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.

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
• 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 Element-wise BDDC Preconditioner
  • 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
  • Projected Jumps
  • 2.9 Fourth order equations
  • 2.10 Dual basis functions
  • 2.11 Matrix free operator application
• 3. Time-dependent and non-linear problems
  • 3.1 Parabolic model problem
  • 3.2 Incompressible Navier-Stokes equations
  • 3.3 Discontinuous Galerkin Discretizations for linear transport
  • 3.3.1 DG for the acoustic wave equation
  • 3.4 A Nonlinear conservation law: shallow water equation in 2D
  • 3.5 Scalar PDE on surfaces (with HDG)
  • 3.6 DG/HDG splitting
  • 3.7 Nonlinear problems
  • 3.8 Nonlinear minimization problems
• 4. Geometric modeling and mesh generation
  • 4.1 Geometries in 2D
  • 4.2 Constructive Solid Geometry (CSG)
  • 4.3 Working with meshes
• 5. MPI - Parallelization
  • 5.1 Basics of MPI-parallel NGSolve
  • 5.2 FETI-DP in NGSolve I: Working with Point-Constraints
  • 5.3 FETI-DP in NGSolve II: Point-Constraints in 3D
  • 5.4 FETI-DP in NGSolve III: Using Non-Point Constraints
  • 5.5 FETI-DP in NGSolve IV: Inexact FETI-DP

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