Tutorials

multiphenicsx is accompanied by several tutorials, that can be run on JupyterLab through a local installation of the library, or on cloud computing platforms such as Google Colab and Kaggle.

01

Block Poisson problem

Gentle introduction to block systems within dolfinx

Block Poisson problem

02

Navier-Stokes problem

Comparing standard assembly with mixed function spaces to block assembly for a nonlinear problem

Navier-Stokes problem

03

Weak imposition of Dirichlet BCs by a Lagrange multiplier

Introduction to multiphenicsx facilities for subdomain/boundary restricted variables

• Linear problem
• Nonlinear problem
• Interface problem

Several tutorials

04

Eigenvalue problems

A collection of tutorials concerning the computation of eigenvalues and inf-sup constants

• First eigenvalue of the Laplacian with Dirichlet BCs
• Inf-sup constant for a Stokes problem
• Inf-sup constant for a Lagrange multiplier problem

Several tutorials

05

(unused)

(former tutorial 05 was merged with tutorial 04)

06

Optimal control problems

Adjoint formulation of optimal control problems, and solving them by a one shot approach

• Case 1a: Poisson problem with distributed control
• Case 1b: Poisson problem with distributed control
• Case 2a: advection diffusion reaction problem with distributed control
• Case 2b: advection diffusion reaction problem with distributed control
• Case 3a: advection diffusion reaction control problem with Neumann control
• Case 3b: advection diffusion reaction control problem with Neumann control
• Case 4a: Poisson problem with Dirichlet control
• Case 4b: Poisson control problem with Neumann control and boundary observation
• Case 5: Stokes problem with distributed control
• Case 6: Navier-Stokes problem with distributed control
• Case 7a: Stokes problem with Dirichlet control
• Case 7b: Stokes problem with Neumann control
• Case 8: Navier-Stokes problem with Neumann control

Several tutorials

07

Understanding restrictions

Visualization of restrictions to subdomain/boundary for several finite element spaces

Understanding restrictions

08

Singular Poisson problem

Creating nullspace vector for pure Neumann problem with restrictions

Singular Poisson problem