Expression¶

Type:	string
Range:	[]
Default:	-/-
Appearance:	simple
Excludes:	Function, Module

This parameter is used to define a tensor field of type “thermal source density” by means of a Python expression within the .jcm input file. The syntax is the following:

ThermalSourceDensity {
  Python {
     Expression = " ... # your python scripting
                    ...
                    value = ... # set return value

                   "

     # define one or more parameters
     Parameter {
       Name = "Para1"
       ...
     }
     Parameter {
       Name = "Para2"
       ...

     }
  }
}

The string value Expression has to be valid Python code and is interpreted in the following way:

The NumPy-package is automatically imported when evaluating the expression.
Any parameter as defined by a Parameter section is available within the Python expression as an NumPy object named accordingly to the value of the parameter Name.
The position $\pvec{x}$ and the time $t$ are available as NumPy objects name X and t respectively.
For time-harmonic electromagnetic problems the angular frequency $\omega$ can be addressed by EMOmega, (EM stands for electromagnetic).
The expression must define a NumPy object named value which contains the return value of appropriate shape (thermal source density is a scalar).
Keep in mind the Python indentation rule.

As a practical example we want to define an inductive heat source stimulated by the presence of an time-harmonic electric field $\VField{E}$ in a lossy medium with electric conductivity tensor $\sigma$ (c.f. ElectricConductivity):

$\begin{eqnarray*} \SField{q} & = & \frac{1}{2} \VField{E}^{\mathrm{H}} \cdot \sigma \cdot \VField{E} \end{eqnarray*}$

This tensor field has two field parameters, namely the electric field strength $\VField{E}$ and the electric conductivity tensor $\pvec{\sigma}$ . It may be defined as follows:

ThermalSourceDensity {
  Python {
    Expression = "sigmaE = dot(sigma, E)
                  E_conj = E.conj()
                  value = 0.5*dot(E_conj.T, sigmaE)"

    Parameter {
       Name = "E"
       FieldValue {
         FieldBagPath = ... # path to an electric field
         Quantity = ElectricFieldStrength
       }
     }
     Parameter {
       Name = "sigma"
       FieldValue {
         Quantity = ElectricConductivity
       }
     }
   }
 }

Since the FieldBagPath tag is missing within the last parameter section, the default value "./" is used. This means that the definition of the electric conductivity is taken from the materials.jcm file located in the same directory.