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
  • Navier Stokes Equations
  • Elasticity
• 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
  • 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
  • 4.1.1 Geometries in 2D
  • 4.1.2 CSG in 2D (NEW)
  • 4.2 Constructive Solid Geometry (CSG)
  • 4.3 Working with meshes
• 5. MPI - Parallelization
  • 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 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
  • 5.6.4 FETI-DP in NGSolve IV: Inexact FETI-DP
• 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

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

Netgen Tutorials

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