We present the Partition of Unity Method (PUM) and its implementation in Fraunhofer SCAI’s PUMA software framework. The fundamental idea and benefit of the PUM is to reduce the necessary number of degrees of freedom of a simulation while attaining the required accuracy of the application by using application-dependent enrichment functions which can resolve highly localized behavior of the solution instead of using mesh-refinement and standard piecewise polynomial basis functions. We discuss how such application-dependent enrichments can be constructed a-priori and on-the-fly during a simulation for e.g. laminated composites, shells and additive manufacturing problems.