Mesh adaptation based on transfinite mean value interpolation

Abstract In this paper, the efficiency in mesh updating (r-adaptivity) of the Transfinite Mean value Interpolation (TMI) and its generalization (k-TMI) are compared on three standardized problems to the well-known Inverse Distance Weighted interpolation (IDW) and Radial Basis Function interpolation (RBF) for unstructured data points and the new k-Transfinite Barycentric Interpolation (k-TBI) for structured data points such as, for instance, curves or surfaces in 3D. This is achieved by introducing a dynamical version of these interpolations via an ordinary differential equation that can be solved by standard ODE methods that are more economical than, for instance, solving vector partial differential equations as in the pseudo-solid method. A review of the very recent mathematical foundations of the k-TMI and k-TBI constructed from the function alone (standard) or from the function and its derivatives (enhanced) is provided in the first part of the paper.

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