  For given matrix $A\in\Z^{d\times n}$, the set $P_{b}=\{z:Az=b,z\in\Z^n_+\}$
describes the preimage or fiber of $b\in\Z^d$ under the $\Z$-linear map
$f_A:\Z^n_+\to\Z^d$, $x\mapsto Ax$. The fiber $P_{b}$ is called atomic, if
$P_{b}=P_{b_1}+P_{b_2}$ implies $b=b_1$ or $b=b_2$. In this paper we present a
novel algorithm to compute such atomic fibers. An algorithmic solution to
appearing subproblems, computational examples and applications are included as
well.
