Course materials for CIVL 5390 (Finite Element Methods) instructed by Tianju Xue at HKUST in Spring 2025.
This graduate-level course explores the Finite Element Method (FEM) as a computational tool for solving continuum mechanics problems. The course provides a comprehensive exploration of computational mechanics, beginning with foundational concepts in 1D and 2D linear boundary value problems, numerical implementation strategies, and error analysis, followed by applications to linear elasticity, structural mechanics (beams and plates), and advanced topics such as nonlinear problems (material and geometric nonlinearities), time-dependent PDEs (transient problems and dynamic systems), and inverse problems for parameter identification. The curriculum integrates modern computational techniques, including differentiable programming for sensitivity analysis and FFT-based methods for homogenization and multi-scale modeling, combining theoretical derivations with hands-on coding exercises in Jupyter notebooks to bridge abstract mathematical formulations with practical engineering solutions.
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For educational purposes.
© [2025] [Tianju Xue]. All course materials licensed under [CC BY-NC 4.0].