Defining External MATLAB® Functions in a Model
Start by defining a MATLAB function in a model so that COMSOL Multiphysics can recognize it as an external function to be evaluated in the MATLAB engine.
1
In the Home ribbon, click Functions . Under the Global section, select MATLAB . On Linux and macOS, this can be found in the Model Toolbar.
2
On the Settings page, under the Functions section, enter conductivity in the Function name field, and enter x in the Arguments field.
By defining the function here, COMSOL knows that conductivity is a MATLAB function. COMSOL automatically starts a MATLAB engine to evaluate the function when necessary.
In case you did not save the function in a directory that is in the MATLAB path you need to save first the model MPH file.
3
In the COMSOL Desktop, from the File menu (Windows users) or from the Options menu (Mac and Linux users), click Save As . Select COMSOL Application (*.mph) in the Save as type list,  and browse to the directory where the files conductivity.m and heatflux.m are stored.
You can display the value of the defined function by first defining the plot limit for the input arguments.
4
Expand the Plot parameters section. In the associated table enter 0 as the Lower limit and 1 as the Upper limit.
5
Click the Plot button . This will start the MATLAB engine where the function is evaluated and produce the following plot.
You can now define a second MATLAB function that returns the heat flux condition.
6
Repeating the above procedure, enter heatflux in the Function name field and enter x,y,x0,y0,Q0,scale in the Arguments field.
7
To display the function, enter the following in the Plot parameters table:
Lower limit
Upper limit
0
1
0
1
0
0
0
0
1e4
1e4
5
5
8
Click the Plot button .
Before you continue with the model settings, you need to manually specify the function derivative with respect to all function arguments. If this is not done, the solver will return a warning message. For this model, the function arguments are not defined using the temperature (the dependent variable) and the numerical problem can be considered linear. For this reason, you can set the derivative to be 0 for all input arguments.
9
Expand the Derivatives section and complete the table as shown below:
Function Name
Argument
Partial Derivative
conductivity
x
0
heatflux
x
0
heatflux
y
0
heatflux
x0
0
heatflux
y0
0
heatflux
Q0
0
heatflux
scale
0
Note: For nonlinear problems, it is necessary to specify the partial derivatives. The Partial Derivative column can be set with an expression or another MATLAB function.