Stochastic modeling in computational electromagnetics

This thesis presents methodologies for the efficient assessment of the impact of statistical variability on the performance of electromagnetic structures and systems. The proposed techniques are based on the Sparse Grid Collocation method which is a more efficient alternative than the standard Monte Carlo method. The high dimensionality challenge associated with certain stochastic problems, defined in terms of correlated random variables, is alleviated with a random-space dimensionality reduction technique that, in combination with an a-priori sensitivity assessment, results in an accurate technique for the statistical characterization and yield estimation of stochastic electromagnetic systems. Two real-world applications demonstrate the benefits of the proposed methodologies, a pair of interconnects with random cross sectional parameters, and a band pass microwave filter with randomly positioned loads. The thesis focuses on methodologies for the assessment of structures exhibiting localized uncertainty, namely random changes in the geometric and material properties occurring throughout the structure under consideration. Among the proposed methodologies, a technique is developed for the stochastic electromagnetic macromodeling of two-dimensional subdomains exhibiting geometric and material uncertainty. The methodology makes use of the theory of polynomial chaos expansion and the concept of a global impedance/admittance matrix relationship defined over a circular surface enclosing the cross-sectional geometry of the domain of interest to construct a stochastic global impedance/admittance matrix boundary condition on the surrounding surface. Such a method is generalized for the broadband response of the random domains through a stochastic model order reduction technique based on the Krylov subspace projection. Numerical examples are used to demonstrate the attributes of the proposed stochastic macromodel to the solution of electromagnetic scattering problems by an ensemble of targets exhibiting uncertainty. Macromodeling is also employed for the assessment of signal integrity performance in high-speed interconnect structures exhibiting localized uncertainty. Specifically, two applications are studied for demonstrative purposes, the first one concerns a coaxial cable with a random permittivity profile and the second one, a multiconducting interconnect structure with variability in its routing. In the first case, an effective stochastic homogeneous model of the dielectric permittivity is constructed that is used to quantify the induced distortion of the transmitted signal in terms of a random jitter. In the second signal-integrity application, a methodology based on a passive parametric macromodeling technique is developed for the predictive analysis of the impact of interconnect routing uncertainty on their transmission properties. The last stochastic application presents an expedient methodology for the predictive analysis of the impact of statistical disorder on the electromagnetic attributes of periodic waveguides. The proposed methodology makes use of ideas from the Anderson localization theory to derive closed-form expressions for the calculation of an effective exponential decay ratio that quantifies the impact of periodicity disorder on the transmission properties of the wave-guide. The computational efficiency of the proposed method over Monte Carlo based alternatives is demonstrated through a specific example involving a periodically-loaded parallel plate waveguide.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Electrical & Computer Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Ochoa Munoz, Juan

Contributors dc:contributor

• Cangellaris, Andreas C.
• Chew, Weng Cho
• Raginsky, Maxim
• Schutt-Ainé, José E.

• Stochastic modeling
• Stochastic collocation
• Computaional electromagnetics
• Yield estimation
• Dimensionality reduction
• Monte Carlo
• Stochastic macromodeling
• Signal integrity
• Disordered periodic waveguides
• Random scattering

Statement dc:rights

• Copyright 2013 Juan Ochoa Munoz

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/46581

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/46581