Date of Award:

12-2025

Document Type:

Thesis

Degree Name:

Master of Science (MS)

Department:

Mathematics and Statistics

Committee Chair(s)

Zilong Song

Committee

Zilong Song

Committee

Tianyi He

Committee

Luis Gordillo

Abstract

Friction stir welding (FSW) is a manufacturing process used to join materials through intense heat and pressure. To better understand and optimize this FSW process, mathematical models incorporating non-Newtonian Navier-stokes equations for large plastic deformation and heat equation for the heat transfer are used to simulate the FSW process. However, solving these coupled and nonlinear equations with high accuracy requires significant computational power and time. This thesis has applied model order reduction, more precisely the Proper Orthogonal Decomposition (POD) and Discrete Empirical Interpolation Method (DEIM), to efficiently solve the FSW system in low-dimensional space. Slight modifications are made regarding the POD and DEIM treatment: (1) preconditioner matrices are used on the original full model system before applied the POD and DEIM to avoid large condition number for the POD and DEIM low-dimensional coefficient matrices, and (2) indicator matrices are used in the full model system to deal with different regions and used to generate the nonlinear data for the DEIM. The results show that this approach dramatically reduces computation time, e.g., over 250 times smaller for the DEIM compared with full model, while maintaining accuracy. This makes simulations of friction stir welding more accessible and easily combined with other machine learning techniques in future study.

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