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

Microwave Sensing and Imaging

In recent years, microwave sensing and imaging have acquired an ever-growing importance in several applicative fields, such as non-destructive evaluations in industry and civil engineering, subsurface prospection, security, and biomedical imaging. Indeed, microwave techniques allow, in principle, for information to be obtained directly regarding the physical parameters of the inspected targets (dielectric properties, shape, etc.) by using safe electromagnetic radiations and cost-effective systems. Consequently, a great deal of research activity has recently been devoted to the development of efficient/reliable measurement systems, which are effective data processing algorithms that can be used to solve the underlying electromagnetic inverse scattering problem, and efficient forward solvers to model electromagnetic interactions. Within this framework, this Special Issue aims to provide some insights into recent microwave sensing and imaging systems and techniques

Full-wave Nonlinear Inverse Scattering for Acoustic and Electromagnetic Breast Imaging.

Acoustic and electromagnetic full-wave nonlinear inverse scattering techniques are explored in both theory and experiment with the ultimate aim of noninvasively mapping the material properties of the breast. There is evidence that benign and malignant breast tissue have different acoustic and electrical properties and imaging these properties directly could provide higher quality images with better diagnostic certainty. In this dissertation, acoustic and electromagnetic inverse scattering algorithms are first developed and validated in simulation. The forward solvers and optimization cost functions are modified from traditional forms in order to handle the large or lossy imaging scenes present in ultrasonic and microwave breast imaging. An antenna model is then presented, modified, and experimentally validated for microwave S-parameter measurements. Using the antenna model, a new electromagnetic volume integral equation is derived in order to link the material properties of the inverse scattering algorithms to microwave S-parameters measurements allowing direct comparison of model predictions and measurements in the imaging algorithms. This volume integral equation is validated with several experiments and used as the basis of a free-space inverse scattering experiment, where images of the dielectric properties of plastic objects are formed without the use of calibration targets. These efforts are used as the foundation of a solution and formulation for the numerical characterization of a microwave near-field cavity-based breast imaging system. The system is constructed and imaging results of simple targets are given. Finally, the same techniques are used to explore a new self-characterization method for commercial ultrasound probes. The method is used to calibrate an ultrasound inverse scattering experiment and imaging results of simple targets are presented. This work has demonstrated the feasibility of quantitative microwave inverse scattering by way of a self-consistent characterization formalism, and has made headway in the same area for ultrasound.Ph.D.Applied PhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91585/1/mshaynes_1.pd

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

Ph.DDOCTOR OF PHILOSOPH

SPICA:revealing the hearts of galaxies and forming planetary systems : approach and US contributions

How did the diversity of galaxies we see in the modern Universe come to be? When and where did stars within them forge the heavy elements that give rise to the complex chemistry of life? How do planetary systems, the Universe's home for life, emerge from interstellar material? Answering these questions requires techniques that penetrate dust to reveal the detailed contents and processes in obscured regions. The ESA-JAXA Space Infrared Telescope for Cosmology and Astrophysics (SPICA) mission is designed for this, with a focus on sensitive spectroscopy in the 12 to 230 micron range. SPICA offers massive sensitivity improvements with its 2.5-meter primary mirror actively cooled to below 8 K. SPICA one of 3 candidates for the ESA's Cosmic Visions M5 mission, and JAXA has is committed to their portion of the collaboration. ESA will provide the silicon-carbide telescope, science instrument assembly, satellite integration and testing, and the spacecraft bus. JAXA will provide the passive and active cooling system (supporting the

The Apertif Surveys:The First Six Months

Apertif is a new phased-array feed for the Westerbork Synthesis Radio Telescope (WSRT), greatly increasing its field of view and turning it into a natural survey instrument. In July 2019, the Apertif legacy surveys commenced; these are a time-domain survey and a two-tiered imaging survey, with a shallow and medium-deep component. The time-domain survey searches for new (millisecond) pulsars and fast radio bursts (FRBs). The imaging surveys provide neutral hydrogen (HI), radio continuum and polarization data products. With a bandwidth of 300 MHz, Apertif can detect HI out to a redshift of 0.26. The key science goals to be accomplished by Apertif include localization of FRBs (including real-time public alerts), the role of environment and interaction on galaxy properties and gas removal, finding the smallest galaxies, connecting cold gas to AGN, understanding the faint radio population, and studying magnetic fields in galaxies. After a proprietary period, survey data products will be publicly available through the Apertif Long Term Archive (ALTA, https://alta.astron.nl). I will review the progress of the surveys and present the first results from the Apertif surveys, including highlighting the currently available public data