Maximum- entropy methods

Within the family of meshfree approximation schemes, those selected by the principle of maximum-entropy [1] are computed considering an equivalence between basis functions and probability distributions. The resulting basis functions are smooth and their evaluations is fast and robust.

I contributed to theoretical topics of maximum-entropy schemes such as the computations of the shape functions derivatives on the boundary [2] and their use in the framework of collocation [3], as well as applications to material forming and cutting simulation [4] and time-harmonic acoustics [5]. I also worked on their combination with accurate geometric descriptions [6-7].

References

[1] Arroyo, Marino, and Michael Ortiz. "Local maximum‐entropy approximation schemes: a seamless bridge between finite elements and meshfree methods." International journal for numerical methods in engineering 65.13 (2006): 2167-2202. 

[2] Greco, F., N., Sukumar. "Derivatives of maximum-entropy basis functions on the boundary: Theory and computations". International Journal for Numerical Methods in Engineering 94. 12(2013): 1123 – 1149.

[3] Greco, F., M., Arroyo. "High-order maximum-entropy collocation methods". Computer Methods in Applied Mechanics and Engineering 367. (2020).

[4] Greco, F., L., Filice, C., Peco, M., Arroyo. "A stabilized formulation with maximum entropy meshfree approximants for viscoplastic flow simulation in metal forming". International Journal of Material Forming 8. 3(2015): 341 – 353.

[5] Greco, F., L., Coox, W., Desmet. "Maximum-entropy methods for time-harmonic acoustics". Computer Methods in Applied Mechanics and Engineering 306. (2016): 1 – 18.

[6]  Greco, F., A., Rosolen, L., Coox, W., Desmet. "Contact mechanics with maximum-entropy meshfree approximants blended with isogeometric analysis on the boundary". Computers and Structures 182. (2017): 165 – 175.

[7] Greco, F., L., Coox, F., Maurin, W., Desmet. "NURBS-enhanced maximum-entropy schemes". Computer Methods in Applied Mechanics and Engineering 317. (2017): 580 – 597.