# FluxIntegration¶

Use this post-process to compute the total fluxes of a tensor field or of an user-defined expression across domain interfaces. To single out specific interfaces use the parameter InterfaceType in combination with DomainIdPairs. It is required that the integrand, e.g., the tensor field, is a flux density 3-vector field (see also the comment below). For example, it is possible to integrate the electromagnetic energy flux density (Poynting vector) on domain interfaces. This will yield the total flux from one domain into a neighboring

Another important post-process for electromagnetic scattering problems is the computation of the electromagnetic energy flux of the scattered field from the interior to the exterior domain. This is done by setting InterfaceType to `ExteriorDomain`

:

```
PostProcess {
FluxIntegration {
FieldBagPath = ...
OutputFileName = ...
OutputQuantity = ElectromagneticFieldEnergyFlux
InterfaceType = ExteriorDomain
}
}
```

Here, FieldBagPath must refer to a solution fieldbag containing one or several electromagnetic fields. Often one is also interested in the electromagnetic flux of the total field across the interfaces of the interior to the exterior domain. These fluxes are computed by setting InterfaceType to `InteriorExterior`

. The differences of both fluxes is precisely the flux of the illuminating field, which is often used for scaling purposes when computing the scattering cross section.

Output format

It is supported to compute several integrals values in one sweep. For example, a JCM fieldbag may contain several fields of the desired flux density type. Then the integrals for the multiple fields are computed separately.

When computing mutual overlap integrals by an expression involving the fields of two fieldbags, the number of integrals will be the product of the numbers of fields in the two fieldbags.

The output is stored in a JCM table file with the following columns:

Columns 1,2:

**DomainIdFirst**,**DomainIdSecond**The integral values are computed domain-interface-wise. A domain interface is an oriented surface separating two neighbored domains. The surface normal is directed from the first domain to the other. The two integers

`DomainIdFirst`

and`DomainIdSecond`

specify a domain interface.Columns 3,4-…:

**<Quantity>_<Suffix>**,**Abs_<Quantity>_<Suffix>**These columns store the actual integral values.

`<Quantity>`

stands for the name of the computed value.`<Suffix>`

is an additional index needed to label separated integral values. For example, a JCM fieldbag may contain several fields of the desired density type.`<Suffix>`

is the field index, i.e.,`<Suffix>`

=`1`

for the first field,`<Suffix>`

=`2`

for the second field, etc. When computing mutual overlap integrals the`<Suffix>`

is a pair of field indices.The entries

`Abs_<Quantity>_<Suffix>`

has no direct physical interpretation. It is the integral value computed from the absolute value of the integrand. This way, there is no canceling out when integrating signed values. Hence, the computed value is useful to get a hint of the quantity’s scaling.`<Quantity>_<Suffix>`

and`Abs_<Quantity>_<Suffix>`

are stored in consecutive order.

Comments

*Flux Density*When using the term “flux density”,

*density*means a surface density, i.e., the projection of the flux density vector onto the surface’s normal can be integrated over the surface. Mathematically, this corresponds to a -differential form.