dune-gdt

dune-gdt is a software library for building applications using grid-based numerical methods. It is a generic discretization toolbox and provides building blocks - like local operators, local evaluations, local assemblers - for discretization methods and suitable discrete function spaces. It is realized as a DUNE module and leverages newer C++ language features and the dune-xtensions to provide an easy-to-use and mathematically sound API. A subset of the API is exposed as Python-bindings using pybind11, and easily available as wheels on pypi.

• Tutorials
  • Tutorial: data functions and interpolation
    • creating functions
      • using the ConstantFunction
      • using the ExpressionFunction
      • discrete functions
    • visualizing functions
      • visualizing scalar functions in 2d
      • visualizing functions in other dimensions
    • The GridFunction
      • visualizing grid functions in all dimension
    • interpolation
      • using dune-gdts interpolation
      • using vectorized Python code
    • performance considerations
      • interpolation test
      • discretization test
  • Tutorial: continuous FEM for the stationary heat equation
    • diffusion with homogeneous Dirichlet boundary condition
      • analytical problem
      • continuous Finite Elements
      • approximate functionals
      • approximate bilinear forms
      • handling the Dirichlet boundary condition
      • walking the grid
      • solving the linear system
      • postprocessing the solution
      • everything in a single function
    • diffusion with non-homogeneous Dirichlet boundary condition
      • analytical problem
      • Dirichlet shift
      • Dirichlet interpolation
      • assembling the shifted system
      • everything in a single function
• Examples
  • Example: prolongations and computing products and norms
    • This is work in progress (WIP), still missing:
    • 1: prolongation onto a finer grid
    • 2: computing products and norms
    • 3: computing errors w.r.t. a known reference solution
  • Example: Grid adaptation
    • keeping track of refined elements
  • Example: a posteriori error estimates based on flux reconstruction
  • Example: working with gmsh grids
    • 1: creating a gmsh file
    • 2: discretization using pyMOR
    • 3: using the gmsh grid in dune
  • Example: residual-based a posteriori error estimates
    • 1: inspect grid properties and relations between elements and intersections
    • 2: solving an elliptic PDE
    • 3: computing the a posterior error estimates and indicators from [MNS2002]
    • 4: data oscialltion
  • Tutorial: discontinuous IPDG for the stationary heat equation
    • 1.9: everything in a single function
  • Example: SIPDG for the instationary heat equation
    • This is work in progress (WIP), still missing:
    • stationary data functions
    • timedependent right hand side
• Bibliography