ME280 - Finite Element Method
Fall 2011 with Professor Zohdi
- Coding - Wrote FEM code in MATLAB from scratch to understand the fundamentals and mathematics of the finite element method. Initially wrote a code to solve a 1D differential equation solution of a cantilever bar with linear basis functions progressing to non-linear basis functions and then a 2D FEM solver. Also wrote code to mesh 2D and 3D shape as well as a mesh refinement scheme for 1D. Compared code perfomance and mount of post-processing for a conjugate gradient solver versus Gaussian elimination. Used numerical methods such as Gaussian integration and Newton’s method to evaluate and solve the solutions.
- Testing - Compared final FEM solutions to analytical solutions of differential equations. Used best approximation theorem to evaluate the potential energy of the solution and assess convergence. Solved simulations for linear, quadratic, and cubic basis functions with varying mesh sizes to find the reasonable combination of computation time and solution accuracy