Browsing by Subject "Computational electromagnetics"
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Item A comprehensive comparison of FFT-accelerated integral equation methods vs. FDTD for bioelectromagnetics(2015-05) Massey, Jackson White; Yılmaz, Ali E.; Biros, GeorgeThe 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.Item Fast algorithms for frequency domain wave propagation(2012-12) Tsuji, Paul Hikaru; Ying, Lexing; Ghattas, Omar N.; Engquist, Bjorn; Fomel, Sergey; Ren, KuiHigh-frequency wave phenomena is observed in many physical settings, most notably in acoustics, electromagnetics, and elasticity. In all of these fields, numerical simulation and modeling of the forward propagation problem is important to the design and analysis of many systems; a few examples which rely on these computations are the development of metamaterial technologies and geophysical prospecting for natural resources. There are two modes of modeling the forward problem: the frequency domain and the time domain. As the title states, this work is concerned with the former regime. The difficulties of solving the high-frequency wave propagation problem accurately lies in the large number of degrees of freedom required. Conventional wisdom in the computational electromagnetics commmunity suggests that about 10 degrees of freedom per wavelength be used in each coordinate direction to resolve each oscillation. If K is the width of the domain in wavelengths, the number of unknowns N grows at least by O(K^2) for surface discretizations and O(K^3) for volume discretizations in 3D. The memory requirements and asymptotic complexity estimates of direct algorithms such as the multifrontal method are too costly for such problems. Thus, iterative solvers must be used. In this dissertation, I will present fast algorithms which, in conjunction with GMRES, allow the solution of the forward problem in O(N) or O(N log N) time.Item Multiple-grid adaptive integral method for general multi-region problems(2011-08) Wu, Mingfeng; Yilmaz, Ali E.; Ling, Hao; Pearce, John; Alu, Andrea; Ying, LexingEfficient electromagnetic solvers based on surface integral equations (SIEs) are developed for the analysis of scattering from large-scale and complex composite structures that consist of piecewise homogeneous magnetodielectric and perfect electrically/magnetically conducting (PEC/PMC) regions. First, a multiple-grid extension of the adaptive integral method (AIM) is presented for multi-region problems. The proposed method accelerates the iterative method-of-moments solution of the pertinent SIEs by employing multiple auxiliary Cartesian grids: If the structure of interest is composed of K homogeneous regions, it introduces K different auxiliary grids. It uses the k^{th} auxiliary grid first to determine near-zones for the basis functions and then to execute AIM projection/anterpolation, propagation, interpolation, and near-zone pre-correction stages in the k^{th} region. Thus, the AIM stages are executed a total of K times using different grids and different groups of basis functions. The proposed multiple-grid AIM scheme requires a total of O(N^{nz,near}+sum({N_k}^Clog{N_k}^C)) operations per iteration, where N^{nz,near} denotes the total number of near-zone interactions in all regions and {N_k}^C denotes the number of nodes of the k^{th} Cartesian grid. Numerical results validate the method’s accuracy and reduced complexity for large-scale canonical structures with large numbers of regions (up to 10^6 degrees of freedom and 10^3 regions). Then, a Green function modification approach and a scheme of Hankel- to Teoplitz-matrix conversions are efficiently incorporated to the multiple-grid AIM method to account for a PEC/PMC plane. Theoretical analysis and numerical examples show that, compared to a brute-force imaging scheme, the Green function modification approach reduces the simulation time and memory requirement by a factor of (almost) two or larger if the structure of interest is terminated on or resides above the plane, respectively. In addition, the SIEs are extended to cover structures composed of metamaterial regions, PEC regions, and PEC-material junctions. Moreover, recently introduced well-conditioned SIEs are adopted to achieve faster iterative solver convergence. Comprehensive numerical tests are performed to evaluate the accuracy, computational complexity, and convergence of the novel formulation which is shown to significantly reduce the number of iterations and the overall computational work. Lastly, the efficiency and capabilities of the proposed solvers are demonstrated by solving complex scattering problems, specifically those pertinent to analysis of wave propagation in natural forested environments, the design of metamaterials, and the application of metamaterials to radar cross section reduction.Item Three-dimensional computation of light scattering by multiple biological cells(2010-05) Starosta, Matthew Samuel, 1981-; Pearce, John A., 1946-; Dunn, Andrew Kenneth, 1970-; Thomas, Robert J.; Milner, Thomas E.; Wilson, Preston S.; Ling, HaoThis work presents an investigation into the optical scattering of heterogeneous cells with an application to two-photon imaging, optical scattering measurements and STED imaging. Using the finite difference time-domain (FDTD) method, the full-wave scattering by many cells containing multiple organelles with varying indices of refraction is computed. These simulations were previously limited to single cells for reasons of computational cost. A superposition approximation that uses the coherent linear superposition of FDTD-determined farfield scattering patterns of small numbers of cells to estimate the scattering from a larger tissue was developed and investigated. It was found that for the approximation to be accurate, the scattering sub-problems must at minimum extend along the incident field propagation axis for the full depth of the tissue, preserving the scattering that takes place in the direction of propagation. The FDTD method was used to study the scattering effects of multiple inhomogeneous cells on the propagation of a focused Gaussian beam with an application to two-photon imaging. It was found that scattering is mostly responsible for the reduction in two-photon fluorescence signal as depth is increased. It was also determined that for the chosen beam parameters and the cell and organelle configurations used, the nuclei are the dominant scatterers. FDTD was also utilized in an investigation of cellular scattering effects on the propagation of a common depletion beam used in STED microscopy and how scattering impacts the image obtained with a STED microscope. An axial doughnut beam was formulated and implemented in FDTD simulations, along with a corresponding focused Gaussian beam to simulate a fluorescence excitation beam. It was determined that the depletion beam will maintain a well-defined axial null in spite of scattering, although scattering will reduce the resulting fluorescence signal with focal depth.