Geodesic
Application of the fast automatic differentiation for calculation of gradients of material's Bulk modulus and Shear modulus
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2017), pp. 95-106.

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In computer modeling of crystal structures the gradient optimization methods are often used. This raises the need to calculate the exact gradients of the Bulk modulus and the Shear modulus of materials. With help of the Fast Automatic Differentiation the formulas that allow the calculation of the exact above-mentioned gradients were derived in the case where the total interatomic energy of the system is determined by Tersoff's Potential. 
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Alla Albu; Vladimir Zubov. Application of the fast automatic differentiation for calculation of gradients of material's Bulk modulus and Shear modulus. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2017), pp. 95-106. https://geodesic-test.mathdoc.fr/item/BASM_2017_1_a8/

[1] Tersof J., “Empirical Interatomic Potential for Silicon with Improved Elastic Properties”, Phys. Rev. B, 38 (1988), 9902–9905 | DOI

[2] Abgaryan K. K., Posypkin M. A., “Optimization Methods as Applied to Parametric Identification of Interatomic Potentials”, Comp. Math. and Math. Phys., 54:12 (2014), 1929–1935 | DOI | MR | Zbl

[3] Albu A. F., “Application of the Fast Automatic Differentiation to the Computation of the Gradient of the Tersoff Potential”, Informacionnye tekhnologii i vychislitel'nye sistemy, 2016, no. 1, 43–49

[4] Evtushenko Y. G., “Computation of Exact Gradients in Distributed Dynamic Systems”, Optimizat. Methods and Software, 9 (1998), 45–75 | DOI | MR | Zbl

[5] Albu A. F., Application of the Fast Automatic Differentiation to Solve Problems of Heat Processes with Phase Transitions, Doctoral Dissertation in Mathematics and Physics, Dorodnicyn Computing Centre, FRC CSC RAS, 2016, 292 pp.