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Robust Numerical Electromagnetic Eigenfunction Expansion Algorithms

Sainath, Kamalesh K

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2016, Doctor of Philosophy, Ohio State University, Electrical and Computer Engineering.
This thesis summarizes developments in rigorous, full-wave, numerical spectral-domain (integral plane wave eigenfunction expansion [PWE]) evaluation algorithms concerning time-harmonic electromagnetic (EM) fields radiated by generally-oriented and positioned sources within planar and tilted-planar layered media exhibiting general anisotropy, thickness, layer number, and loss characteristics. The work is motivated by the need to accurately and rapidly model EM fields radiated by subsurface geophysical exploration sensors probing layered, conductive media, where complex geophysical and man-made processes can lead to micro-laminate and micro-fractured geophysical formations exhibiting, at the lower (sub-2MHz) frequencies typically employed for deep EM wave penetration through conductive geophysical media, bulk-scale anisotropic (i.e., directional) electrical conductivity characteristics. When the planar-layered approximation (layers of piecewise-constant material variation and transversely-infinite spatial extent) is locally, near the sensor region, considered valid, numerical spectral-domain algorithms are suitable due to their strong low-frequency stability characteristic, and ability to numerically predict time-harmonic EM field propagation in media with response characterized by arbitrarily lossy and (diagonalizable) dense, anisotropic tensors. If certain practical limitations are addressed, PWE can robustly model sensors with general position and orientation that probe generally numerous, anisotropic, lossy, and thick layers. The main thesis contributions, leading to a sensor and geophysical environment-robust numerical modeling algorithm, are as follows: (1) Simple, rapid estimator of the region (within the complex plane) containing poles, branch points, and branch cuts (``critical points") (Chapter 2), (2) Sensor and material-adaptive azimuthal coordinate rotation, integration contour deformation, integration domain sub-region partition and sub-region-dependent integration order (Chapter 3), (3) Integration partition-extrapolation-based (Chapter 3) and Gauss-Laguerre Quadrature (GLQ)-based (Chapter 4) evaluations of the deformed, semi-infinite-length integration contour ``tails", (4) Robust ``in-situ"-based (i.e., at the spectral-domain integrand level) ``direct"/homogeneous-medium field contribution subtraction and analytical curbing of the source current spatial spectrum function's ill behavior (Chapter 5), and (5) Analytical re-casting of the direct-field expressions when the source is embedded within a NBAM, short for non-birefringent anisotropic medium (Chapter 6). The benefits of these contributions are, respectively, (1) Avoiding computationally intensive critical-point location and tracking (computation time savings), (2) Sensor and material-robust curbing of the integrand's oscillatory and slow decay behavior, as well as preventing undesirable critical-point migration within the complex plane (computation speed, precision, and instability-avoidance benefits), (3) sensor and material-robust reduction (or, for GLQ, elimination) of integral truncation error, (4) robustly stable modeling of scattered fields and/or fields radiated from current sources modeled as spatially distributed (10 to 1000-fold compute-speed acceleration also realized for distributed-source computations), and (5) numerically stable modeling of fields radiated from sources within NBAM layers. Having addressed these limitations, are PWE algorithms applicable to modeling EM waves in tilted planar-layered geometries too? This question is explored in Chapter 7 using a Transformation Optics-based approach, allowing one to model wave propagation through layered media that (in the sensor's vicinity) possess tilted planar interfaces. The technique leads to spurious wave scattering however, whose induced computation accuracy degradation requires analysis. Mathematical exhibition, and exhaustive simulation-based study and analysis of the limitations of, this novel tilted-layer modeling formulation is Chapter 7's main contribution.
Fernando Teixeira (Advisor)
Joel Johnson (Committee Member)
Robert Burkholder (Committee Member)
297 p.

Recommended Citations

Citations

  • Sainath, K. K. (2016). Robust Numerical Electromagnetic Eigenfunction Expansion Algorithms [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1480340627500682

    APA Style (7th edition)

  • Sainath, Kamalesh. Robust Numerical Electromagnetic Eigenfunction Expansion Algorithms. 2016. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1480340627500682.

    MLA Style (8th edition)

  • Sainath, Kamalesh. "Robust Numerical Electromagnetic Eigenfunction Expansion Algorithms." Doctoral dissertation, Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1480340627500682

    Chicago Manual of Style (17th edition)