A meta-grid for dune grids mapping flat geometries to curved geometries

dune-grid dune-curvedgeometry
Suggests: dune-localfunctions dune-functions dune-foamgrid dune-alugrid
Maintainer: Simon Praetorius, Florian Stenger
Git repository:

Dune-CurvedGrid - A Dune module for geometry parametrization

This Dune module provides a meta-grid for wrapping other grid implementations and providing a curved geometry on each element, parametrized by a Dune-CurvedGeometry class.

Example of usage

// 1. Construct a reference grid
auto refGrid = GmshReader< FoamGrid<2,3> >::read("sphere.msh");

// 2. Define the geometry mapping
auto sphere = [](const auto& x) { return x / x.two_norm(); };
auto sphereGF = analyticDiscreteFunction(sphere, *refGrid, order);

// 3. Wrap the reference grid to build a curved grid
CurvedGrid grid{*refGrid, sphereGF};

At first, we have to create a reference grid that acts as a parametrization domain for the target curved grid. In the example, we use Dune-FoamGrid and read a piece-wise flat grid from a GMsh file sphere.msh.

In a second step, we describe the parametrization of the curved surface/domain by a closest-point projection to the sphere. This projection is given by a callable sphere and is wrapped into a grid-function by a call to analyticDiscreteFunction. This grid-function wrapper associates the lambda-expression with a grid and a polynomial order for the local interpolation of the projection into a Lagrange basis. This interpolation allows to obtain values and derivatives of the geometry mapping.

Finally, the reference grid and the parametrization together build the curved grid. This meta-grid CurvedGrid implements the Dune grid interface and can thus be used as replacement for, e.g., the reference grid.

Further reading

The description of the module for surface parametrizations is written in the paper

S. Praetorius, F. Stenger: “Dune-CurvedGrid - A Dune module for surface parametrization”. Arch Num Soft, 6(1), 2022, arXiv

and an illustration of its functionality is given in the presentation

S. Praetorius: “Curved Grid, A Dune module for surface parametrization”. 2020

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