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Date Available

9-25-2026

Year of Publication

2026

Document Type

Thesis

Degree Name

Master of Electrical Engineering (MEE)

College

Engineering

Department/School/Program

Electrical and Computer Engineering

Faculty

John Young

Daniel Lau

Abstract

Large-scale computational electromagnetic simulations frequently require the assembly of dense system matrices, whose computation time and memory cost grow rapidly with problem size and can render high-resolution simulations impractical. This thesis presents a benchmark of the H2 hierarchical matrix method applied to the construction of a coupling matrix that maps magnetization current in a structure to the magnetic field at observation points external to the structure. The underlying field interaction is derived from Maxwell's equations and discretized using a Nyström approach, producing a dense matrix.

The method is benchmarked across various geometries of increasing complexity and for increasing mesh resolution and observation point density. Post-processing performance is measured in terms of fill time, memory usage, and relative root-mean-square (RMS) error against either a dense baseline or an analytic solution. Across all geometries the H2 method achieves substantial reductions in fill time and memory usage at larger problem sizes. Relative RMS error decreases monotonically with mesh refinement. At small problem sizes the compression cost outweighs its benefit, identifying a problem-size threshold below which dense assembly remains preferable. These results demonstrate that H2 compression is a scalable and accurate alternative to dense assembly for large-scale field post-processing.

Digital Object Identifier (DOI)

https://doi.org/10.13023/etd.2026.441

Archival?

Archival

1st Funding Information

Naval Sea Systems Command (HQ)

N0002425C2109

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