02 Elliptic

This chapter moves from simple 1D PDEs to classical elliptic benchmark problems in one and two spatial dimensions.

In This Chapter

• Poisson 2D

  Compare automatic differentiation and finite-difference Laplacians on the same problem.

  Walk through the example

• Anisotropic Poisson 2D

  Change the diffusion strength independently in the x and y directions.

  Walk through the example

• Variable-Coefficient Poisson 2D

  Solve an elliptic problem with spatially varying conductivity.

  Walk through the example

• Mixed-Boundary Poisson 2D

  Combine Dirichlet and Neumann conditions on different parts of the boundary.

  Walk through the example

• Helmholtz 2D

  Add oscillatory behavior through a wave-number-dependent Helmholtz term.

  Walk through the example

• Diffusion-Reaction 1D

  Study a steady problem that balances diffusion and a reaction term.

  Walk through the example

Download Source Files

• poisson_2d.py
• anisotropic_poisson_2d.py
• variable_coefficient_poisson_2d.py
• mixed_boundary_poisson_2d.py
• helmholtz_2d.py
• diffusion_reaction_1d.py