Interactive NGSolve Tutorial

What are the i-tutorials ?

The i-tutorials are interactive tutorials to NGS-Py, the Python front-end to NGSolve. The i-tutorials are Jupyter notebooks which allow you to explore the features of NGS-Py.

The i-tutorials have been setup for the 2017 NGSolve user meeting. The authors of the sections are Jay Gopalakrishnan (Getting Started), Joachim Schöberl (Advanced Topics), Christoph Lehrenfeld (Time-dependent and non-linear problems), Christoph Wintersteiger (Geometric modeling and mesh generation). Big thanks to Matthias Hochsteger for integrating the Netgen-GUI into Jupyter.

Copyright: The i-tutorials are a part of NGSolve and are covered by the LGPL open source license. You may extend and modify them for your use, but you have to refer to the original source.

We acknowledge support from the TU Wien and by the Austrian Science Foundation FWF within project grant SFB65 Taming Complexity in Partial Differential Systems.

Installation

To work through the i-tutorials, you first have to install

• Netgen/NGSolve, see http://www.ngsolve.org/downloads

• Jupyter from http://www.jupyter.org. You can use the pip package manager: "pip3 install jupyter"

• download and unpack the i-tutorials from here.

To use the webgui visualization within jupyter you need

pip3 install webgui_jupyter_widgets
jupyter nbextension install --user --py widgetsnbextension
jupyter nbextension enable --user --py widgetsnbextension
jupyter nbextension install --user --py webgui_jupyter_widgets
jupyter nbextension enable --user --py webgui_jupyter_widgets

Some of the tutorials require packages from scipy and matplotlib, so it is a good idea to install them as well:

pip3 install scipy matplotlib matplotlib

i-tutorials on Youtube

We have recorded the tutorial sessions from the 3rd NGSolve Usermeeting in which most of these tutorial files were presented. You can watch the presentations on the NGSolve Youtube channel.

Starting

You start with the interactive tutorial by opening a terminal, go to the main folder containing the i-tutorials, and start

jupyter-notebook index.ipynb

Whetting the Appetite

• Poisson Equation
• Adaptivity
• Maxwell Equations
• Magnetostatics
• Navier Stokes Equations
• Elasticity
• 3D Solid Mechanics
• Rotating domains

1. Getting started

• 1.1 First NGSolve example
• 1.2 CoefficientFunctions
• 1.3 Dirichlet boundary conditions
• 1.4 Static Condensation
• 1.5 Spaces and forms on subdomains
• 1.6 Error estimation & adaptive refinement
• 1.7 Complex-valued waves
• 1.7.1 Perfectly Matched Layer (PML)
• 1.8 Exploring the mesh topology

2. Advanced Topics

• 2.1.1 Preconditioners in NGSolve
• 2.1.2 Building blocks for programming preconditioners
• 2.1.3 Multigrid and Multilevel Methods
• 2.1.4 Element-wise BDDC Preconditioner
• 2.1.5 Algebraic Multigrid Methods
• 2.2 Programming an eigenvalue solver
• 2.3 H(curl) and H(div) function spaces
• 2.4 Maxwell’s Equations
• 2.4.1 Maxwell eigenvalue problem
• 2.5 Mixed formulation for second order equations
• 2.6 Stokes equation
• 2.7 Facet spaces and hybrid methods
• 2.8 Discontinuous Galerkin Methods
• 2.9 Fourth order equations
• 2.10 Dual basis functions
• 2.11 Matrix free operator application
• 2.12 Periodic Spaces
• Eigenvalue problem for phase shift
• 2.13 Interface resisitivity
• 2.14 Coupling of FEM with plane waves

3. Time-dependent and non-linear problems

• 3.1 Parabolic model problem
• 3.2 Incompressible Navier-Stokes equations
• 3.3 Nonlinear problems
• 3.4 Nonlinear minimization problems
• 3.5.1 Operator applications for Discontinuous Galerkin discretizations - linear transport
• 3.5.2 DG for the acoustic wave equation
• 3.6 Scalar PDE on surfaces (with HDG)
• 3.7 DG/HDG splitting
• 3.8 A Nonlinear conservation law: shallow water equation in 2D

4. Geometric modeling and mesh generation

• 4.1.1 Geometries in 2D
• 4.1.2 CSG in 2D
• 4.2 Constructive Solid Geometry (CSG)
• 4.3 Working with meshes
• 4.4 Open Cascade Technology Geometry (NEW)
• 4.4.1 OpenCascade Bottle-tutorial
• 4.4.2 Workplanes

5. MPI - Parallelization and CUDA Support

• 5.1 Poisson Equation in Parallel
• 5.2 Parallel dofs and Vector-types
• 5.3.1 Using PETSc
• 5.3.2 NGSolve - PETSc interface

More on PETSc coupling is available by Stefano Zampini and Umberto Zerbinati at https://ngspetsc.readthedocs.io/en/latest/ngsPETSc.html

CUDA Device support:

• 5.5.1 Solving the Poisson Equation on devices
• 5.5.2 Discontinuous Galerkin for the Wave Equation
• 5.5.3 Euler equations

some more MPI examples:

• 5.5.1 MPI-Parallelization with NGSolve
• 5.5.2 Basics of MPI-parallel NGSolve
• 5.6.1 FETI-DP in NGSolve I: Working with Point-Constraints
• 5.6.2 FETI-DP in NGSolve II: Point-Constraints in 3D
• 5.6.3 FETI-DP in NGSolve III: Using Non-Point Constraints

6. Various Topics

• 6.1.1 Generating surface meshes
• 6.1.2 Surface PDEs
• 6.1.3 Reissner-Mindlin plate
• 6.1.4 Shell model
• 6.2 Contact Problems
• 6.3 Elasto-Plasticity

7. Shape- and Topology Optimization

Peter Gangl and Kevin Sturm

• 7.1 Shape optimization via the shape derivative
• 7.2 PDE-Constrained Shape Optimization
• 7.3 PDE-Constrained Shape Optimization (semi-automated)
• 7.5 PDE-Constrained Shape Optimization (fully automated)
• 7.6 Topology Optimization based on the Topological Derivative
• 7.7 PDE-Constrained Topology Optimization

8. Unfitted Finite Elements

3. Lehrenfeld and the ngsxfem authors

These units require the Add-on ngsxfem to be installed. There are further ngsxfem-tutorials here.

• 8.1 Fundamental concepts of ngsxfem
• 8.2 Integration on level set domains
• 8.3 Unfitted FEM discretizations
• 8.4 Space-time discretizations on fitted geometry
• 8.5 Space-time discretizations on unfitted geometries
• 8.6 Integration over domains described by multiple level sets
• 8.7 Unfitted FEM for domains described by multiple level sets
• 8.8 Cell and basis aggregation in ngsxfem
• 8.9 Unfitted Mixed FEM (using HDiv FE spaces)

9. Extending by C++ programming

• 9.1 Implementation of Finite Elements
• 9.2 Implement our own system assembling
• 9.3 High Order Finite Elements

10. NGSolve and ...

• 10.1 Coupling NGSolve and NGSpice
• 10.2 NGSolve with tensor-flow

Appendix

• Parallel computing with TaskManager
• Webgui
• Webgui - programming and internal features
• VTK - Output
• Pickling of NGSolve objects