NGSolve Shape Optimization

NGSolve Shape Optimization#

Welcome to the NGSolve Shape Optimization project. This Jupyter Book demonstrates PDE-constrained shape optimization using the NGSolve finite element library.

Project Overview#

This project implements shape optimization problems of the form:

\[ \min_{\Omega \subset \mathsf{D}} J(u) := \int_\Omega |\nabla u_\Omega - \nabla u_{ref}|^2 \, dx \]

subject to the PDE constraint:

\[ \int_\Omega \nabla u_\Omega \cdot \nabla v + u_\Omega v \, dx = \int_\Omega f v \, dx \quad \text{for all } v \in H_0^1(\Omega) \]

Contents#

This book contains:

  • Main optimization implementation in ngsolve/netgen

  • Mathematical derivations

  • Numerical experiments

Contents