Work
Projects in SUSTech
- Variational Method, Finite Element Implementation and Their Applications to LCEs,
Simeng Wu,
Unpublished, June, 2022.
A general introduction to the huge subject of minimization of functionals, i.e., variational method, for whose writing I followed a rigorous mathematical way, rather than just intuitively thinking.
It contains several applications in both electronics and elasticity theory, including derivation of governing equations of linear elasticity from the so-called energy opinion.
- Homogenization of Elliptic Operators --- in Modern Perspective,
Simeng Wu,
Unpublished, April, 2022.
History of elliptical homogenization. Prerequisite knowledge for general homogenization theory are introduced mildly. Then we've discussed the 1-D case elaborately under functional analytical framework, which show rigor maths again.
- Stochastic Homogenization --- Analysis and Numerics,
Simeng Wu,
Unpublished, October, 2022.
Modern intro for homogenization is all about randomness. It's natural since microstructures' periodicity is a strong restriction for real solid matters to satisfy. In this work we tried a lot of new techniques including Convolutional Neural Network, Fourier Neural Operators, and we make comparison of these results with traditional Finite Element based results.