with machineprecision the strongly singular Kernelcontributions in the impedance elements with the direct evaluation method.
We present two new facetoriented discretizations in method of moments (MoM) of the electricmagnetic field integral equation (EMFIE) with the recently proposed Taylororthogonal (TO) and divergenceTaylororthogonal (divTO) 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 sharpedged 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 sharpedged objects tested becomes much closer to the RCS computed with the RWG discretization of the electricfield integral equation (EFIE), which is wellknown 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 nonnull static quasisolenoidal current does not contribute in the far field computation; (ii) we compute with machineprecision the strongly singular Kernelcontributions in the impedance elements with the direct evaluation method. 
Accelerated direct solution of the methodofmoments linear system
Heldring, Alexander; Tamayo Palau, José María; Ubeda Farre, Eduardo; Rius Casals, Juanmanuel
Proceedings of the IEEE
Vol. 101, num. 2, p. 364371
DOI: 10.1109/JPROC.2012.2193369
Date of publication: 201302
Journal article
Read the abstract View Share Reference managersThis paper addresses the direct (noniterative) solution of the methodofmoments (MoM) linear system, accelerated through blockwise compression of the MoM impedance matrix. Efficient matrix block compression is achieved using the adaptive crossapproximation (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 problemdependent 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 (MSCBD) 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 MSCBD. 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 MSCBD to the volume integral equation (VIE) for inhomogeneous dielectrics.
This paper addresses the direct (noniterative) solution of the methodofmoments (MoM) linear system, accelerated through blockwise compression of the MoM impedance matrix. Efficient matrix block compression is achieved using the adaptive crossapproximation (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 problemdependent 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 (MSCBD) 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 MSCBD. 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 MSCBD 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, Juanmanuel
IEEE transactions on antennas and propagation
Vol. 61, num. 1, p. 240246
DOI: 10.1109/TAP.2012.2215292
Date of publication: 201301
Journal article
Read the abstract View Share Reference managersThis 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 subsampling 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 kernelindependent and needs no problemspecific 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 subsampling 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 kernelindependent and needs no problemspecific 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. 
Dispositivos pasivos avanzados para cabezales multibanda, multimodo
Ubeda Farre, Eduardo
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Iterative method of moments solution of problems involving electrically large and concave geometries
Heldring, Alexander; Rius Casals, Juanmanuel; Ubeda Farre, Eduardo
International Conference on Electromagnetics in Advanced Applications
p. 266269
DOI: 10.1109/ICEAA.2013.6632235
Presentation's date: 20130909
Presentation of work at congresses
Read the abstract View Share Reference managersThis 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 wellknown state of the art preconditioner (ILU) and a recently introduced preconditioning method, the Multiscale Compressed Block Decomposition.
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 wellknown 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 electricfield surface integral equation
Ubeda Farre, Eduardo; Rius Casals, Juanmanuel; Heldring, Alexander
International Conference on Electromagnetics in Advanced Applications
p. 121124
DOI: 10.1109/ICEAA.2013.6632202
Presentation's date: 201309
Presentation of work at congresses
Read the abstract View Share Reference managersImplementations in Method of Moments of the ElectricField Integral Equation (EFIE) are traditionally carried out with divergenceconforming sets, with normal continuity of the current across edges. This gives rise to awkward implementations around junctions in composite dielectric objects. Also, RWGimplementations of the CombinedField Integral Equation for sharpedged 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 hypersingular Kernel contributions numerically manageable. We show that the decomposition of the current into normallycontinuous and discontinuous contributions leads to enhanced accuracy in the computed RCS.
Implementations in Method of Moments of the ElectricField Integral Equation (EFIE) are traditionally carried out with divergenceconforming sets, with normal continuity of the current across edges. This gives rise to awkward implementations around junctions in composite dielectric objects. Also, RWGimplementations of the CombinedField Integral Equation for sharpedged 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 hypersingular Kernel contributions numerically manageable. We show that the decomposition of the current into normallycontinuous 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, Juanmanuel; Heldring, Alexander
IEEE International Symposium on Antennas and Propagation
p. 448449
DOI: 10.1109/APS.2013.6710885
Presentation's date: 20130708
Presentation of work at congresses
Read the abstract View Share Reference managersThe discretization in Method of Moments (MoM) of the ElectricField 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 hypersingular Kernel contributions arising from the discretization of the EFIE. Divergenceconforming sets, like the RWG set, appear then as suitable choices to generate successful MoMEFIE implementations. In this paper, we present a novel MoM discretization of the EFIE with the nonconforming 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 normalcontinuous RWGimplementation. 
Preconditioning the Electric Field Integral Equation with the MSCBD method
Heldring, Alexander; Ubeda Farre, Eduardo; Rius Casals, Juanmanuel
Iberian Meeting on Computational Electromagnetics
Presentation's date: 20130514
Presentation of work at congresses
Read the abstract Share Reference managersA 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, Juanmanuel; Carbo, Alex; Ubeda Farre, Eduardo; Heldring, Alexander
Iberian Meeting on Computational Electromagnetics
Presentation's date: 20130514
Presentation of work at congresses
Read the abstract View Share Reference managersGRECO code has been updated by replacing the graphical processing technique for computation of Physical Optics surface integral by a hybrid CPUgraphical 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 CPUgraphical 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, Juanmanuel
European Conference on Antennas and Propagation
p. 390393
Presentation's date: 20130408
Presentation of work at congresses
Read the abstract View Share Reference managersA 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. 
GRECO Code Rejuvenated: hybrid CPUgraphical processing
Rius Casals, Juanmanuel; Carbo, Alex; Ubeda Farre, Eduardo; Heldring, Alexander
European Conference on Antennas and Propagation
p. 23482351
Presentation's date: 20130410
Presentation of work at congresses
Read the abstract View Share Reference managersGRECO code has been updated by replacing the graphical processing technique for computation of Physical Optics surface integral by a hybrid CPUgraphical 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. 
Procedimiento para la incorporación de discontinuidades a través de las aristas en la aproximación de la corriente eléctrica obtenida a través de la discretización de la ecuación integral de campo eléctrico
Ubeda Farre, Eduardo
Date of request: 20130705
Invention patent
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Discretization of surface integral equations using conforming and nonconforming basis functions
Ubeda Farre, Eduardo; YläOijala, Pasi; Tamayo Palau, Jose Maria; Kiminki, Sami P.; Rius Casals, Juanmanuel; Järvenpää, Seppo
IEEE International Symposium on Antennas and Propagation
Presentation's date: 20120711
Presentation of work at congresses
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Stable discretization of the electricmagnetic field integral equation with the divergence TaylorOrthogonal basis functions
Ubeda Farre, Eduardo; Tamayo Palau, Jose Maria; Rius Casals, Juanmanuel
IEEE International Symposium on Antennas and Propagation
DOI: 10.1109/APS.2012.6348616
Presentation's date: 20120712
Presentation of work at congresses
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Discretization of the electricmagnetic field integral equation with the divergence TaylorOrthogonal basis functions free from the magneticfield and the electricfield lowfrequency breakdowns
Ubeda Farre, Eduardo; Tamayo Palau, Jose Maria; Rius Casals, Juanmanuel
European Conference on Antennas and Propagation
p. 707711
DOI: 10.1109/EuCAP.2012.6206631
Presentation's date: 2012
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Divergenceconforming discretization of secondkind integral equations for the RCS computation in the Rayleigh frequency region
Ubeda Farre, Eduardo; Rius Casals, Juanmanuel
Radio science
Vol. 46, num. 5, p. 110
DOI: 10.1029/2010RS004550
Date of publication: 20110915
Journal article
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Taylororthogonal basis functions for the discretization in method of moments of second kind integral equations in the scattering analysis of perfectly conducting or dielectric objects
Ubeda Farre, Eduardo; Tamayo Palau, José María; Rius Casals, Juanmanuel
Progress in electromagnetics research (PIER)
Vol. 119, p. 85105
DOI: 10.2528/PIER11051715
Date of publication: 2011
Journal article
Read the abstract Access to the full text Share Reference managersWe present new implementations in Method of Moments of two types of second kind integral equations: (i) the recently proposed ElectricMagnetic Field Integral Equation (EMFIE), for perfectly conducting objects, and (ii) the Müller formulation, for homogeneous or piecewise homogeneous dielectric objects. We adopt the Taylororthogonal basis functions, a recently presented set of facetoriented 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 Taylororthogonal discretization of the EMFIE mitigates the discrepancy in the computed Radar Cross Section observed in conventional divergenceconforming implementations for moderately small, perfectly conducting, sharpedged objects. Furthermore, we show that the Taylordiscretization of the Müllerformulation represents a valid option for the analysis of sharpedged homogenous dielectrics, especially with low dielectric contrasts, when compared with other RWGdiscretized implementations for dielectrics. Since the divergenceTaylor Orthogonal basis functions are facetoriented, they appear better suited than other, edgeoriented, 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. 
Multiscale compressed block decomposition for fast direct solution of method of moments linear system
Heldring, Alexander; Rius Casals, Juanmanuel; Tamayo Palau, Jose Maria; Parrón, Josep; Ubeda Farre, Eduardo
IEEE transactions on antennas and propagation
Vol. 59, num. 2, p. 526536
DOI: 10.1109/TAP.2010.2096385
Date of publication: 201102
Journal article
Read the abstract View Share Reference managersThe multiscale compressed block decomposition algorithm (MSCBD) 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, MSCBD is independent of the Greens function of the problem. 
ZerothOrder Complete Discretizations of IntegralEquation formulations involving conducting or dielectric objects at very low frequencies
Ubeda Farre, Eduardo; Tamayo Palau, José María; Rius Casals, Juanmanuel; Heldring, Alexander
IEEE transactions on antennas and propagation
Vol. 59, num. 7, p. 27352741
DOI: 10.1109/TAP.2011.2152316
Date of publication: 20110510
Journal article
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Discretization of the ElectricMagnetic field integral equation with the DivergenceTaylorOrthogonal basis functions
Ubeda Farre, Eduardo; Tamayo Palau, Jose Maria; Rius Casals, Juanmanuel
European Conference on Antennas and Propagation
p. 26132617
Presentation's date: 20110411
Presentation of work at congresses
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DivergenceTaylorOrthogonal basis functions for the discretization of secondkind surface integral equations in the Method of Moments
Ubeda Farre, Eduardo; Tamayo Palau, Jose Maria; Rius Casals, Juanmanuel
Computational Electromagnetics International Workshop
p. 812
DOI: 10.1109/CEM.2011.6047318
Presentation's date: 20110811
Presentation of work at congresses
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FacetOriented Discretization of the ElectricMagnetic Field Integral Equation for the accurate scattering analysis of perfectly conducting sharpedged objects
Tamayo Palau, Jose Maria; Ubeda Farre, Eduardo; Rius Casals, Juanmanuel
IEEE International Symposium on Antennas and Propagation
p. 194196
DOI: 10.1109/APS.2011.5996675
Presentation's date: 20110704
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Sparsified ACA for accelerated iterative solution of the MoM linear system
Heldring, Alexander; Rius Casals, Juanmanuel; Ubeda Farre, Eduardo; Tamayo Palau, Jose Maria
Iberian Meeting on Computational Electromagnetics
p. 1315
Presentation's date: 20111102
Presentation of work at congresses
Read the abstract View Share Reference managersA 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 kernelindependent 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) 
TECNOLOGIA Y NUEVAS TECNICAS DE DISEÑO PARA INTEGRACION EN CHIP DE CABECERAS DE MICROONDAS
Mateu Mateu, Jordi; González Arbesú, José María; Heldring, Alexander; Ubeda Farre, Eduardo; Collado Gomez, Juan Carlos
Competitive project
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New electricmagnetic field integral equation for the scattering analysis of perfectly conducting sharpedged objects at very low or extremely low frequencies
Ubeda Farre, Eduardo; Rius Casals, Juanmanuel
IEEE International Symposium on Antennas and Propagation
DOI: 10.1109/APS.2010.5561038
Presentation's date: 20100714
Presentation of work at congresses
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Orthogonal basis functions for the discretization of the Magneticfield Integral Equation in the low frequency regime
Ubeda Farre, Eduardo; Tamayo Palau, Jose Maria; Rius Casals, Juanmanuel
European Conference on Antennas and Propagation
p. 14
Presentation's date: 20100415
Presentation of work at congresses
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Accelerated direct solution of the MoMVIE for dielectric scatterers
Heldring, Alexander; Tamayo Palau, Jose Maria; Rius Casals, Juanmanuel; Ubeda Farre, Eduardo
Iberian Meeting on Computational Electromagnetics
p. 2529
Presentation's date: 20100519
Presentation of work at congresses
Read the abstract Access to the full text Share Reference managersThe Multiscale Compressed Block Decomposition algorithm (MSCBD), a direct (noniterative) linear solver, is applied to accelerate the solution of the MoMVIE 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, Juanmanuel; Herrero, J. A.; Tamayo Palau, Jose Maria; Heldring, Alexander; Ubeda Farre, Eduardo; Parrón, Josep; LópezPeña, Sergio; Polimeridis, Athanasios G.; Mosig, Juan Ramón; Espinosa, Hugo; Boag, Amir
European Conference on Antennas and Propagation
p. 12
Presentation's date: 20100415
Presentation of work at congresses
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Simulation of shipborne small HF antennas with RWG discretization and fast solver
Rius Casals, Juanmanuel; 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: 20100901
Presentation of work at congresses
Read the abstract View Share Reference managersIn this paper, an alternative approach has been used to analyze an electrically small antenna (1.2m in the 230 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. 
Very accurate computation of the impedance elements on the discretization of the magnetic field integral equation with the orthogonal basis functions
Tamayo Palau, Jose Maria; Ubeda Farre, Eduardo; Polimeridis, Athanasios G.; Rius Casals, Juanmanuel; Mosig, Juan Ramón
Iberian Meeting on Computational Electromagnetics
p. 4852
Presentation's date: 20100519
Presentation of work at congresses
Read the abstract Access to the full text Share Reference managersWe show a novel integrating technique, the direct evaluation method, that provides maximum accuracy in the computation of the MFIEinteractions between neighboring noncoplanar basis functions sharing an edge or a vertex of the discretization. Unlike the previous techniques, this strategy requires no extraction of quasisingular terms from the Kernel and accounts for both inner and outerintegrals. We show that the recently proposed discretization of the MFIE with orthogonal facetoriented basis functions provide best accuracy in the RCS computation of objects with small electrical dimensions when compared with other conventional basis functions sets. 
Framework for integration of fast solvers in method of moments kernels
Rius Casals, Juanmanuel; Tamayo Palau, Jose Maria; Heldring, Alexander; Parrón, Josep; Ubeda Farre, Eduardo
LEMAEPFL Workshop on Integral Techniques for Electromagnetics
Presentation's date: 20090908
Presentation of work at congresses
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Zerothorder divergencecomplete discretizations of the EFIE at very low frequencies
Ubeda Farre, Eduardo; Tamayo Palau, Jose Maria; Rius Casals, Juanmanuel
Computational Electromagnetics Workshop
p. 14
Presentation's date: 20090720
Presentation of work at congresses
Read the abstract Access to the full text Share Reference managersWe present the SelfLoop basis functions, an edgeoriented divergenceconforming set with zero charge density. These basis functions allow a rearrangement of the Linearlinear basis functions set to overcome the lowfrequency breakdown of the Electricfield Integral Equation. 
Novel selfloop basis functions for the stability of the Linearlinear discretization of the Electric Field Integral Equation at very low frequencies
Tamayo Palau, Jose Maria; Ubeda Farre, Eduardo; Rius Casals, Juanmanuel
IEEE International Symposium on Antennas and Propagation
p. 26192622
DOI: 10.1109/APS.2009.5172153
Presentation's date: 200906
Presentation of work at congresses
Read the abstract Access to the full text Share Reference managersA selfloop basis functions is presented, a new set of solenoidal basis functions, which, together with the loopstar basis functions, define a rearrangement of the LLdiscretization 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, Juanmanuel; Parron, J; Heldring, Alexander; Ubeda Farre, Eduardo; Tamayo Palau, Jose Maria
IEEE transactions on antennas and propagation
Vol. 56, num. 8, p. 23142324
DOI: 10.1109/TAP.2008.926762
Date of publication: 200809
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Comments on ¿The Use of CurlConforming Basis Functions for the MagneticField Integral Equation¿
Ubeda Farre, Eduardo; Rius Casals, Juanmanuel
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: 200807
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RCS convergence versus the number of unknowns and very low frequency behavior of the Galerkin MFIE discretizations of sharpedged objects with monopolar RWG and nxRWG basis functions
Ubeda Farre, Eduardo; Rius Casals, Juanmanuel
IEEE International Antennas and Propagation Symposium
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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, Juanmanuel
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, Juanmanuel
VI Encuentro Ibérico de Electromagnetismo Computacional
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Multiscale CBD for Fast Direct Solution of MoM Linear System
Heldring, Alexander; Tamayo Palau, Jose Maria; Rius Casals, Juanmanuel; Parrón, J; Ubeda Farre, Eduardo
IEEE International Antennas and Propagation Symposium
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Accurate computation of the impedance elements of the magneticfield integral equation with RWG basis functions through fielddomain and sourcedomain integral swapping
Ubeda Farre, Eduardo; Heldring, Alexander; Rius Casals, Juanmanuel
Microwave and optical technology letters
Vol. 49, num. 3, p. 709712
Date of publication: 200703
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Fast Direct Solution of MoM linear system
Heldring, Alexander; Tamayo Palau, Jose Maria; Ubeda Farre, Eduardo; Rius Casals, Juanmanuel
IEEE transactions on antennas and propagation
Vol. 55, num. 11, p. 32203228
Date of publication: 200711
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Advances in Numerical Electromagnetics at UPC AntennaLab
Ubeda Farre, Eduardo; Heldring, Alexander; Rius Casals, Juanmanuel; 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, Juanmanuel; Espinosa, H; Tamayo Palau, Jose Maria; Parrón, J
V Encuentro Ibérico de Electromagnetismo Computacional
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Preconditioning techniques in the analysis of finite metamaterial slabs
Ubeda Farre, Eduardo; Rius Casals, Juanmanuel; Romeu Robert, Jordi
IEEE transactions on antennas and propagation
Vol. 54, num. 1, p. 265268
Date of publication: 200601
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Read the abstract Access to the full text Share Reference managersIn the method of moments (MoM) electric field integral equation (EFIE) analysis of slabs of metamaterials, we show that a leftpreconditioning scheme by blocks gathering interactions between basis functions belonging to each basic cell of the metamaterial reaches convergence in less iterations and with less computational time than a leftpreconditioner based on discarding interactions between basis functions beyond a given distance. 
Efficient scattering computation for arrays of long thinstrips
Ubeda Farre, Eduardo; Heldring, Alexander; Rius Casals, Juanmanuel
Microwave and optical technology letters
Vol. 48, num. 1, p. 127131
Date of publication: 200601
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Efficient computation of the effect of wire ends in thin wire analysis
Heldring, Alexander; Ubeda Farre, Eduardo; Rius Casals, Juanmanuel
IEEE transactions on antennas and propagation
Vol. 54, num. 10, p. 30343037
Date of publication: 200610
Journal article
Read the abstract Access to the full text Share Reference managersComputationally 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. 
Novel monopolar MFIE MoMDiscretization for the scattering analysis of small objects
Ubeda Farre, Eduardo; Rius Casals, Juanmanuel
IEEE transactions on antennas and propagation
Vol. 54, num. 1, p. 5057
Date of publication: 200601
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Read the abstract Access to the full text Share Reference managersWe present a novel method of moments (MoM)magnetic field integral equation (MFIE) discretization that performs closely to the MoMEFIE in the electromagnetic analysis of moderately small objects. This new MoMMFIE discretization makes use of a new set of basis functions that we name monopolar RaoWiltonGlisson (RWG) and are derived from the RWG basis functions. We show for a wide variety of small objects curved and sharpedgedthat the new monopolar MoMMFIE formulation outperforms the conventional MoMMFIE with RWG basis functions. 
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
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