The aim of this paper is to provide a fast and efficient procedure for (real-time) target identification in imaging based on matching on a dictionary of precomputed generalized polarization tensors (GPTs). The approach is based on some important properties of the GPTs and new invariants. A new shape representation is given and numerically tested in the presence of measurement noise. The stability and resolution of the proposed identification algorithm is numerically quantified. We compare the proposed GPT-based shape representation with a moment-based one.

We implemented an adaptively refined least-squares finite element approach for the Navier-Stokes equations that govern generalized Newtonian fluid flows using the Carreau model. To capture the flow region, we developed an adaptive mesh refinement approach based on the least-squares method. The generated refined grids agree well with the physical attributes of the flows. We also proved that the least-squares approximation converges to the linearized versions solutions of the Carreau model at the best possible rate. Model problems considered in the study are the flow past a planar channel and 4-to-1 contraction problems. We presented the numerical results of the model problems, revealing the efficiency of the proposed scheme, and investigated the physical parameter effects.

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