Jake Harmon
Ph.D. PreliminaryJan 11, 2022, 10:00 am - 12:00 pm
Virtual (Teams)
Accelerated Adaptive Numerical Methods for Computational Electromagnetics: Enhancing Goal-Oriented Approaches to Error Estimation, Refinement, and Uncertainty Quantification
Abstract: This proposal develops strategies to enhance adaptive numerical methods for partial differential equation (PDE) and integral equation (IE) problems in computational electromagnetics (CEM). Through a goal-oriented emphasis, with a particular focus on scattered field and radar cross-section (RCS) quantities of interest (QoIs), we study automated acceleration techniques for the analysis of scattering targets. A primary contribution of this work, we propose an error prediction refinement strategy, which, in addition to providing rigorous global error estimates (as opposed to just error indicators), promotes equilibration of local error contribution estimates, a key requirement of efficient discretizations. Furthermore, we pursue consistent exponential convergence of the QoIs with respect to the number of degrees of freedom without prior knowledge of the solution behavior (whether smooth or otherwise) or the sensitivity of the QoIs to the discretization quality.
Moreover, aside from the need for rigorous error estimation and fully-automated discretization error control, practical simulations necessitate a study of uncertain effects arising, for example, from manufacturing tolerances. Therefore, by repeating the emphasis on the QoI, we leverage the computational efforts expended in error estimation and adaptive refinement to relate perturbations in the model to perturbations of the QoI in the context of applications in CEM. This combined approach permits simultaneous control of deterministic discretization error and its effect on the QoI as well as a study of the QoI behavior in a statistical sense.
Moreover, aside from the need for rigorous error estimation and fully-automated discretization error control, practical simulations necessitate a study of uncertain effects arising, for example, from manufacturing tolerances. Therefore, by repeating the emphasis on the QoI, we leverage the computational efforts expended in error estimation and adaptive refinement to relate perturbations in the model to perturbations of the QoI in the context of applications in CEM. This combined approach permits simultaneous control of deterministic discretization error and its effect on the QoI as well as a study of the QoI behavior in a statistical sense.
Adviser: Branislav Notaros
Co-Adviser: N/A
Non-ECE Member: Don Estep, Statistics
Member 3: Milan Ilic, ECE
Addional Members: Iuliana Oprea, Math
Co-Adviser: N/A
Non-ECE Member: Don Estep, Statistics
Member 3: Milan Ilic, ECE
Addional Members: Iuliana Oprea, Math
Publications:
Peer-Reviewed Journal Papers:
[1] C. Key, J. J. Harmon, and B. M. Notaroš, "Correlations in a posteriori Error Trends for the Finite Element
Method in the Presence of Changing Material Parameters," in IEEE Antennas and Wireless Propagation
Letters, doi: 10.1109/LAWP.2021.3116167.
[2] J. J. Harmon, C. Key, D. Estep, T. Butler, and B. M. Notaroš, "Adjoint Sensitivity Analysis for Uncertain
Material Parameters in Frequency-Domain 3-D FEM," in IEEE Transactions on Antennas and Propagation,
vol. 69, no. 10, pp. 6669-6679, Oct. 2021, doi: 10.1109/TAP.2021.3070059.
[3] S. Kasdorf, B. Troksa, C. Key, J. J. Harmon, and B. M. Notaroš, "Advancing Accuracy of Shooting and
Bouncing Rays Method for Ray-Tracing Propagation Modeling Based on Novel Approaches to Ray Cone
Angle Calculation," in IEEE Transactions on Antennas and Propagation, vol. 69, no. 8, pp. 4808-4815, Aug.
2021, doi: 10.1109/TAP.2021.3060051.
[4] J. J. Harmon, C. Key, D. Estep, T. Butler, and B. M. Notaroš, "Adjoint-Based Accelerated Adaptive
Refinement in Frequency Domain 3-D Finite Element Method Scattering Problems," in IEEE Transactions on
Antennas and Propagation, vol. 69, no. 2, pp. 940-949, Feb. 2021, doi: 10.1109/TAP.2020.3016162.
[5] C. Key, J. J. Harmon, and B. M. Notaroš, "Discrete Surface Ricci Flow for General Surface Meshing in
Computational Electromagnetics Using Iterative Adaptive Refinement," in IEEE Transactions on Antennas
and Propagation, vol. 69, no. 1, pp. 332-346, Jan. 2021, doi: 10.1109/TAP.2020.3008657.
In Review Journal Papers:
[1] J. J. Harmon and B. M. Notaroš, “Accelerated Adaptive Error Control and Refinement for SIE Scattering
Problems,” in Review.
[2] J. J. Harmon and B. M. Notaroš, “Adaptive hp-Refinement for 2-D Maxwell Eigenvalue Problems: Method
and Benchmarks,” in Review.
Preprints (Not Refereed):
[1] J. Corrado, J. J. Harmon, and B. M. Notaroš, “A Refinement-by-Superposition Approach to Fully Anisotropic
hp-Refinement for Improved Efficiency in CEM,” TechRxiv, Oct. 2021, doi: 10.36227/techrxiv.16695163.v1.
[2] J. J. Harmon, J. Corrado, and B. M. Notaroš, “A Refinement-by-Superposition hp-Method for H(curl)- and
H(div)-Conforming Discretizations,” TechRxiv, Jun. 2021, doi: 10.36227/techrxiv.14807895.v1.
Peer-Reviewed Journal Papers:
[1] C. Key, J. J. Harmon, and B. M. Notaroš, "Correlations in a posteriori Error Trends for the Finite Element
Method in the Presence of Changing Material Parameters," in IEEE Antennas and Wireless Propagation
Letters, doi: 10.1109/LAWP.2021.3116167.
[2] J. J. Harmon, C. Key, D. Estep, T. Butler, and B. M. Notaroš, "Adjoint Sensitivity Analysis for Uncertain
Material Parameters in Frequency-Domain 3-D FEM," in IEEE Transactions on Antennas and Propagation,
vol. 69, no. 10, pp. 6669-6679, Oct. 2021, doi: 10.1109/TAP.2021.3070059.
[3] S. Kasdorf, B. Troksa, C. Key, J. J. Harmon, and B. M. Notaroš, "Advancing Accuracy of Shooting and
Bouncing Rays Method for Ray-Tracing Propagation Modeling Based on Novel Approaches to Ray Cone
Angle Calculation," in IEEE Transactions on Antennas and Propagation, vol. 69, no. 8, pp. 4808-4815, Aug.
2021, doi: 10.1109/TAP.2021.3060051.
[4] J. J. Harmon, C. Key, D. Estep, T. Butler, and B. M. Notaroš, "Adjoint-Based Accelerated Adaptive
Refinement in Frequency Domain 3-D Finite Element Method Scattering Problems," in IEEE Transactions on
Antennas and Propagation, vol. 69, no. 2, pp. 940-949, Feb. 2021, doi: 10.1109/TAP.2020.3016162.
[5] C. Key, J. J. Harmon, and B. M. Notaroš, "Discrete Surface Ricci Flow for General Surface Meshing in
Computational Electromagnetics Using Iterative Adaptive Refinement," in IEEE Transactions on Antennas
and Propagation, vol. 69, no. 1, pp. 332-346, Jan. 2021, doi: 10.1109/TAP.2020.3008657.
In Review Journal Papers:
[1] J. J. Harmon and B. M. Notaroš, “Accelerated Adaptive Error Control and Refinement for SIE Scattering
Problems,” in Review.
[2] J. J. Harmon and B. M. Notaroš, “Adaptive hp-Refinement for 2-D Maxwell Eigenvalue Problems: Method
and Benchmarks,” in Review.
Preprints (Not Refereed):
[1] J. Corrado, J. J. Harmon, and B. M. Notaroš, “A Refinement-by-Superposition Approach to Fully Anisotropic
hp-Refinement for Improved Efficiency in CEM,” TechRxiv, Oct. 2021, doi: 10.36227/techrxiv.16695163.v1.
[2] J. J. Harmon, J. Corrado, and B. M. Notaroš, “A Refinement-by-Superposition hp-Method for H(curl)- and
H(div)-Conforming Discretizations,” TechRxiv, Jun. 2021, doi: 10.36227/techrxiv.14807895.v1.
Program of Study:
ECE540
ECE541
ECE656
ENGR665
MATH519
MATH560
MATH651
MATH652
ECE540
ECE541
ECE656
ENGR665
MATH519
MATH560
MATH651
MATH652