Dune-MeshDist

Compute the Hausdorff-distance between parametrized grids.

The one-sided Hausdorff-distance between two grids G_1 and G_2 is defined as

d^H(G_1,G_2) = \sup_{p \in G_1} \inf_{q \in G_2} \|p - q\|_2

and the symmetric (two-sided) Hausdorff-distance as

d^S(G_1,G_2) = \max\{d^H(G_1,G_2), d^H(G_2,G_1)\}

The surface distance d(p, G_2) for p\in G_1 is implemented using a box background grid to identify the elements in G_2 that are "close" to p. In those elements the minimization problem to find the closest point is solved using a constrained LM method.

Example

Assume you have a reference grid and two parametrizations X1 and X2 on this grid describing possibly curved geometries.

The following computes the one-sided Hausdorff-distance:

Dune::MeshDist::hausdorffDistance(X1, X2)

The two-sided (symmetric) Hausdorff-distance can be computed with

Dune::MeshDist::symmetricHausdorffDistance(X1, X2)

Additionally, there are L^1-distance and L^2-distance called the meanError(X1,X2) and meanSquareError(X1,X2) also with symmetric versions.

Dependencies

In order to use this module, the following Dune dependencies must be installed

• dune-functions