FFT and multigrid accelerated integral equation solvers for multi-scale electromagnetic analysis in complex backgrounds

textNovel integral-equation methods for efficiently solving electromagnetic problems that involve more than a single length scale of interest in complex backgrounds are presented. Such multi-scale electromagnetic problems arise because of the interplay of two distinct factors: the structure under study and the background medium. Both can contain material properties (wavelengths/skin depths) and geometrical features at different length scales, which gives rise to four types of multi-scale problems: (1) twoscale, (2) multi-scale structure, (3) multi-scale background, and (4) multi-scale-squared problems, where a single-scale structure resides in a different single-scale background, a multi-scale structure resides in a single-scale background, a single-scale structure resides in a multi-scale background, and a multi-scale structure resides in a multi-scale background, respectively. Electromagnetic problems can be further categorized in terms of the relative values of the length scales that characterize the structure and the background medium as (a) high-frequency, (b) low-frequency, and (c) mixed-frequency problems, where the wavelengths/skin depths in the background medium, the structure’s geometrical features or internal wavelengths/skin depths, and a combination of these three factors dictate the field variations on/in the structure, respectively. This dissertation presents several problems arising from geophysical exploration and microwave chemistry that demonstrate the different types of multi-scale problems encountered in electromagnetic analysis and the computational challenges they pose. It also presents novel frequency-domain integral-equation methods with proper Green function kernels for solving these multi-scale problems. These methods avoid meshing the background medium and finding fields in an extended computational domain outside the structure, thereby resolving important complications encountered in type 3 and 4 multi-scale problems that limit alternative methods. Nevertheless, they have been of limited practical use because of their high computational costs and because most of the existing ‘fast integral-equation algorithms’ are not applicable to complex Green function kernels. This dissertation introduces novel FFT, multigrid, and FFT-truncated multigrid algorithms that reduce the computational costs of frequency-domain integral-equation methods for complex backgrounds and enable the solution of unprecedented type 3 and 4 multi-scale problems. The proposed algorithms are formulated in detail, their computational costs are analyzed theoretically, and their features are demonstrated by solving benchmark and challenging multi-scale problems.Electrical and Computer Engineerin

An open-source implementation for full-wave 2D scattering by million-wavelength-size objects

In this contribution, we demonstrate that recent improvements in "fast methods" allow for fully error-controlled full-wave simulations of two-dimensional objects with sizes over a million wavelengths using relatively simple computing environments. We review how a fully scalable parallel version of the Multilevel Fast Multipole Algorithm (MLFMA) is obtained to accelerate a two-dimensional boundary integral equation for the scattering by multiple large dielectric and/or perfectly conducting objects. Several complex and large-scale examples demonstrate the capabilities of the algorithm. This implementation is available as open source under GPL license (http://www.openfmm.net)

The Unified-FFT Method for Fast Solution of Integral Equations as Applied to Shielded-Domain Electromagnetics

Electromagnetic (EM) solvers are widely used within computer-aided design (CAD) to improve and ensure success of circuit designs. Unfortunately, due to the complexity of Maxwell\u27s equations, they are often computationally expensive. While considerable progress has been made in the realm of speed-enhanced EM solvers, these fast solvers generally achieve their results through methods that introduce additional error components by way of geometric approximations, sparse-matrix approximations, multilevel decomposition of interactions, and more. This work introduces the new method, Unified-FFT (UFFT). A derivative of method of moments, UFFT scales as O(N log N), and achieves fast analysis by the unique combination of FFT-enhanced matrix fill operations (MFO) with FFT-enhanced matrix solve operations (MSO). In this work, two versions of UFFT are developed, UFFT-Precorrected (UFFT-P) and UFFT-Grid Totalizing (UFFT-GT). UFFT-P uses precorrected FFT for MSO and allows the use of basis functions that do not conform to a regular grid. UFFT-GT uses conjugate gradient FFT for MSO and features the capability of reducing the error of the solution down to machine precision. The main contribution of UFFT-P is a fast solver, which utilizes FFT for both MFO and MSO. It is demonstrated in this work to not only provide simulation results for large problems considerably faster than state of the art commercial tools, but also to be capable of simulating geometries which are too complex for conventional simulation. In UFFT-P these benefits come at the expense of a minor penalty to accuracy. UFFT-GT contains further contributions as it demonstrates that such a fast solver can be accurate to numerical precision as compared to a full, direct analysis. It is shown to provide even more algorithmic efficiency and faster performance than UFFT-P. UFFT-GT makes an additional contribution in that it is developed not only for planar geometries, but also for the case of multilayered dielectrics and metallization. This functionality is particularly useful for multi-layered printed circuit boards (PCBs) and integrated circuits (ICs). Finally, UFFT-GT contributes a 3D planar solver, which allows for current to be discretized in the z-direction. This allows for similar fast and accurate simulation with the inclusion of some 3D features, such as vias connecting metallization planes

Incomplete-Leaf Multilevel Fast Multipole Algorithm for Multiscale Penetrable Objects Formulated with Volume Integral Equations

Recently introduced incomplete-leaf (IL) tree structures for multilevel fast multipole algorithm (referred to as IL-MLFMA) is proposed for the analysis of multiscale inhomogeneous penetrable objects, in which there are multiple orders of magnitude differences among the mesh sizes. Considering a maximum Schaubert-Wilton-Glisson function population threshold per box, only overcrowded boxes are recursively divided into proper smaller boxes, leading to IL tree structures consisting of variable box sizes. Such an approach: 1) significantly reduces the CPU time for near-field calculations regarding overcrowded boxes, resulting a superior efficiency in comparison with the conventional MLFMA where fixed-size boxes are used and 2) effectively reduces the computational error of the conventional MLFMA for multiscale problems, where the protrusion of the basis/testing functions from their respective boxes dramatically impairs the validity of the addition theorem. Moreover, because IL-MLFMA is able to use deep levels safely and without compromising the accuracy, the memory consumption is significantly reduced compared with that of the conventional MLFMA. Several examples are provided to assess the accuracy and the efficiency of IL-MLFMA for multiscale penetrable objects. © 2017 IEEE

A comprehensive comparison of FFT-accelerated integral equation methods vs. FDTD for bioelectromagnetics

textThe performance of two FFT-accelerated integral equation methods--the adaptive integral method (AIM) and GMRES-FFT--and the finite-difference time-domain (FDTD) method are systematically compared for their use in bioelectromagnetic (BioEM) analysis. The comparison involves four steps: (i) A BioEM benchmark is developed. The power absorbed by a human model illuminated by an impressed time-harmonic source is selected as the problem of interest. The benchmark consists of three inhomogeneous models (a multilayered spherical head phantom, an anatomical male, and an anatomical female model), two types of models (pixel or surface based), two types of sources (far or near), and three frequencies in the UHF band (402 MHz, 900 MHz, and 2.45 GHz). (ii) Error and cost measures are identified: The total power absorbed, the power absorbed in different tissues, and the absorbed power density are compared to either analytical results or results from other methods. The peak memory requirement and computation time of the simulations are recorded. (iii) The benchmark problems are solved using each method with optimized parameters. (iv) Plots of results, errors, and computational costs are presented and the tradeoff between increased accuracy and cost is quantified for each method. The data show that when surface-based models can be used AIM generally outperforms GMRES-FFT and FDTD: AIM achieves lower errors at the same computational cost or costs less to achieve the same error. When restricted to pixel-based models, however, FDTD generally outperforms GMRES-FFT and AIM: All three methods yield comparable errors, in most cases FDTD is less costly than GMRES-FFT (especially for anatomical models, far sources, and higher frequencies), and GMRES-FFT is slightly less expensive than AIM. These results suggest that for the type of BioEM analysis represented by the benchmark, AIM should be used whenever surface-based models are available and FDTD should be used if only pixel-based models are available.Electrical and Computer Engineerin

Characterisation of magnetic nanostructures for spintronic applications by electron microscopy

The work presented in this PhD thesis concerns the characterisation of the physical structure, composition and domain structure of advanced magnetic materials by electron microscopy within the FP6 European Research Training Network "Spinswitch". In particular the investigations concerned MgO/CoFeB/MgO multilayers to be employed in magnetic sensors (this work was done in collaboration with INESC-MN Lisbon-Portugal); Ni80Fe20/Cu electrodeposited nanowires to be employed as spin transfer torque devices (this work was done in collaboration with NIRDTP Iasi-Romania and University of Salamanca); multilayers with perpendicular anisotropy which represent potential candidates to be employed in the next generation of MRAMs (this work was done in collaboration with Spintec-CEA-Grenoble). Chapter 1 will provide an overview of the physics behind the topics treated during this work and a description of the general motivations of the research carried out. Chapter 2 will provide an overview of all the experimental techniques employed for the fabrication and characterisation of the samples investigated for this research. Chapter 3 aims to present an investigation using conventional transmission electron microscopy (CTEM) and Lorentz microscopy (LTEM) to characterise respectively the physical microstructure and the domain structure of the CoFeB free layer, embedded in a multilayer composed by SiN/MgO(50)/CoFeB(t)/MgO(15), with t from 30 Å down to 14 Å. We carried out first the investigation of the physical structure performed by selected area diffraction and bright field imaging of planar samples and physically the plan view sections show the structure of the films appears similar. The magnetization reversal behaviour observed during Lorentz TEM experiments are found to vary considerably with the CoFeB thickness, with both domain wall formation and magnetisation rotation seen. In the thicker film the behaviour was characteristic of a typical soft magnetic material with uniaxial anisotropy. However the magnetic reversal of the thinner film was more complex. A particular characteristic of the 14 Å CoFeB layer is the variation of domain wall angle seen when varying the orientation of the applied field This wall asymmetry suggests the presence of a unidirectional anisotropic energy term. To assist in the interpretation of these experimental results a modified Stoner–Wohlfarth model has been constructed and calculations have been carried out by using a MATLAB code. The purpose of the project presented in Chapter 4 was the advanced characterisation of multilayered electrodeposited NiFe/Cu nanowires grown in alumina and polycarbonate templates. In particular the objective was the characterisation of the structure and local chemistry of the nanowires by TEM and the classification of nanowire switching deduced by Lorentz microscopy experiments, which are challenging for this specific material system. In order to perform TEM studies on single nanowires, they should be extracted from their template. The chemical etching used to remove the nanowires from the template in addition to issues related to the deposition of Cu, led to nanowires with edge and compositional irregularities, detrimental for their magnetic properties. Indeed, we were not able to classify the nanowire switching and investigate domain walls forming during the reversal process, but we could only observe a change in the magnetising state. A lot of the work described in this chapter deals with the difficulties associated with imaging these challenging nanowires. Issues were discovered that may have resulted from deposition and/or etching for TEM preparation, therefore we do rely heavily on simulations and calculations. The research presented in Chapter 5 will describe the investigation of the reorientation process of the easy axis for two different multilayer systems magnetised out of plane, and the evolution of their domain structure for increasing temperature, and trying to understand the role of the insertion of a Co/Pt/Ni/Pt multilayer from a microscopic point of view. The two multilayers represent the free layer of a perpendicular MTJ (pMTJ) and this study represents a state of development of materials for pMTJs. Experiments were performed by MOKE magnetometry in polar configuration and Lorentz Microscopy in Fresnel mode. Materials were prepared in Spintec-CEA, Grenoble (France) where the MOKE experiments were also carried out, and Lorentz Microscopy experiments were performed in Glasgow. For the first multilayer (with Co/Pt/Ni/Pt) we found that for lower temperatures (25°C - 220°C) the specimen appears to have a strong perpendicular anisotropy. We observed a small scale random domain structure that we can ascribe to perpendicularly magnetised domains. For higher temperatures (220°C - 300°C) we found a behaviour typical of a soft magnetic material magnetised in plane with low anisotropy and high susceptibility. For the second multilayer (without Co/Pt/Ni/Pt), for instrumental reasons, we were not able to investigation of the magnetic behaviour of the specimen for temperatures above 110°C. The magnetisation is out of plane for all the temperatures investigated. The sample develops a different domain structure when the sample is heated below 100°C or above 100°C. In the first case isotropic serpentine domain structure is visible, with a large periodicity, whereas in the second case, an anisotropic stripe domain structure is visible with a small periodicity

Towards a more efficient spectrum usage: spectrum sensing and cognitive radio techniques

The traditional approach of dealing with spectrum management in wireless communications has been through the definition on a license user granted exclusive exploitation rights for a specific frequency.Peer ReviewedPostprint (published version

Numerics of photonic and plasmonic nanostructures with advanced material models

In dieser Arbeit untersuchen wir mehrere Anwendungen von photonischen und plasmonischen Nanostrukturen unter Verwendung zweier verschiedener numerischer Methoden: die Fourier-Moden-Methode (FMM) und ein unstetiges Galerkin-Zeitraumverfahren (discontinuous Galerkin time-domain method, DGTD method). Die Methoden werden für vier verschiedene Anwendungen eingesetzt, die alle eine Materialmodellerweiterung in der Implementierung der Methoden erfordern. Diese Anwendungen beinhalten die Untersuchung von dünnen, freistehenden, periodisch perforierten Goldfilmen. Wir charakterisieren die auftretenden Oberflächenplasmonenpolaritonen durch die Berechnung von Transmissions- und Elektronenenergieverlustspektren, die mit experimentellen Messungen verglichen werden. Dazu stellen wir eine Erweiterung der DGTD-Methode zur Verfügung, die sowohl absorbierende, impedanzangepasste Randschichten als auch Anregung mit geglätteter Ladungsverteilung für materialdurchdringende Elektronenstrahlen beinhaltet. Darüber hinaus wird eine Erweiterung auf nicht-dispersive anisotrope Materialien für eine Formoptimierung einer volldielektrischen magneto-optischen Metaoberfläche verwendet. Diese Optimierung ermöglicht eine verstärkte Faraday-Rotation zusammen mit einer hohen Transmission. Zusätzlich untersuchen wir abstimmbare hyperbolische Metamaterialresonatoren im nahen Infrarot mit Hilfe der FMM. Wir berechnen deren Resonanzen und vergleichen sie mit dem Experiment. Zum Schluss wird die Implementierung eines nichtlinearen Vier-Niveau-System-Materialmodells in der DGTD-Methode verwendet, um die Laserschwellen eines Mikroresonators mit Bragg-Spiegeln zu berechnen. Bei Einführung eines Silbergitters mit variablen Spaltgrößen wird eine defektinduzierte Kontrolle der Laserschwellen ermöglicht. Die Berechnung der vollständigen, zeitaufgelösten Felddynamik innerhalb des Resonator gibt dabei Aufschluss über die beteiligten Lasermoden.In this thesis, we study several applications of photonic and plasmonic nanostructures by employing two different numerical methods: the Fourier modal method (FMM) and discontinuous Galerkin time-domain (DGTD) method. The methods are used for four different applications, all of which require a material model extension for the implementation of the methods. These applications include the investigation of thin, free-standing periodically perforated gold films. We characterize the emerging surface plasmon polaritons by computing both transmittance and electron energy loss spectra, which are compared to experimental measurements. To this end, we provide an extension of the DGTD method, including absorbing stretched coordinate perfectly matched layers as well as excitations with smoothed charge distribution for material-penetrating electron beams. Furthermore, an extension to non-dispersive anisotropic materials is used for shape optimization of an all-dielectric magneto-optic metasurface. This optimization enables an enhanced Faraday rotation along with high transmittance. Additionally, we study tuneable near-infrared hyperbolic metamaterial cavities with the help of the FMM. We compute the cavity resonances and compare them to the experiment. Finally, the implementation of a non-linear four-level system material model in the DGTD method is used to compute lasing thresholds of a distributed Bragg reflector microcavity. Introducing a silver grating with variable gap sizes allows for a defect-induced lasing threshold control. The computation of the full time-resolved field dynamics of the cavity provides information on the involved lasing modes

Electrical performance analysis of high-speed interconnects and circuits by numerical modeling methods

Ph.DDOCTOR OF PHILOSOPH