# Visualization and Postprocessing on Unstructured Grids and Meshes with FEATool Functions

This post explains how to use MATLAB and the FEATool postprocessing
function library to import, plot, and visualize general data on
unstructured grids and meshes. Although MATLAB do include
visualization functionality for surface and contour plots (with the
*surf* and *contour* functions), it is currently limited to regular
structured tensor-product grids (such as those created with
*meshgrid*). As detailed below, in this case one can then easily make
use of FEATool postprocessing functions to plot surface, height,
arrow, and contour plots even for external non-FEATool or general non
finite element analysis FEM data.

## Unstructured Grid and Data Import

The first processing step is to import the unstructured grid data and convert it to FEATool format. The FEATool grid and mesh format is described in the grid reference section of the FEATool User’s Guide. FEATool includes several built-in functions for importing and exporting grid and mesh files from external grid generation tools and formats such as GiD, Gmsh, GMV, and XML. An tutorial showing how to import grids from text files can be found in the corresponding grid import and export section. Moreover, it is straight forward to convert pure ASCII grid data to FEATool format from just having access to the grid point vertices or coordinates and grid cell connectivities.

For example, here a random distribution of points is used with a Delaunay triangulation, however, importing grid data from external files would proceed similarly

```
grid.p = rand(2,100); % 2d random distribution of 100 points.
grid.c = delaunay( grid.p' )'; % Delaunay triangulation for grid cell connectivities.
```

Having the grid point vertices and connectivities one can use the grid
utility functions `gridadj`

and `gridbdr`

to reconstruct
the other grid data struct fields

```
grid.a = gridadj( grid.c, size(grid.p,1) ); % Grid cell adjacency.
grid.b = gridbdr( grid.p, grid.c, grid.a ); % Grid boundary data.
grid.s = ones(1,size(grid.c,2)); % Set subdomain number 1 for all cells.
fea.grid = grid; % Assign grid to fea struct.
fea.sdim = {'x' 'y'}; % Assign space dimension coordinate names.
```

After the grid has been imported and extended one can proceed with
importing the unstructured data to be visualized. If the data is
available in *ASCII*, *CSV*, or MATLAB binary *mat* file format, then
one can simply use the `load filename.txt`

command and the
data will be loaded into a variable in the main workspace labeled
`filename`

.

## Data to FEA Struct Conversion

The data must now be converted and reshaped to FEATool solution vector
format which is specified as a column vector of size *nvars*np x 1*,
where *np* is the number of grid points and *nvars* the number of
variables to visualize. That is, the solution or visualization vector
should conform to *nvars* vertically stacked column vectors, where
each block with contains variable data corresponding to the grid
points.

Continuing the example, assuming that two visualization variables have
been loaded, the first with *sin(x)* coordinates and the second with
*y^2* values (instead of loading and importing they are for simplicity
constructed directly here)

```
u1 = sin( grid.p(1,:) )';
u2 = grid.p(2,:).^2';
fea.sol.u = [u1;u2]; % Assign variables to solution vector.
```

In order to use and apply FEATool postprocessing and plotting functions to these variables they must first be represented as finite element FEM dependent variables or unknowns (solving for them is not necessary as they are only used for visualization)

```
fea.dvar = {'u' 'v'};
fea.sfun = repmat({'sflag1'},1,length(fea.dvar));
```

The *dvar* field is the name string or tag used to access and call the
variables in the postprocessing functions. The *sfun* field represents
the finite element shape function, and in this case node oriented
linear first order *P1* functions (*sflag1*) are prescribed, as is
appropriate when the imported visualization data is defined in the
grid points or nodes. As can be seen one will need to assign one
*dvar* name and *sfun* entry for each imported data block (equal to
the number of stacked column blocks in the solution
vector *fea.sol.u*).

## Posprocessing with FEATool Plot Functions

To enable FEATool postprocessing the *parseprob* function is first
called to automatically generate some additional fields such as
degrees of freedom maps. Now it is possible to use the created *fea*
finite element data struct with imported unstructured data in
postprocessing with for example the
`postplot`

function

```
fea = parseprob( fea );
% Plot grid.
subplot(1,3,1)
plotgrid( fea )
% Plot iso-contour lines 'u+v' and arrows 'u' and 'v'.
subplot(1,3,2)
postplot( fea, 'isoexpr', 'u+v', 'arrowexpr', {'u' 'v'} )
% Plot height surface expression 'pi*du/dx'.
subplot(1,3,3)
postplot( fea, 'surfexpr', 'pi*ux', 'surfhexpr', 'pi*ux' )
```

Note, that the imported data has here been assigned as general finite
element solution variables. In this way they can be included in
general FEATool expressions (for example expressions such as
*1+u^2+x*sin(v)*) and also processed like *ux* for the first
derivative (which is computed from the first order finite element
basis function approximation). Thus having imported the data into
FEATool FEM format one is not limited to the data as is, but can
process it using the full FEATool functionality.

One can for example also perform boundary and subdomain integration, and general expression evaluation in any coordinates like

```
% Evaluate expression 2*x+sqrt(ux^2+vy^2) at p.
p = [0.1 0.8;0.2 0.3]; % Evaluation coordinates.
val = evalexpr( '2*x+sqrt(ux^2+vy^2)', p, fea )
```

In addition to creating plots in MATLAB it is also possible to use the the Plotly functionality to create and export interactive web and html graphics and plots as described in the plotly FEATool tutorial article.

Lastly, if desired one can import the created *fea* data struct into
the FEATool GUI and use the GUI postprocessing functionality instead
of working on the command line. This can be done by starting a new
FEATool model with the same space dimensions as the data, switching to
*Postprocessing* mode, and using the *Import > Variables From Main
Workspace…* *File* menu option.