J. M. Taboada

MLFMA-FFT PARALLEL ALGORITHM FOR THE SO- LUTION OF LARGE-SCALE PROBLEMS IN ELECTRO- MAGNETICS (INVITED PAPER)

MLFMA-FFT PARALLEL ALGORITHM FOR THE SO-LUTION OF LARGE-SCALE PROBLEMS IN ELECTRO-MAGNETICS (INVITED PAPER)J. M. TaboadaDepartment Tecnolog¶‡as de los Computadores y de lasComunicaciones, Escuela Polit¶ecnicaUniversidad de ExtremaduraC¶aceres 10071, SpainM. G. Araujo¶ and J. M. B¶ertoloDepartment Teor¶‡a do Sinal e Comunicaci¶ons, E.T.S.E.Telecomunicaci¶onUniversidade de VigoVigo (Pontevedra) 36310, SpainL. LandesaDepartment Tecnolog¶‡as de los Computadores y de lasComunicaciones, Escuela Polit¶ecnicaUniversidad de ExtremaduraC¶aceres 10071, SpainF. Obelleiro and J. L. RodriguezDepartment Teor¶‡a do Sinal e Comunicaci¶ons, E.T.S.E.Telecomunicaci¶onUniversidade de VigoVigo (Pontevedra) 36310, SpainAbstract|An e–cient hybrid MPI/OpenMP parallel implementationof an innovative approach that combines the Fast Fourier Transform(FFT) and Multilevel Fast Multipole Algorithm (MLFMA) has beensuccessfully used to solve an electromagnetic problem involving 620millions of unknowns. The MLFMA-FFT method can deal withextremely large problems due to its high scalability and its reducedcomputational complexity. The former is provided by the use of the

Method-of-moments formulation for the analysis of plasmonic nano-optical antennas

We present a surface integral equation (SIE) to model the electromagnetic behavior of metallic objects at optical frequencies. The electric and magnetic current combined field integral equation considering both tangential and normal equations is applied. The SIE is solved by using a method-of-moments (MoM) formulation. The SIE-MoM approach is applied only on the material boundary surfaces and interfaces, avoiding the cumbersome volumetric discretization of the objects and the surrounding space required in differential-equation formulations. Some canonical examples have been analyzed, and the results have been compared with analytical reference solutions in order to prove the accuracy of the proposed method. Finally, two plasmonic Yagi-Uda nanoantennas have been analyzed, illustrating the applicability of the method to the solution of real plasmonic problems.

Toward Ultimate Nanoplasmonics Modeling

Advances in the field of nanoplasmonics are hindered by the limited capabilities of simulation tools in dealing with realistic systems comprising regions that extend over many light wavelengths. We show that the optical response of unprecedentedly large systems can be accurately calculated by using a combination of surface integral equation (SIE) method of moments (MoM) formulation and an expansion of the electromagnetic fields in a suitable set of spatial wave functions via fast multipole methods. We start with a critical review of volume versus surface integral methods, followed by a short tutorial on the key features that render plasmons useful for sensing (field enhancement and confinement). We then use the SIE-MoM to examine the plasmonic and sensing capabilities of various systems with increasing degrees of complexity, including both individual and interacting gold nanorods and nanostars, as well as large random and periodic arrangements of ∼1000 gold nanorods. We believe that the present results and methodology raise the standard of numerical electromagnetic simulations in the field of nanoplasmonics to a new level, which can be beneficial for the design of advanced nanophotonic devices and optical sensing structures.

Gold Nanorod–pNIPAM Hybrids with Reversible Plasmon Coupling: Synthesis, Modeling, and SERS Properties

The thermoresponsive optical properties of Au nanorod-doped poly(N-isopropylacrylamide) (Au NR-pNIPAM) microgels with different Au NR payloads and aspect ratios are presented. Since the volume phase transition of pure pNIPAM microgels is reversible, the optical response reversibility of Au NR-pNIPAM hybrids is systematically analyzed. Besides, extinction cross-section and near-field enhancement simulations for Au NR-microgel hybrids are performed using a new numerical method based on the surface integral equation method of moments formulation (M3 solver). Additionally, the Au NR-microgel hybrid systems are expected to serve as excellent broadband surface-enhanced Raman scattering (SERS) substrates due to the temperature-controlled formation of hot spots and the tunable optical properties. The optical enhancing properties related to SERS are tested with three laser lines, evidencing excitation wavelength-dependent efficiency that can be easily controlled by either the aspect ratio (length/width) of the assembled Au NR or by the Au NR payload per microgel. Finally, the SERS efficiency of the prepared Au NR-pNIPAM hybrids is found to be stable for months.

Comparison of surface integral equation formulations for electromagnetic analysis of plasmonic nanoscatterers

The performance of most widespread surface integral equation (SIE) formulations with the method of moments (MoM) are studied in the context of plasmonic materials. Although not yet widespread in optics, SIE-MoM approaches bring important advantages for the rigorous analysis of penetrable plasmonic bodies. Criteria such as accuracy in near and far field calculations, iterative convergence and reliability are addressed to assess the suitability of these formulations in the field of plasmonics.

Surface integral equation formulation for the analysis of left-handed metamaterials

A surface integral equation (SIE) formulation is applied to the analysis of electromagnetic problems involving three-dimensional (3D) piecewise homogenized left-handed metamaterials (LHM). The resulting integral equations are discretized by the well-known method of moments (MoM) and solved via an iterative process. The unknowns are defined only on the interfaces between different media, avoiding the discretization of volumes and surrounding space, which entails a drastic reduction in the number of unknowns arising in the numerical discretization of the equations. Besides, the SIE-MoM formulation inherently includes the radiation condition at infinity, so it is not necessary to artificially include termination absorbing boundary conditions. Some 3D numerical examples are presented to confirm the validity and versatility of this approach on dealing with LHM, also providing some intuitive verifications of the singular properties of these amazing materials.

Optimization of an optical wireless nanolink using directive nanoantennas

Optical connects will become a key point in the next generation of integrated circuits, namely the upcoming nanoscale optical chips. In this context, nano-optical wireless links using nanoantennas have been presented as a promising alternative to regular plasmonic waveguide links, whose main limitation is the range propagation due to the metal absorption losses. In this paper we present the complete design of a high-capability wireless nanolink using matched directive nanoantennas. It will be shown how the use of directive nanoantennas clearly enhances the capability of the link, improving its behavior with respect to non-directive nanoantennas and largely outperforming regular plasmonic waveguide connects.

Solution of large-scale plasmonic problems with the multilevel fast multipole algorithm.

A surface integral equation together with the multilevel fast multipole algorithm is successfully applied to fast and accurate resolution of plasmonic problems involving a large number of unknowns. The absorption, scattering, and extinction efficiencies of several plasmonic gold spheres of increasing size are efficiently obtained solving the electric and magnetic current combined-field integral equation. The numerical predictions are compared with reference analytic results to demonstrate the accuracy, suitability, and capabilities of this approach when dealing with large-scale plasmonic problems.

SUPERCOMPUTER AWARE APPROACH FOR THE SOLUTION OF CHALLENGING ELECTROMAGNETIC PROBLEMS

Abstract|It is a proven fact that The Fast Fourier Transform(FFT) extension of the conventional Fast Multipole Method (FMM)reduces the matrix vector product (MVP) complexity and preservesthe propensity for parallel scaling of the single level FMM. In thispaper, an e–cient parallel strategy of a nested variation of the FMM-FFT algorithm that reduces the memory requirements is presented.The solution provided by this parallel implementation for a challengingproblem with more than 0.5 billion unknowns has constituted the worldrecord in computational electromagnetics (CEM) at the beginning of2009.1. INTRODUCTIONRecent years have seen an increasing efiort in the development of fastand e–cient electromagnetic solutions with a reduced computationalcost regarding the conventional Method of Moments. Among others,the Fast Multipole Method (FMM) [1] and its multilevel version, theMLFMA [2,3] have constituted one of the most important advances inthat context.This development of fast electromagnetic solvers has gone handin hand with the constant advances in computer technology. Dueto this simultaneous growth, overcoming the limits in the scalabilityof the available codes became a priority in order to take advantageof the large amount of computational resources and capabilities thatare available in modern High Performance Computer (HPC) systems.For this reason, works focused on the parallelization improvement ofthe Multilevel Fast Multipole Algorithm (MLFMA) [4{13] have gainedinterest in last years.Besides, the FMM-Fast Fourier Transform (FMM-FFT) deservesbe taken into account as an alternative to beneflt from massivelyparallel distributed computers. This variation of the single-level FMMwas flrst proposed in [14] as an acceleration technique applied to almostplanar surfaces. Later on, a parallelized implementation was applied togeneral three-dimensional geometries [15]. The method uses the FFTto speedup the translation stage resulting in a dramatic reduction ofthe matrix-vector product (MVP) time requirement with respect tothe FMM. Although in general the FMM-FFT is not algorithmically ase–cient as the MLFMA, it has the advantage of preserving the naturalparallel scaling propensity of the single-level FMM in the spectral (

Application of geostatistical techniques to exploitation planning in slate quarries

When planning workings of slate extraction by mechanical means, it is important to know the quality of the rock mass to optimize the results of the cuttings in the extraction bank, because techniques to be used depend on relative percent of first quality or second quality slate. In this paper, a methodology for quality evaluation applied to slate extraction is developed in three phases, as a tool of support to the planning. The first phase consists of defining the geotechnical parameters that affect the bank and to appraise them in the visible faces. The second phase consists of applying multivariate statistical techniques related to discriminant analysis data to evaluate a quality function. This function can be seen as a recovery index of the slate mass, being its variance intervals established in the analyzed faces. The third phase consists of a forecast of the values of the index from visible faces to the inside of the extraction bank, using geostatistics to evaluate the quality of the mass and to plan the mechanical cutting works, in order to get the best results.