A celebrated result of Dixmier-Malliavin says that every element of the smooth convolution algebra $A=C_c^\infty(G)$ of a Lie group $G$ can be expressed as a finite sum of products. That is, the map $A\otimes A\to A$ is surjective. In previous work, I extended this result to the case where $G$ is a Lie groupoid. Continuing this work, I recently showed that $A$ is in fact $H$-unital in the sense of Wodzicki. This means the bar complex $\cdots A^{\otimes 3} \to A^{\otimes 2} \to A \to 0$ is exact, and is the key notion for excision in cyclic homology. I furthermore established H-unitality of infinite-order vanishing ideals in $A$ associated to invariant submanifolds which means excision holds for these ideals. This work gives a principle for calculating cyclic homology of smooth groupoid algebras: localize the calculation around invariant submanifolds.