How do I used data exported from the PDE toolbox in order to create specific XY plots?

Using the partial differential equation toolbox, I have solved a few heat transfer problems. I understand how to export the data from the mesh and the solution, but am unable to use it to create a proper script. I am attempting to create two specific XY plots with the data from the toolbox, but am unsure how to use the appropriate functions with the mesh data that is exported.

The first thing I am attempting to create is a script a graph of the solution value along an arbitrary line drawn over the solution showed in the PDE toolbox. In other words, with the mesh data I can export I need to specify a certain straight line along the solution given in the toolbox, then plot the resulting temperature versus that line in an XY plot. I need to create a script in which I specify that line and then graph the solution at points along it.

The second plot I am attempting to create is an XY plot that shows the solution value (temperature) at a given point against the time that the heat is being applied in my problem. I need a script that will allow me to use the mesh data to specify a point, then graph the temperature at that point against time.

Answer 1

[Alan Weiss]

Depending on your toolbox version, there are differing ways to plot things. If you have a relatively recent version, then use Plot 2-D Solutions and their Gradients, especially the latter part of the example, which shows how to interpolate the results to a straight line segment.

If you are using an old toolbox version where you have to use a [p e t] representation of the mesh, then you can use pdeInterpolant to create an interpolant, and use evaluate to create the interpolated values. The evaluate function reference page has several examples.

Alan Weiss

MATLAB mathematical toolbox documentation

[Alex Johnson]

I realize I am using the old toolbox version. The pdeInterpolant and evaluate functions worked very well when plotting a point's solution versus time, however I am still unsure how to plot the solution along an arbitrary line. Can I use pdeInterpolant for that too? And how would I define my line? Thanks!

[Alan Weiss]

I think that this example shows you how to plot along an arbitrary curve. Define your line however you want, such as

x = linspace(-4,3);
y = linspace(1,-2);
uout = evaluate(F,x,y); % assumes that you have F

Alan Weiss

MATLAB mathematical toolbox documentation

[Alex Johnson]

Great! Thank you for the patience, that did work for me. Although the y axis correctly displayed the temperature, I am unsure what the x axis is displaying. It is not correctly representing the distance of the line. Could the x axis be representing the number of nodes or triangles? And if so, is there anyway to make it correctly display the distance of the line? Mine should be starting at around .01 and ending at .25 (x=linspace(.01, .25) and y=linspace(0, 0)), but it instead starts at 0 and ends at 72. Thanks again!

[Alan Weiss]

I'm not sure what plotting command you used, so I don't know what you are seeing. I would use something like this:

x = linspace(0.01,0.25);
y = zeros(size(x));
uout = evaluate(F,x,y); % assumes that you have F
plot(x,uout)
xlabel('x')
ylabel('Temp')
title('Temperature Vs. x')

Alan Weiss

MATLAB mathematical toolbox documentation

[Alex Johnson]

That worked well thank you. But lets say that I wanted to plot along a line that is not horizontal. It would be something like this.

x=linspace(x1,x2); y=linspace(y1,y2); uout=evaluate(F,x,y);

But then I get stuck when plotting. I cannot plot against the x or y axis because my arbitrary line is diagonal, so the end of my plot should end at whatever distance the line is. I would think that to do this you would plot uout against the line because you cannot make a 2d plot with x, y, and uout. However, I am unable to create a line that I could plot this along that is in the correct format with agreeing matrices. I have also gotten errors which say line cannot be child of line when I tried to manually enter the line to plot against. Thanks!

[Alan Weiss]

There are many ways to plot in MATLAB. Again, I suggest that you look at the latter part of this example and see how the plotting on a diagonal was done (look for "Plot the interpolated solution along the line." and the immediately following figures).

Alternatively, if you have a line parameterized by t, plot along the parametrization, such as

t = linspace(0,1);
x = -1 + 0.5*t;
y = 2 - 0.1*t;
uout = evaluate(F,x,y); % Assumes F exists
plot(t,uout)

Alan Weiss

MATLAB mathematical toolbox documentation

Answer 2

[Ravi Kumar]

If you are using MATLAB R2017a, refer to the examples in this page, particularly the last one.

[Alex Johnson]

My confusion comes when I try to use those functions with my exported values (p e t u) instead of X and Y.