How to express sum of areas of triangular elements meeting a criteria

Question

I have a metric for rating the results of a finite element simulation.

I am summing the area of the triangular elements which have a single value associated with them.

If the value associated with each triangle meets my criteria, I add the area of the triangle to the total, and the total for the simulation forms my metric.

How can/should I express this using a capital sigma notation?

I think it should be quite simple - e.g. just summing the elements of a set $S$, where $S$ is the area of triangles for which the value $v$ is within range? If this is the case, how can I express the set nicely?

I don't want/need to show the actual area calculation.

Answer 1

You can use the Indicator function. Let $A_i$ be the area of the $i$th triangle with associated value $x_i$.

Then your sum is

$$\sum_i A_i \mathbf{1}_C(x_i),$$

where $C$ is set of values for $x_i$ that meets your criteria.