Novel 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. / text

Polyetherimide/(Ba0.8Sr0.2)(Ti0.9Zr0.1)O3 (PEI/BSTZ8291) composites are fabricated using PEI, dispersant, solvents, and BSTZ powder. The effects of the content of BSTZ8291 filler on the chemical, physical, mechanical and dielectric properties of PEI/BSTZ8291 composites are studied in this paper. As the content of BSTZ filler increases from 10 wt% to 70 wt%, the relative permittivity of PEI/BSTZ8291 composites at 1 MHz increase from 2.58 to 17.71. The measurement of relative permittivity of PEI/BSTZ8291 composites is developed using the ¡§Rectangular Cavity Resonator¡¨ method from 1 GHz to 13.5 GHz. The relative permittivity is calculated by observing the frequencies of resonant cavity modes. The relative permittivity of PEI/BSTZ8291 composites is almost unchanged as the measured frequency increases from 1 GHz to 13.5 GHz. The presented characteristics are better than those of polymer/BaTiO3 composites. The improvement in the tensile strength of PEI/BSTZ8291 composites may be caused by the increased interactions between neat PEI and BSTZ8291 ceramic powder, and no phase separation phenomenon occurred. The Young¡¦s modulus of the PEI/BSTZ8291 composites is improved by about 58% as the content of BSTZ8291 filler from 0 to 50 wt% and the elongation at break of the composites decreases as the content of BSTZ8291 filler increases, indicating that the composite becomes somewhat brittle as compared with neat PEI. PEI/BSTZ8291 composite substrates are developed for the applications of circularly polarized (CP) antennas. A CP antenna with a simple structure is developed as the ultra high frequency (UHF) band radio frequency identification (RFID) reader application. The fabricated antenna has an impedance bandwidth spanning from 901 to 949 MHz, which covers the entire band of Taiwan UHF-RFID frequency. The measured return loss, Smith chart, axial ratio, radiation patterns and CP gain characteristics of antennas fabricated on PEI/BSTZ8291 composites are excellent in the band of Taiwan UHF-RFID frequency. It is demonstrated that the CP antenna fabricated on PEI/BSTZ substrate has the better characteristics and small size than those fabricated on FR4 substrate.