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Interactive NGSolve Tutorial

Whetting the appetite

Getting started

  • 1.1 Poisson equation

  • 1.2 CoefficientFunctions

  • 1.3 Dirichlet boundary conditions

  • 1.4 Static condensation

  • 1.5 Spaces and forms on sub-domains

  • 1.6 Error estimation and refinement

  • 1.7 Helmholtz equation

    • 1.7.1 Perfectly matched layers (PML)

  • 1.8 Exploring the mesh topology

Advanced topics

  • 2.1 Preconditioning

    • 2.1.1 Available preconditioners and solvers

    • 2.1.2 Programming preconditioners

    • 2.1.3 Multigrid preconditioners

    • 2.1.4 p-version BDDC preconditioner

  • 2.2 Eigenvalue solver

  • 2.3 \(H(curl)\) and \(H(div)\) finite element spaces

  • 2.4 Solving Maxwell equations

    • 2.4.1 Maxwell eigenvalue problem

  • 2.5 Mixed formulations for second order equations

  • 2.6 Stokes equation

  • 2.7 Facet-spaces and hybrid methods

  • 2.8 (Hybrid) Discontinuous Galerkin methods

  • 2.9 Fourth order equations - Kirchhoff plates

  • 2.10 Dual basis functions

  • 2.11 Matrix-free operator application

  • 2.12 Periodic Spaces

  • 2.13 Interface resistivity

  • 2.14 Global Spaces (plane waves)

Time-dependent and non-linear problems

  • 3.1 Time-stepping methods for parabolic equations

  • 3.2 Time-dependent Navier-Stokes equation

  • 3.3 Non-linear equations

  • 3.4 Non-linear minimization problems

  • 3.5 Operator applications for DG-methods

    • 3.5.1 DG-method for convection (operator application)

    • 3.5.2 DG-method for acoustic wave propagation (tuned operator applications)

  • 3.6 Scalar HDG on surface

  • 3.7 DG/HDG operator splitting methods

  • 3.8 DG for hyperbolic conservation laws

Geometric modeling and mesh generation

  • 4.1.1 Spline geometries in 2D

  • 4.1.2 CSG geometries in 2D

  • 4.2 CSG geometries in 3D

  • 4.3 Working with meshes

  • 4.4 OpenCascade geometries (NEW)

    • 4.4.1 OpenCascade bottle tutorial

    • 4.4.2 Workplanes

MPI-parallel NGSolve and Accelerator Support

NGSolve with CUDA (NEW)

  • 5.5.1 Poisson Equation using CUDA

  • 5.5.2 Explicit time-stepping for the wave equation

  • 5.5.3 Solving non-linear conservation laws

some more MPI tutorials

Various Topics

  • 6.1 Plates and Shells

    • 6.1.1 Surface meshes

    • 6.1.2 Surface PDE examples

    • 6.1.3 Reissner–Mindlin plate elements

    • 6.1.4 Naghdi/Koiter shells

  • 6.2 Contact Problems

  • 6.3 Elasto-plasticity

Shape- and Topology Optimization

Peter Gangl and Kevin Sturm

  • 7.1 Shape Derivative Levelset

  • 7.2 Shape Derivative Laplace

  • 7.3 Shape Derivative SemiAuto

  • 7.4 Shape Derivative Laplace SemiAuto

  • 7.5 Shape Derivative Laplace FullyAuto

  • 7.6 Topological Derivative Levelset

  • 7.7 Topological Derivative Transmission

Unfitted Finite Elements

  1. 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

  • 8.2 Integration on level set domains

  • 8.3 Unfitted FEM PDE discretizations

  • 8.4 Space-time discretizations on fitted geometry

  • 8.5 Space-time discretizations on unfitted geometries

  • 8.6 Integration on 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 with \(H(\text{div})\) elements

Extending by C++ programming

  • 9.1 Implementation of Finite Elements

  • 9.2 Implement our own system assembling

  • 9.3 High Order Finite Elements

NGSolve and …

  • 10.1 Coupling with NGSpice

  • 10.2 Coupling with TensorFlow

Appendix

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