NGS-Py Finite Element Tool

Netgen/NGSolve 6 contains a rich Python interface. Program flow as well as geometry description and equation setup can be controlled from Python. You should be familiar with weak formulations of partial differential equations and the finite element method (NGSolve-oriented lecture notes are here: Scientific Computing) and the Python programming language. The interface to Python is inspired by the FEniCS project.

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

Whetting the appetite

• Poisson equation
• Adaptive mesh refinement
• Symbolic definition of forms : magnetic field
• Navier Stokes Equation
• Nonlinear elasticity

Tutorial on Using NGSpy by Jay Gopalakrishnan

Installation

• Download installer
• Install from sources
• Getting started with Netgen/NGSolve
• Using Jupyter notebook

i-Tutorials

• Interactive NGSolve Tutorial
  • What are the i-tutorials ?
  • Installation
  • Starting
• 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
  • 5.5.1 Solving the Poisson Equation on devices
  • 5.5.2 Discontinuous Galerkin for the Wave Equation
  • 5.5.3 Euler equations
  • 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
  • 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
  • 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

Central Concepts

• Meshes

How-to

• Working with CoefficientFunctions
• Setting inhomogeneous Dirichlet boundary conditions
• Define and update preconditioners
• The Trace() operator
• Vectors and matrices
• Static condensation of internal bubbles
• Discontinuous Galerkin methods
• Parallel computing with NGS-Py
• Interfacing to numpy/scipy
• Periodicity
• Symbolic Integrators
• Spaces and forms on sub-domains
• Perfectly Matched Layers

MyLittleNGSolve - An Introduction into C++ Programming with NGSolve

This project is divided into 3 sections:

The basic section should provide you with knowledge about NGSolve's classes and how to overload them or provide C++ utility functions, as well as export all that to python.

The advanced section gives some more useful examples to browse through.

The legacy section contains old code, it may be useful mainly for people working already for some time with NGSolve and looking something up. Please keep in mind, that these things are not maintained and may contain code that does not work (efficiently) any more.

C++ Tutorials

• NGSolve Basics
• Advanced NGSolve Examples

Netgen Tutorials

• Define and mesh 2D geometries
• Constructive Solid Geometry CSG
• Working with meshes
• Manual mesh generation
• Mesh Size and Refinement