The application representation in POEMS has been designed with a view towards meeting all of the goals described in the previous section. The representation is based on the task graph, a widely used representation of parallel programs for many purposes including performance modeling [5,12], task scheduling [22], and graphical programming languages [9,14]. The task graph provides an abstract yet precise description of parallelism, communication and synchronization, while permitting the sequential parts of the computation (the ``tasks'') to be represented at almost arbitrary levels of detail, ranging from a single execution time number to exact execution of object code. To meet the diverse goals of POEMS, we use two flavors of the task graph, the static and the dynamic task graph. These and other key terms are defined in the following section. Sections 3.2 and 3.3 briefly describe the components of the application representation. Section 3.4 then discusses how we expect to meet the challenges raised by the above goals. Finally, Section 3.5 gives an example of the task graphs for Sweep3D.