Graphical notation for diagramming coupled systems

Multiphysics and multiscale-or coupled-systems share one fundamental requirement: Construction of coupling mechanisms to implement complex data exchanges between a system's constituent models. I have created a graphical schema for describing coupling workflows that is based on a theoretical framework for describing coupled systems. The schema combines an expanded set of traditional flowchart symbols with pictograms representing data states. The data pictograms include distributed mesh, field, and domain decomposition descriptors and spatiotemporal integration and accumulation registers. Communications pictograms include: blocking- and non-blocking point-to-point and M ×N parallel data transfer; parallel data transposes; collective broadcast, scatter, gather, reduction and barrier operators. The transformation pictograms include: intergrid interpolation; spatiotemporal integral operators for accumulation of state and flux data; and weighted merging of output data from multiple source models for input to a destination model. I apply the schema to simple problems illustrating real situations in coupler design and implementation.