Kinetic theory models involving the Fokker-Planck equation can be accurately discretized using a mesh support (finite elements, finite differences, finite volumes, spectral techniques, etc.). However, these techniques involve a high number of approximation functions. In the finite element framework, widely used in complex flow simulations, each approximation function is related to a node that defines the associated degree of freedom. When the model involves high dimensional spaces (including physical and conformation spaces and time), standard discretization techniques fail due to an excessive computation time required to perform accurate numerical simulations. One appealing strategy that allows circumventing this limitation is based on the use of reduced approximation basis within an adaptive procedure making use of an efficient separation of variables.

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We present a general coarse-grained model for predicting the linear viscoelasic properties of branched polymers from the knowledge of their molecular structure and three viscoelastic parameters, i.e., the Rouse time of an entanglement segment, the plateau modulus, and the entanglement molecular weight. The model uses the ingredients of the tube-based theories of McLeish and co-workers, and its implementation is based on a timemarching algorithm; this conceptual approach was already successfully applied to linear and star polymers, and it is appropriately modified here to account for more complex branched architectures, within the framework of dynamic tube dilation (using the criteria of Graessley). Whereas the molecular physics behind this model is the well-established hierarchical tube-based motion, the new element is a different macromolecular coordinate system and account of the branch points diffusion. With proper account of polydispersity, successful description of a wide range of rheological data of H and pompom polymers is obtained, with the use of the dilution exponent R ) 1 and the parameter p 2 ) 1. The proposed methodology thus represents a generic approach for predicting the linear rheology of branched polymers.