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2PLenary session
the characteristic size of the simulated semiconductor should be taken at least tens of thousands nanometers
while the dislocation diameter is 6 nm, and the piezofield is varying in the cylindrical region of radius 100 nm
around the dislocation.This means if a finite.difference method would be applied to solve this problem we
would have to introduce a mesh with at least several billions of nodes which is unrealistic. The RWS algorithm
developed is meshfree and calculates directly the fluxes and cathodoluminesence intensity in a semiconductor
which includes hundreds of dislocations with the piezoelectric fields around them.
The support of the Russian Science Foundation under grant���19.11.00019 is gratefully acknowledged.
References
1. Sabelfeld K.K. Random walk on spheres algorithm for solving transient drift.diffusion.reaction problems // Monte
Carlo Methods Appl. 2017.V. 23 (3), P. 189�212.
2. Kaganer Vladimir M., Lahnemann Jonas, Pfuller Carsten, Sabelfeld Karl K., Kireeva Anastasya E., and Brandt Oliver.
Determination of the Carrier Diffusion Length in GaN from Cathodoluminescence Maps Around Threading Dislocations:
Fallacies and Opportunities // Physical Review Applied. 2019.V. 12, 054038.
3. Sabelfeld Karl K. and Kireeva A. Supercomputer Simulation of Cathodoluminescence Transients in the Vicinity of
Threading Dislocations // PCT 2018, CCIS. 2018.V. 910, P. 1�14.
Sensitivity of functionals in variational data assimilation
V. Shutyaev1, E. Parmuzin1, I. Gejadze2
1Marchuk Institute of Numerical Mathematics, RAS
2French National Research Institute for Agriculture, Food, and Environment, Montpellier, France
Email: victor.shutyaev@mail.ru
DOI 10.24412/cl.35065.2021.1.01.53
The problem of variational data assimilation for a nonlinear evolution modelis formulated as an optimal
control problem to find the initial state and the unknown parameters of the model. A response function is
considered as a functional of the optimal solution after assimilation. The sensitivity of the response function to
the observation data is studied.The gradient of the response function with respect to observations is related
to the solution of a non.standard problem involving the coupled system of direct and adjoint equations. Based
on the Hessian of the original cost function, the solvability of the non.standard problem is studied.Algorithms
to compute the gradient of the response function with respect to observation data are formulated and justified.
Numerical examples are presented for variationaldata assimilation problem for the Black Sea thermodynamics
model.
This work was carried out within the Russian Science Foundation project 20.11.20057.
References
1. I. Gejadze, F..X. Le Dimet and V. Shutyaev. On analysis error covariances in variational data assimilation. SIAM J.
Sci. Comput., 30(4), 1847.1874 (2008).
2. I. Gejadze and V.Shutyaev. On gauss.verifiability of optimal solutions in variational data assimilation problems with
nonlinear dynamics. J. Comp. Phys., 280, 439.456 (2015).
3. I. Gejadze, P.�.O. Malaterre and V. Shutyaev. On the use of derivatives in the polynomial chaos based global
sensitivity and uncertainty analysis applied to the distributed parameter models. J. Comp.Phys., 381, 218.245 (2019).
4. V.P. Shutyaev, F..X. Le Dimet. Sensitivity of functionals of variational data assimilation problems. Doklady
Mathematics, 99(3), 295.298 (2019).
5. V. Shutyaev, F..X. Le Dimet and E. Parmuzin. Sensitivity of response functions in variational data assimilation for
joint parameter and initial state estimation. J. Comp. Appl. Math., 373 (112368), 1.14 (2020).
