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iwr
dune-curvedgrid
Commits
766c9f94
Commit
766c9f94
authored
Oct 07, 2020
by
Praetorius, Simon
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Update README.md
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README.md
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...
...
@@ -3,8 +3,8 @@ This Dune module provides a meta-grid for wrapping other grid implementations an
a curved geometry on each element, parametrized by a
[
Dune-CurvedGeometry
](
https://gitlab.mn.tu-dresden.de/iwr/dune-curvedgeometry
)
class.
For an overview about the Curved
Surface
Grid and the CurvedGeometry, see also the presentation
[
Dune-Curved
Surface
Grid - A Dune module for surface parametrization
](
http://wwwpub.zih.tu-dresden.de/~praetori/presentations/dune-curvedgrid
)
.
For an overview about the CurvedGrid and the CurvedGeometry, see also the presentation
[
Dune-CurvedGrid - A Dune module for surface parametrization
](
http://wwwpub.zih.tu-dresden.de/~praetori/presentations/dune-curvedgrid
)
.
## Installation Instructions
`dune-curvedgrid`
requires the DUNE core modules, version 2.7 or later.
...
...
@@ -22,7 +22,7 @@ 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
Curved
Surface
Grid
grid
{
*
refGrid
,
sphereGF
};
CurvedGrid
grid
{
*
refGrid
,
sphereGF
};
```
At first, we have to create a reference grid that acts as a parametrization domain for the
...
...
@@ -37,7 +37,7 @@ interpolation of the projection into a Lagrange basis. This interpolation allows
values and derivatives of the geometry mapping.
Finally, the reference grid and the parametrization together build the curved grid. This
meta-grid
`Curved
Surface
Grid`
implements the Dune grid interface and can thus be used as
meta-grid
`CurvedGrid`
implements the Dune grid interface and can thus be used as
replacement for, e.g., the reference grid.
## Two Different Geometry Mappings
...
...
@@ -51,7 +51,7 @@ projection function into a (Lagrange) basis on the reference element. This requi
projection mapping just that it allows to map local coordinates in the reference element to
global coordinates on the surface.
The
`Curved
Surface
Grid`
constructs on request of the element geometry a LocalFiniteElement
The
`CurvedGrid`
constructs on request of the element geometry a LocalFiniteElement
of Lagrange basis functions for the internal parametrization of the geometry. The
`ParametrizedGeometry`
is constructed, if the grid gets a polynomial order
`k > 0`
.
...
...
@@ -67,7 +67,7 @@ template <int order>
using
Order_t
=
std
::
integral_constant
<
int
,
order
>
;
// Wrap the reference grid to build a curved grid
Curved
Surface
Grid
grid
{
*
refGrid
,
sphere
,
Order_t
<
k
>
{}};
CurvedGrid
grid
{
*
refGrid
,
sphere
,
Order_t
<
k
>
{}};
```
### LocalFunction-Geometry
...
...
@@ -88,5 +88,5 @@ auto f = discreteGridViewFunction<3>(gv, k);
Functions
::
interpolate
(
f
.
basis
(),
f
.
coefficients
(),
sphere
);
// Wrap the reference grid and the grid-function
Curved
Surface
Grid
grid
{
*
refGrid
,
f
};
CurvedGrid
grid
{
*
refGrid
,
f
};
```
\ No newline at end of file
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