Governing Equation and Weak Form

This section summarizes the physical simulation models used in Scikit-Topt. The framework currently supports:

• Linear Elasticity – deformation and structural mechanics

• Steady-State Heat Conduction – temperature distribution and thermal flow

Each model is formulated through a standard FEM pipeline:

1. Governing equation (strong form)

2. Weak formulation

3. Boundary conditions

4. Matrix assembly

5. Solving a linear system

See the detailed pages below.

• The Weak Form of Linear Elasticity
• The Weak Form of Heat Conduction