%INTEGRATION_BE_DIRECT%

surface integration of a scalar value on boundary elements

INTEGRATION($IntInd$) = ( %INTEGRATION_BE_DIRECT%, ExpressionOfIntegrand, $PostprocessTag1$, $PostprocessTag2$, ... )

The POSTPROCESS-flags $PostprocessTag1$, $PostprocessTag2$, ... define the IntegrationArea. Their number is not limited. This computes the integral of a functional $ f$ (ExpressionOfIntegrand) with respect to the region $ \partial\Omega$ identified by the POSTPROCESS-flags

\begin{align} I_\text{BEDirect} = \int\limits_{\partial\Omega} f dA\end{align}

by a sum approximation

\begin{align} I_\text{BEDirect} \approx \sum_{i \in BE} f_i \cdot A_i,\end{align}

where $ BE$ is the set of all boundary elements with the given postprocess flags. $ f_i$ is the function value and $ A_i$ is the area of the i-th boundary element. Example:

INTEGRATION($area_PostprocessTag1$) = ( %INTEGRATION_BE_DIRECT%, [1.0], $PostprocessTag1$ )

Note: In contrast to %INTEGRATION_BND_DIRECT%, ExpressionOfIntegrand is defined and evaluated on the boundary elements and not on the MESHFREE point cloud!