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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

  • 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.

    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.

  • 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.

    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.

  • 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.

    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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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

  • 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.

    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.

  • Multilevel adaptive cross approximation and direct evaluation method for fast and accurate discretization of electromagnetic integral equations  Open access  awarded activity

     Tamayo Palau, José María
    Department of Signal Theory and Communications, Universitat Politècnica de Catalunya
    Theses

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    El objetivo de esta tesis es dotarse de una metodología de análisis dinámica en el tiempo que permite revalorar permanentemente la problemática de la escasez de agua dulce en función de la oferta y la demanda. Para ello, hemos tenido en cuenta las variaciones de sus factores conductores, y entre ellos sobre todo el de las necesidades en el desarrollo humano. La metodología es de manejo operativo, en la que se puedan introducir de manera rápida y sencilla los cambios en las variables que van a determinar la oferta y la demanda dinámica de agua dulce.La propuesta metodológica se caracteriza por varios puntos clave. En primer lugar, desarrollamos una discusión terminológica y conceptual en la que, a partir del estado del arte actual llegamos a definir los conceptos de la oferta y la demanda dinámica de agua dulce renovable como primer paso fundamental de nuestra metodología, elaborando un glosario terminológico y conceptual propio para este trabajo.A partir de la caracterización de la oferta y la demanda dinámica se analiza el escenario business as usual constatándose y valorándose la gravedad de la situación de los nueve países que forman la región del golfo de Guinea, debida fundamentalmente a la no existencia o a la no implementación de gestión de extracción, distribución y abastecimiento de agua dulce por falta de recursos económicos o voluntades políticas. Nuestro segundo paso metodológico permite corroborar la calificación usual de la situación de estos países como de escasez económica. Para poder cubrir esta etapa de la propuesta metodológica ha sido necesario resolver, también metodológicamente, la muy importante escasez de datos para la mayoría de países en desarrollo.Nuestra propuesta metodológica parte por supuesto de trabajar con la realidad, detectando inconvenientes y limitaciones al aplicarla al caso de estudio de los países de nuestra región. Una de estas limitaciones es claramente la falta de datos necesarios para elaborar nuestros escenarios o para determinar los estándares o confeccionar el nuevo índice; en la medida que se han ido presentando estas circunstancias, hemos recurrido a soluciones metodológicas que nos han permitido estimar nuevos datos a partir de correlaciones y/o extrapolaciones de los datos existentes.El siguiente punto clave y una de las aportaciones principales de este trabajo de propuesta metodológica es a partir de unas determinadas objetivizaciones de estándares de demanda de agua dulce ligados a unos niveles aceptables de bienestar y calidad de vida, reanalizar mediante la construcción y análisis de los escenarios de futuro correspondientes, las posibilidades y debilidades reales de estos países en relación con la escasez de agua dulce.El último punto clave es la elaboración de una propuesta de un índice que nos permite evaluar de forma sintética y rápida la situación de un país o región según el nivel de capacidad para satisfacer demandas de agua dulce correspondientes a un estándar de demanda establecido de forma clara y explícita. Dicho índice nos permite detectar de forma temprana posibles alertas que más allá de una escasez física o económica nos sean útiles (al igual que en el caso de la representación y el análisis de los resultados de los distintos escenarios de futuro) para la toma decisiones, en función de los objetivos pretendidos.La herramienta de apoyo para elaborar las representaciones de los escenarios es, en sí misma, otro elemento instrumental que además de tener una buena resolución de diseño gráfico, debe facilitar los cálculos necesarios para el análisis de los escenarios, así como almacenar la información de forma cómoda y en la que se puedan introducir cambios fácilmente.La metodología es una herramienta objetiva y útil dirigida a responsables políticos y técnicos, estudiosos e investigadores que dé soporte a la toma de decisiones y/o a la visualización de la valoración de la escasez de agua dulce en el marco de un pretendido desarrollo humano sostenible.

    This thesis describes a methodology for dynamic analysis over time that makes it possible to continually re-assess fresh-water scarcity as a function of supply and demand. The methodology takes into account variations in the driving factors, including, most importantly, human-development needs. The methodology can be controlled operationally. Changes in the variables that determine the dynamic fresh-water supply and demand can be entered quickly and easily.Our methodological proposal contains several key points. We begin with a discussion of terminology and concepts. Taking the current state of the art as our starting point, as a fundamental first step in our methodology we define the concepts of dynamic renewable fresh-water supply and demand. We then present a glossary of the terms and concepts used in this thesis.Following the characterisation of dynamic supply and demand, we analyse the "business-as-usual" scenario. We point out the seriousness of the situation in the nine Gulf of Guinea countries. The fundamental reason for this situation is the non-existence or non-implementation of policies aimed at extracting, distributing and supplying fresh water, due to a lack of economic resources or political will. The second step in our methodology is to corroborate the usual description of the situation in these countries, particularly in terms of the economic scarcity that characterises them. To properly complete this stage of the methodology, it has been necessary to find a solution to the inadequacy of the data available in most developing countries.Our proposal works with reality, which involves detecting disadvantages and limitations when applying the methodology in the countries of this particular region. One such limitation, clearly, is the lack of the necessary data for constructing the scenarios, determining the standards and creating the new index; as these circumstances have arisen, we have implemented methodological solutions that have enabled us to estimate new data on the basis of correlations and/or extrapolations of existing data.The next key point is also one of the main contributions of this methodological proposal. We set the goal of achieving certain standards of fresh-water demand based on acceptable levels of welfare and quality of life. Then, by constructing and analysing the corresponding future scenarios, we re-examine the real possibilities and weaknesses of each country as relates to the scarcity of fresh water.The last key point of our proposal is the generation of an index that enables us to evaluate, quickly and synthetically, the situation of a particular country or region on the basis of its capacity to satisfy fresh-water demand in a way that meets a clearly and specifically defined standard. This index enables the early detection of possible problems that go beyond physical or economic scarcity. Like the representation and analysis of the results of the various future scenarios, this early-warning system will enable decisions to be made in accordance with the established goals.The support tool used to generate the representations of the scenarios must have good graphic-design resolution, be able to make the calculations necessary for analysing the scenarios, and store the information in a practical way that allows changes to be entered easily.This methodology is meant to be used by politicians, engineers, scholars and researchers as a useful and objective support tool for decision-making and/or visualising levels of fresh-water scarcity as part of larger efforts to achieve the goal of sustainable human development.

  • Multilevel adaptive cross approximation and direct evaluation method for fast and accurate discretization of electromagnetic inegral equations  Open access

     Tamayo Palau, José María
    Department of Signal Theory and Communications, Universitat Politècnica de Catalunya
    Theses

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    El objetivo de esta tesis es dotarse de una metodología de análisis dinámica en el tiempo que permite revalorar permanentemente la problemática de la escasez de agua dulce en función de la oferta y la demanda. Para ello, hemos tenido en cuenta las variaciones de sus factores conductores, y entre ellos sobre todo el de las necesidades en el desarrollo humano. La metodología es de manejo operativo, en la que se puedan introducir de manera rápida y sencilla los cambios en las variables que van a determinar la oferta y la demanda dinámica de agua dulce.La propuesta metodológica se caracteriza por varios puntos clave. En primer lugar, desarrollamos una discusión terminológica y conceptual en la que, a partir del estado del arte actual llegamos a definir los conceptos de la oferta y la demanda dinámica de agua dulce renovable como primer paso fundamental de nuestra metodología, elaborando un glosario terminológico y conceptual propio para este trabajo.A partir de la caracterización de la oferta y la demanda dinámica se analiza el escenario business as usual constatándose y valorándose la gravedad de la situación de los nueve países que forman la región del golfo de Guinea, debida fundamentalmente a la no existencia o a la no implementación de gestión de extracción, distribución y abastecimiento de agua dulce por falta de recursos económicos o voluntades políticas. Nuestro segundo paso metodológico permite corroborar la calificación usual de la situación de estos países como de escasez económica. Para poder cubrir esta etapa de la propuesta metodológica ha sido necesario resolver, también metodológicamente, la muy importante escasez de datos para la mayoría de países en desarrollo.Nuestra propuesta metodológica parte por supuesto de trabajar con la realidad, detectando inconvenientes y limitaciones al aplicarla al caso de estudio de los países de nuestra región. Una de estas limitaciones es claramente la falta de datos necesarios para elaborar nuestros escenarios o para determinar los estándares o confeccionar el nuevo índice; en la medida que se han ido presentando estas circunstancias, hemos recurrido a soluciones metodológicas que nos han permitido estimar nuevos datos a partir de correlaciones y/o extrapolaciones de los datos existentes.El siguiente punto clave y una de las aportaciones principales de este trabajo de propuesta metodológica es a partir de unas determinadas objetivizaciones de estándares de demanda de agua dulce ligados a unos niveles aceptables de bienestar y calidad de vida, reanalizar mediante la construcción y análisis de los escenarios de futuro correspondientes, las posibilidades y debilidades reales de estos países en relación con la escasez de agua dulce.El último punto clave es la elaboración de una propuesta de un índice que nos permite evaluar de forma sintética y rápida la situación de un país o región según el nivel de capacidad para satisfacer demandas de agua dulce correspondientes a un estándar de demanda establecido de forma clara y explícita. Dicho índice nos permite detectar de forma temprana posibles alertas que más allá de una escasez física o económica nos sean útiles (al igual que en el caso de la representación y el análisis de los resultados de los distintos escenarios de futuro) para la toma decisiones, en función de los objetivos pretendidos.La herramienta de apoyo para elaborar las representaciones de los escenarios es, en sí misma, otro elemento instrumental que además de tener una buena resolución de diseño gráfico, debe facilitar los cálculos necesarios para el análisis de los escenarios, así como almacenar la información de forma cómoda y en la que se puedan introducir cambios fácilmente.La metodología es una herramienta objetiva y útil dirigida a responsables políticos y técnicos, estudiosos e investigadores que dé soporte a la toma de decisiones y/o a la visualización de la valoración de la escasez de agua dulce en el marco de un pretendido desarrollo humano sostenible.

    This thesis describes a methodology for dynamic analysis over time that makes it possible to continually re-assess fresh-water scarcity as a function of supply and demand. The methodology takes into account variations in the driving factors, including, most importantly, human-development needs. The methodology can be controlled operationally. Changes in the variables that determine the dynamic fresh-water supply and demand can be entered quickly and easily.Our methodological proposal contains several key points. We begin with a discussion of terminology and concepts. Taking the current state of the art as our starting point, as a fundamental first step in our methodology we define the concepts of dynamic renewable fresh-water supply and demand. We then present a glossary of the terms and concepts used in this thesis.Following the characterisation of dynamic supply and demand, we analyse the "business-as-usual" scenario. We point out the seriousness of the situation in the nine Gulf of Guinea countries. The fundamental reason for this situation is the non-existence or non-implementation of policies aimed at extracting, distributing and supplying fresh water, due to a lack of economic resources or political will. The second step in our methodology is to corroborate the usual description of the situation in these countries, particularly in terms of the economic scarcity that characterises them. To properly complete this stage of the methodology, it has been necessary to find a solution to the inadequacy of the data available in most developing countries.Our proposal works with reality, which involves detecting disadvantages and limitations when applying the methodology in the countries of this particular region. One such limitation, clearly, is the lack of the necessary data for constructing the scenarios, determining the standards and creating the new index; as these circumstances have arisen, we have implemented methodological solutions that have enabled us to estimate new data on the basis of correlations and/or extrapolations of existing data.The next key point is also one of the main contributions of this methodological proposal. We set the goal of achieving certain standards of fresh-water demand based on acceptable levels of welfare and quality of life. Then, by constructing and analysing the corresponding future scenarios, we re-examine the real possibilities and weaknesses of each country as relates to the scarcity of fresh water.The last key point of our proposal is the generation of an index that enables us to evaluate, quickly and synthetically, the situation of a particular country or region on the basis of its capacity to satisfy fresh-water demand in a way that meets a clearly and specifically defined standard. This index enables the early detection of possible problems that go beyond physical or economic scarcity. Like the representation and analysis of the results of the various future scenarios, this early-warning system will enable decisions to be made in accordance with the established goals.The support tool used to generate the representations of the scenarios must have good graphic-design resolution, be able to make the calculations necessary for analysing the scenarios, and store the information in a practical way that allows changes to be entered easily.This methodology is meant to be used by politicians, engineers, scholars and researchers as a useful and objective support tool for decision-making and/or visualising levels of fresh-water scarcity as part of larger efforts to achieve the goal of sustainable human development.

  • 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.

  • Multilevel adaptive cross approximation (MLACA)

     Tamayo Palau, Jose Maria; Heldring, Alexander; Rius Casals, Juan-manuel
    IEEE transactions on antennas and propagation
    Vol. 59, num. 12, p. 4600-4608
    DOI: 10.1109/TAP.2011.2165476
    Date of publication: 2011-12
    Journal article

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  • A recursive acceleration technique for static potential Green's functions of a rectangular cavity combining image and modal series

     Tamayo Palau, Jose Maria; López-Peña, Sergio; Mattes, Michael; Heldring, Alexander; Rius Casals, Juan-manuel; Mosig, Juan Ramón
    IEEE transactions on microwave theory and techniques
    Vol. 59, num. 3, p. 542-551
    DOI: 10.1109/TMTT.2010.2103088
    Date of publication: 2011-03
    Journal article

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    A hybrid acceleration algorithm for the computation of the static potential Green’s functions of a rectangular cavity is proposed. Similarly to Ewald’s method, it combines the series expansions in terms of images and modes. The main particularity with respect to Ewald resides in the fact that it does not need the evaluation of a nonalgebraic function such as the complementary error function (erfc) while maintaining the rapid convergence of the Ewald technique. Finally, the method requires the computation of eight terms (original source plus seven images) and of several modal series corresponding to bigger cavities, which can be efficiently performed. Numerical results are provided to verify the feasibility of the algorithm, which appears as a promising alternative to the existing methods in the literature.

  • 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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  • 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)

  • Accelerated direct solution of the MoM linear system using block compression and nested factorization

     Heldring, Alexander; Rius Casals, Juan-manuel
    International Conference on Electromagnetics in Advanced Applications
    p. 636-639
    DOI: 10.1109/ICEAA.2011.6046415
    Presentation's date: 2011-09-13
    Presentation of work at congresses

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    A comparison is presented between different algorithms for direct (non-iterative) accelerated solution of the Method of Moments. The alternatives are common block LU factorization and Compressed Block Decomposition (CBD), and their respective nested, or Multi Scale (MS) implementations. The comparison includes theoretical considerations and numerical examples.

  • Block LU decomposition versus partitioned matrix inverse for compressed direct solution of method of moments linear system

     Heldring, Alexander; Rius Casals, Juan-manuel
    Iberian Meeting on Computational Electromagnetics
    p. 9-12
    Presentation's date: 2011-11-02
    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; González Arbesú, José María; Ubeda Farre, Eduardo; Heldring, Alexander; Collado Gomez, Juan Carlos
    Competitive project

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    Fast direct solution of the combined field integral equation  Open access

     Heldring, Alexander; Tamayo Palau, Jose Maria; Rius Casals, Juan-manuel
    URSI Commission B International Symposium on Electromagnetic Theory
    Presentation's date: 2010-08-17
    Presentation of work at congresses

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    The Method of Moments for electromagnetic scattering and radiation problems is often used in conjunction with the EFIE because the EFIE allows the analysis of open surfaces. For electrically large closed surfaces, the CFIE is often much more efficient because it yields a well conditioned impedance matrix. This is particularly important when an iterative solution method is used. This paper compares the EFIE and the CFIE for a novel fast direct (non-iterative) solution method, the Multiscale Compressed Block Decomposition method.

  • 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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  • 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
    Presentation of work at congresses

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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.

  • Comments on "Fast direct solution of method of moments linear system"

     Heldring, Alexander; Rius Casals, Juan-manuel; Tamayo Palau, Jose Maria
    IEEE transactions on antennas and propagation
    Vol. 58, num. 3, p. 1015-1016
    DOI: 10.1109/TAP.2009.2039330
    Date of publication: 2010-03
    Journal article

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    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.

  • Direct MoM solution of electrically large problems with N2 complexity

     Heldring, Alexander; Rius Casals, Juan-manuel; Tamayo Palau, Jose Maria
    European Conference on Antennas and Propagation
    Presentation's date: 2010-04-15
    Presentation of work at congresses

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  • Analysis of numerical integration in the evaluation of hyper-singular integrals in Galerkin surface integral equation formulations via the direct evaluation method

     Tamayo Palau, Jose Maria; Polimeridis, Athanasios G.; Rius Casals, Juan-manuel; Heldring, Alexander; Mosig, Juan Ramón
    European Conference on Antennas and Propagation
    p. 1-5
    Presentation's date: 2010-04-16
    Presentation of work at congresses

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    Compression of the MoM matrix using macrobasis functions with a full-controlable accuracy  Open access

     Tamayo Palau, Jose Maria; Heldring, Alexander; Rius Casals, Juan-manuel
    European Conference on Antennas and Propagation
    Presentation of work at congresses

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    A new accuracy-controlable method for compressing the MoM impedance matrix of an electromagnetic problem based on a basis change plus a truncation with a threshold is presented here. The idea is to switch to singular basis functions, which are defined on relatively large subdomains of the object, representing perfectly the far field of the subdomain and yielding compression for well-separated blocks. Although the construction of the matrix is not computationally efficient compared with other matrix compression methods, it is still quite interesting from a theoretical point of view. Furthermore, it clearly explains certain characteristics of some of those methods, particularly the errors in the solution of those based in pseudoglobal functions.

    Postprint (author’s final draft)

  • 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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    Multilevel adaptive cross approximation (MLACA)  Open access

     Tamayo Palau, Jose Maria; Heldring, Alexander; Rius Casals, Juan-manuel
    2012 IEEE International Symposium on Antennas and Propagation
    p. 1-4
    Presentation of work at congresses

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    In recent years, several methods have been developed for accelerating the iterative solution of the electromagnetic integral equations discretized by Method of Moments (MoM). Most of them are based on the compressibility of parts of the MoM matrix when they correspond to the interaction between two distant boxes. Among them, a promising one is the Adaptive Cross Approximation (ACA) [1] which combined with a SVD recompression achieves very good results, especially for moderately large number of unknowns N. In this paper we propose a multilevel implementation of the ACA leading to a highly enhanced compression rate.

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    On the degrees of freedom in the interaction between sets of elementary scatterers  Open access

     Heldring, Alexander; Tamayo Palau, Jose Maria; Rius Casals, Juan-manuel
    European Conference on Antennas and Propagation
    p. 2413-2416
    Presentation's date: 2009-03
    Presentation of work at congresses

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    A series of numerical experiments has been executed to investigate the number of degrees of freedom in the interaction between large scattering bodies. The relation between degrees of freedom and operating frequency establishes the computational complexity for integral equation methods fast solvers based on matrix block compression. In 2D the theoretical asymptotic relation for large frequency soon becomes clear. On the other hand, in 3D even a tendency towards the asymptotic value fails to appear for bodies of hundreds of wavelengths in diameter.

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    Application of Multilevel Adaptive Cross Approximation (MLACA) to electromagnetic scattering and radiation problems  Open access

     Tamayo Palau, Jose Maria; Heldring, Alexander; Rius Casals, Juan-manuel
    International Conference on Electromagnetics in Advanced Applications
    p. 1-4
    Presentation's date: 2009-09-14
    Presentation of work at congresses

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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
    Presentation of work at congresses

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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
    Presentation of work at congresses

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  • Polynomial Interpolators of variable order for Method of Moments acceleration with the Multilevel Field Interpolation Algorithm (MLFIA)

     Espinosa, Hugo G; Heldring, Alexander; Tamayo Palau, Jose Maria; Rius Casals, Juan-manuel
    IEEE International Antennas and Propagation Symposium
    Presentation of work at congresses

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  • Compressed block-decomposition algorithm for fast capacitance extraction

     Heldring, Alexander; Rius Casals, Juan-manuel; Parron, J; Tamayo Palau, Jose Maria
    IEEE transactions on computer-aided design of integrated circuits and systems
    Vol. 27, num. 2, p. 265-271
    DOI: 10.1109/TCAD.2007.907236
    Date of publication: 2008-02
    Journal article

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  • 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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  • Integration of CBLU Solver in the Finite Array GSM Code

     Rubio, J.; Heldring, Alexander; Rius Casals, Juan-manuel; González, M A; Zapata, J
    European Conference on Antennas and Propagation (EuCAP 2007)
    Presentation of work at congresses

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  • Integration of UPC-UAB Fast Solvers into the Antenna Simulation Software of UNEX-UPM, KUL, UPV and EPFL ACE Partners

     Heldring, Alexander; Rius Casals, Juan-manuel; Tamayo Palau, Jose Maria; Rubio, J.; Zapata, J; Volski, V; Vandenbosh, G; Mattes, M; Valero, A; Parrón, J
    European Conference on Antennas and Propagation (EuCAP 2007)
    Presentation of work at congresses

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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
    Presentation of work at congresses

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  • Analysis of an artifical magnetic reflector using MLMDA

     Parrón, J; Junkin, G; Villarino Villarino, Ramon; Heldring, Alexander; González Arbesú, José María
    V Encuentro Ibérico de Electromagnetismo Computacional
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  • Application of the Multilevel Field Interpolation Algorithm to Large PEC Structures in 2-D

     Espinosa, H G; Heldring, Alexander; Rius Casals, Juan-manuel
    IEEE International Antennas and Propagation Symposium
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  • Multilevel MDA-CBI for Fast Direct Solution of Large Scattering and Radiation Problems

     Heldring, Alexander; Rius Casals, Juan-manuel; Tamayo Palau, Jose Maria; Parrón, J
    IEEE International Antennas and Propagation Symposium
    Presentation of work at congresses

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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
    Presentation of work at congresses

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  • The MDA-SVD Algorithm for Fast Direct or Iterative Solution of Discrete Integral Equations

     Rius Casals, Juan-manuel; Heldring, Alexander; Parron, J; Tamayo Palau, Jose Maria
    European Conference on Antennas and Propagation (EuCAP 2007)
    Presentation of work at congresses

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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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  • The S-Transform and its inverses: Side effects of discretizing and filtering

     Simon, C; Ventosa, S; Schimmel, M; Heldring, Alexander; Danobeitia, J J; Gallart, J; Manuel Lazaro, Antonio
    IEEE transactions on signal processing
    Vol. 55, num. 10, p. 4928-4937
    Date of publication: 2007-10
    Journal article

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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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