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Proper Orthogonal Decomposition and Model Order Reduction in Computational Electromagnetics

de Lima Nicolini, Julio
http://orcid.org/0000-0002-6979-1096
http://rave.ohiolink.edu/etdc/view?acc_num=osu1689601503698921

Abstract Details

2023, Doctor of Philosophy, Ohio State University, Electrical and Computer Engineering.
We present a discussion on the reduced-order modeling of electromagnetic simulation in general, and kinetic plasma simulations in particular, using the Proper Orthogonal Decomposition technique. Computational electromagnetics has been an important tool for physicists and engineers since the mid-1960s, when the increasing availability of modern high-speed computers started to allow the numerical solution of practical problems for which closed-form analytic solutions did not exist or were impractical to calculate. The study of kinetic plasmas is of great interest both for theoretical exploration and technological applications such as design of vacuum electronic devices, the study of the interaction of space-borne assets and cosmic radiation, fusion experiments, among others. Due to the theoretical complexity of these problems and the difficulty in performing physical experiments, simulations are instrumental for obtaining new insights or developing new device designs by resolving the field and plasma behaviors when changes are made. Several variants of simulations exist, but particle-in-cell algorithms for solving particle dynamics coupled with finite-differences or finite-elements field solvers are particularly successful. Despite their success, such algorithms are still constrained by computational cost such as processing time and memory/storage limitations. The Proper Orthogonal Decomposition is a technique that extracts the spatiotemporal behavior from a function of interest or a set of data points. This spatiotemporal behavior is characterized by a set of coupled spatial and temporal modes, which makes the Proper Orthogonal Decomposition especially suitable for analyses and applications in dynamic systems; it has been used for creation of reduced-order models in the past, especially in the fluid dynamics community where it originated from but also in many other areas. We have explored the application of the Proper Orthogonal Decomposition technique to computational electromagnetics with a focus on kinetic plasma simulations, using finite-element-based particle-in-cell algorithms. We show that the decomposition of the electromagnetic field behavior in such simulations is able to generate greatly reduced models while keeping a controllable accuracy threshold even for complicated non-linear cases, and extend the method to be applicable in advection-dominated problems, which are historically problematic for mode-based algorithms.
Fernando Teixeira (Advisor)
Casey Wade (Committee Member)
Kubilay Sertel (Committee Member)
Robert Burkholder (Committee Member)
130 p.
Electrical Engineering; Electromagnetics
electromagnetics; finite-elements; reduced order modeling; proper orthogonal decomposition; kinetic plasmas; particle-in-cell

Recommended Citations

Citations

  • de Lima Nicolini, J. (2023). Proper Orthogonal Decomposition and Model Order Reduction in Computational Electromagnetics [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1689601503698921

    APA Style (7th edition)

  • de Lima Nicolini, Julio. Proper Orthogonal Decomposition and Model Order Reduction in Computational Electromagnetics. 2023. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1689601503698921.

    MLA Style (8th edition)

  • de Lima Nicolini, Julio. "Proper Orthogonal Decomposition and Model Order Reduction in Computational Electromagnetics." Doctoral dissertation, Ohio State University, 2023. http://rave.ohiolink.edu/etdc/view?acc_num=osu1689601503698921

    Chicago Manual of Style (17th edition)

osu1689601503698921
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This open access ETD is published by The Ohio State University and OhioLINK.