Abdulkadir C. Yucel

A Fast Stroud-Based Collocation Method for Statistically Characterizing EMI/EMC Phenomena on Complex Platforms

A fast stochastic collocation method for statistically characterizing electromagnetic interference and compatibility (EMI/EMC) phenomena on electrically large and loaded platforms is presented. Uncertainties in electromagnetic excitations and/or system geometries and configurations are parameterized in terms of random variables having normal or beta probability density functions. A fast time-domain integral-equation-based field-cable-circuit simulator is used to perform deterministic EMI/EMC simulations for excitations and/or system geometries and configurations specified by Stroud integration rules. Outputs of these simulations then are processed to compute averages and standard deviations of pertinent observables. The proposed Stroud-based collocation method requires far fewer deterministic simulations than Monte Carlo or tensor-product integrators. To demonstrate the accuracy, efficiency, and practicality of the proposed method, it is used to statistically characterize coupled voltages at the feed pins of cable-interconnected and shielded computer cards as well as the terminals of cables situated inside the bay of an airplane cockpit.

Exact evaluation of retarded-time potential integrals for the RWG bases

A new analytical approach for obtaining the time samples of the retarded-time scalar and vector potentials due to an impulsively excited Rao-Wilton-Glisson (RWG) basis function is presented. The approach is formulated directly in the time-domain without any assumptions regarding the temporal behavior of the currents represented by the RWG bases. To the best knowledge of the authors, analytical evaluation of the potential integrals due to the RWG bases have not been formulated prior to the present work either in the time domain or the frequency domain. It is shown that the aforementioned potentials are related to the arc segments formed by the intersection of the triangular supports of the RWG basis and the sphere that is centered at the observation point and that has a radius R=ct, where c is the speed of light. In particular, the scalar potential is directly proportional to the total arc length and the vector potential is a function of the bisectors of these arc segments. A simple algorithm to evaluate these quantities is also presented. The validity of the obtained time-domain formulae is demonstrated through comparison of results to those obtained in the frequency domain by using numerical quadrature and transformed into time domain

An Adaptive Multi-Element Probabilistic Collocation Method for Statistical EMC/EMI Characterization

An adaptive multi-element probabilistic collocation (ME-PC) method for quantifying uncertainties in electromagnetic compatibility and interference phenomena involving electrically large, multi-scale, and complex platforms is presented. The method permits the efficient and accurate statistical characterization of observables (i.e., quantities of interest such as coupled voltages) that potentially vary rapidly and/or are discontinuous in the random variables (i.e., parameters that characterize uncertainty in a systems geometry, configuration, or excitation). The method achieves its efficiency and accuracy by recursively and adaptively dividing the domain of the random variables into subdomains using as a guide the decay rate of relative error in a polynomial chaos expansion of the observables. While constructing local polynomial expansions on each subdomain, a fast integral-equation-based deterministic field-cable-circuit simulator is used to compute the observable values at the collocation/integration points determined by the adaptive ME-PC scheme. The adaptive ME-PC scheme requires far fewer (computationally costly) deterministic simulations than traditional polynomial chaos collocation and Monte Carlo methods for computing averages, standard deviations, and probability density functions of rapidly varying observables. The efficiency and accuracy of the method are demonstrated via its applications to the statistical characterization of voltages in shielded/unshielded microwave amplifiers and magnetic fields induced on car tire pressure sensors.

Uncertainty Quantification in Transcranial Magnetic Stimulation via High-Dimensional Model Representation

A computational framework for uncertainty quantification in transcranial magnetic stimulation (TMS) is presented. The framework leverages high-dimensional model representations (HDMRs), which approximate observables (i.e., quantities of interest such as electric (E) fields induced inside targeted cortical regions) via series of iteratively constructed component functions involving only the most significant random variables (i.e., parameters that characterize the uncertainty in a TMS setup such as the position and orientation of TMS coils, as well as the size, shape, and conductivity of the head tissue). The component functions of HDMR expansions are approximated via a multielement probabilistic collocation (ME-PC) method. While approximating each component function, a quasi-static finite-difference simulator is used to compute observables at integration/collocation points dictated by the ME-PC method. The proposed framework requires far fewer simulations than traditional Monte Carlo methods for providing highly accurate statistical information (e.g., the mean and standard deviation) about the observables. The efficiency and accuracy of the proposed framework are demonstrated via its application to the statistical characterization of E-fields generated by TMS inside cortical regions of an MRI-derived realistic head model. Numerical results show that while uncertainties in tissue conductivities have negligible effects on TMS operation, variations in coil position/orientation and brain size significantly affect the induced E-fields. Our numerical results have several implications for the use of TMS during depression therapy: 1) uncertainty in the coil position and orientation may reduce the response rates of patients; 2) practitioners should favor targets on the crest of a gyrus to obtain maximal stimulation; and 3) an increasing scalp-to-cortex distance reduces the magnitude of E-fields on the surface and inside the cortex.

An ME-PC Enhanced HDMR Method for Efficient Statistical Analysis of Multiconductor Transmission Line Networks

An efficient method for statistically characterizing multiconductor transmission line (MTL) networks subject to a large number of manufacturing uncertainties is presented. The proposed method achieves its efficiency by leveraging a high-dimensional model representation (HDMR) technique that approximates observables (quantities of interest in MTL networks, such as voltages/currents on mission-critical circuits) in terms of iteratively constructed component functions of only the most significant random variables (parameters that characterize the uncertainties in MTL networks, such as conductor locations and widths, and lumped element values). The efficiency of the proposed scheme is further increased using a multielement probabilistic collocation (ME-PC) method to compute the component functions of the HDMR. The ME-PC method makes use of generalized polynomial chaos (gPC) expansions to approximate the component functions, where the expansion coefficients are expressed in terms of integrals of the observable over the random domain. These integrals are numerically evaluated and the observable values at the quadrature/collocation points are computed using a fast deterministic simulator. The proposed method is capable of producing accurate statistical information pertinent to an observable that is rapidly varying across a high-dimensional random domain at a computational cost that is significantly lower than that of gPC or Monte Carlo methods. The applicability, efficiency, and accuracy of the method are demonstrated via statistical characterization of frequency-domain voltages in parallel wire, interconnect, and antenna corporate feed networks.

Statistical Characterization of Electromagnetic Wave Propagation in Mine Environments

A computational framework for statistically characterizing electromagnetic (EM) wave propagation through mine tunnels and galleries is presented. The framework combines a multi-element probabilistic collocation method with a full-wave fast Fourier transform and fast multipole method accelerated surface integral equation-based EM simulator to statistically characterize fields from wireless transmitters in complex mine environments.

Efficient stochastic EMC/EMI analysis using HDMR-generated surrogate models

Stochastic methods have been used extensively to quantify effects due to uncertainty in system parameters (e.g. material, geometrical, and electrical constants) and/or excitation on observables pertinent to electromagnetic compatibility and interference (EMC/EMI) analysis (e.g. voltages across mission-critical circuit elements) [1]. In recent years, stochastic collocation (SC) methods, especially those leveraging generalized polynomial chaos (gPC) expansions, have received significant attention [2, 3]. SC-gPC methods probe surrogate models (i.e. compact polynomial input-output representations) to statistically characterize observables. They are nonintrusive, that is they use existing deterministic simulators, and often cost only a fraction of direct Monte-Carlo (MC) methods. Unfortunately, SC-gPC-generated surrogate models often lack accuracy (i) when the number of uncertain/random system variables is large and/or (ii) when the observables exhibit rapid variations.

An h-adaptive stochastic collocation method for stochastic EMC/EMI analysis

The analysis of electromagnetic compatibility and interference (EMC/EMI) phenomena is often fraught by randomness in a systems excitation (e.g., the amplitude, phase, and location of internal noise sources) or configuration (e.g., the routing of cables, the placement of electronic systems, component specifications, etc.). To bound the probability of system malfunction, fast and accurate techniques to quantify the uncertainty in system observables (e.g., voltages across mission-critical circuit elements) are called for. Recently proposed stochastic frameworks [1–2] combine deterministic electromagnetic (EM) simulators with stochastic collocation (SC) methods that approximate system observables using generalized polynomial chaos expansion (gPC) [3] (viz. orthogonal polynomials spanning the entire random domain) to estimate their statistical moments and probability density functions (pdfs). When constructing gPC expansions, the EM simulator is used solely to evaluate system observables at collocation points prescribed by the SC-gPC scheme. The frameworks in [1–2] therefore are non-intrusive and straightforward to implement. That said, they become inefficient and inaccurate for system observables that vary rapidly or are discontinuous in the random variables (as their representations may require very high-order polynomials).

A fast and parallel stroud-based stochastic collocation method for statistical EMI/EMC analysis

A fast and parallel Stroud-based stochastic collocation method for statistically characterizing electromagnetic interference and compatibility (EMI/EMC) phenomena on loaded multiscale platforms with uncertain system configurations and subject to variable electromagnetic excitations is described. The proposed method uses a previously developed hybrid time domain integral equation based field-cable-circuit to carry out deterministic EMI/EMC simulations permitting the statistical characterization of pertinent observables. The number of simulations required by the proposed method is far fewer than those needed by Monte-Carlo methods. The proposed method is used to characterize cable-induced coupling onto PC cards located in shielding enclosures. Both the hybrid simulator and the stochastic collocation code execute with near-full efficiency on distributed memory clusters.

Low-Frequency Stable Internally Combined Volume-Surface Integral Equation for High-Contrast Scatterers

Volume integral equations (VIEs) are commonly used to analyze scattering from inhomogeneous dielectric objects. Unfortunately, when VIEs are applied to high-contrast scatterers, their discretization results in ill-conditioned systems of equations. Oftentimes volume-surface integral equations (VSIEs) are used to eliminate this effect. However, when the scatterer’s mesh has elements that are much smaller than the wavelength, VSIEs become ill-conditioned, too. This letter introduces a new set of internally combined VSIEs (ICVSIEs) that exhibit neither of these ill-conditioning phenomena. Just like in previous VSIE methods, surface currents are used to artificially increase the effective permittivity of the background medium in which volume polarization currents radiate. To remove ill-conditioning due to electrical size, coupling between the surface and volume is accounted for by judiciously adding contributions due to “exterior” and “interior” surface currents. Numerical data obtained by analyzing time-harmonic TE scattering from various 2-D layered cylinders suggests that discretization of the new ICVSIE yields matrices that are unaffected by the scatterer’s maximum permittivity and electrical size.