# SurfaceDensityIntegration¶

Use this post-process to integrate a surface density or a user-defined expression over a surface. It is required that the integrand, e.g., the tensor field, is scalar surface density field.

It is possible to compute several integrals in one sweep. For example, a JCM fieldbag may contain several fields of the desired surface 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 number of fields in the two fieldbags.

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

Column 1-2:

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

`DomainIdFirst`

and`DomainIdSecond`

specify a domain interface. The integrand tensor field is taken from the first domain. This way, a jump of the surface density across the interface can be taken into account.Column 3-…:

**<Quantity>_<Suffix>**,**Abs_<Quantity>_<Suffix>**These fields 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. Then`<Suffix>`

is the field index. When computing mutual overlap integrals the`<Suffix>`

is a pair of field indices.The entries

`Abs_<Quantity>_<Suffix>`

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

and`Abs_<Quantity>_<Suffix>`

are stored in consecutive order.