Integrated Volume

The Grids | Calculate | Calculus differential and integral operator, Integrated Volume, gives the accumulated volume over the grid from the southwest to the northeast corner, or over a subgrid from southwest to northeast. This method can calculate volumes over

Mathematically, the integrated volume is defined by

image\img00182.png

Consider a surface defined over a rectangular region extending from X min to X max and Y min to Y max:

V(x,

The Integrated Volume option enables easy computation of volumes under rectangular subgrids. For example, the volume under the shaded area in the figure below is simply V(xr,

The integral of the bilinear form over the grid cell is the average value of the four corners times the area of the grid cell. Therefore, the underlying formula is

image\img00183.png

See Also

Grid Calculus

Differential and Integral Operators

Gradient Operator

Laplacian Operator

Biharmonic Operator

Integrated Volume

Grid Operations References

Grid Volume