Hilbert Book Model Project/Slide S5

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hbmp Hilbert Book Model Project S5

We separate all point-like discontinuities from the domain by encapsulating them in an extra boundary

In fact, it is sufficient that surrounds the current location of the elementary module

We will select a boundary, which has the shape of a small cube of which the sides run through
a region of the parameter spaces where the manifolds are continuous.

If we take everywhere on the boundary the unit normal to point outward, then this reverses the direction of the normal on which negates the integral

Thus, in this formula, the contributions of boundaries
are subtracted from the contributions of boundary

This means that also surrounds the regions

This fact renders the integration sensitive to the sequencing of the participating domains

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