Author ORCID Identifier

https://orcid.org/0000-0002-4265-1763

Date of Award

Fall 10-10-2025

Document Type

Thesis (Ph.D.)

Department or Program

Computer Science

First Advisor

Bo Zhu

Abstract

Computational tools play a vital role in structural analysis and design, enabling engineers and researchers to optimize performance, reduce material usage, and explore novel configurations across solids and fluids. Capturing, analyzing, and optimizing these structures while balancing efficiency, stability, and adaptability remains a central challenge. This thesis proposes three complementary methods that advance representation, simulation, and optimization. We present an impulse (gauge) fluid formulation that utilizes the impulse gauge variable to reduce numerical diffusion and better preserve coherent flow features such as vorticity at practical resolutions. We introduce a differentiable Voronoi representation for cellular solids that provides smooth implicit boundaries and natural topology change via seed motions, enabling end-to-end sensitivities for compliance-driven objectives under manufacturability filters. We further develop a reduced-order nonlinear thin-shell topology optimization framework that retains essential geometric nonlinearity while lowering per-iteration analysis cost, delivering accurate adjoint gradients for large-deformation shell design. Together, these methods improve the fidelity and scalability of structure-aware simulation and design in engineering and computer graphics.

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