Topology Optimization

September 2020 - July 2021

This repository contains all the programs I will use for my iSURP project on Topology Optimization.

• Using Finite Difference Method to numerically solve u"(x) + f(x) = 0, where you will have to enter the function f

• Using Finite Difference Method to numerically solve u"(x) + sin(x) = 0

• A simple C++ code to find the square root of any number

• A python code to demostrate a sequence that converges to sqrt 2 for any positive first element

• A python code demonstrating Steepest Gradient Descent to find local/global minima/maxima of a continuous, differentiable function

• Demonstrating the Forward and Backward Euler Method for x'(t) = f(x)

• Demonstrating 1D Finite Element Method for u"(x) + f(x) = 0, where you will have to enter the function f

Shape optimization of a rectangular membrane:

• Building the mesh

• Visualizing the Primal problem, i.e. the object to be optimized

• Obtaining the Optimal Thickness without Regularization

• Obtaining the Optimal Thickness using Regularization

Visualising the mesh of a Cantilever Beam:

• Building the mesh

Creating Quantum Potentials in an Infinite Well to minimize probability in a certain region (Final Project):

• Building the mesh

• Visualising the problem

• Solving the Adjoint problem