Numerical simulation of heat transfer in semiconductor heterostructures
https://doi.org/10.17073/1609-3577-2017-4-256-261
Abstract
The paper deals with the construction of numerical models of heat transfer in a multilayer AlAs/GaAs nanostructure. The problem is solved using a hybrid finite-difference-mesh-free method based on radial-basis functions. The obtained solutions are compared for various bases, as well as with and without normalization of the approximating model. The possibility of increasing the speed of computations due to the parallelizability of computations is investigated, it is shown that, using multiprocessor systems, one can achieve a significant increase in performance.
Keywords
About the Authors
K. K. AbgaryanRussian Federation
40 Vavilov Str., Moscow 119333;
4 Volokolamskoe Shosse, Moscow 125993
Karine K. Abgaryan: Cand. Sci. (Phys.-Math.), Head of the Department
I. S. Kolbin
Russian Federation
40 Vavilov Str., Moscow 119333
Ilya S. Kolbin: Cand. Sci. (Phys.-Math.), Researcher
References
1. Vasilyev A. N., Kolbin I. S., Reviznikov D. L. Meshfree computational algorithms based on normalized radial basis functions. In: Cheng L., Liu Q., Ronzhin A. (eds) Advances in Neural Networks — ISNN 2016. Lecture Notes in Computer Science. V. 9719. Cham: Springer, 2016, pp. 583—591. DOI: 10.1007/978-3-319-40663-3_67
2. Kolbin I. S., Reviznikov D. L. Solving mathematical physics problems using normalized radial basis functions neural-like networks. Neurocomputers: Developing, Applications. 2012, no. 2, pp. 12—19. (In Russ.)
3. Vasilev A. N., Tarkhov D. A. Neirosetevoe modelirovanie. Printsipy, algoritmy, prilozheniya [Neural network modelling principles, algorithms, applications]. St. Petersburg: Izdatel’stvo Politekhnicheskogo universiteta, 2009, 528 p. (In Russ.)
4. Hager W. W., Zhang H. A new conjugate gradient method with guaranteed descent and an efficient line search. SIAM J. Optim., 2005, vol. 16, no. 1, pp. 170—192. DOI: 10.1137/030601880
5. Nocedal J., Wright S. J. Numerical optimization. New York: Springer Verlag, 1999.
6. Nocedal J. Updating quasi-Newton matrices with limited storage. Math. Comp., 1980, vol. 35, no. 151, pp. 773—782. DOI: 10.2307/2006193
7. Hardy R. L. Multiquadric equations of topography and other irregular surfaces. J. Geophysical Research, 1971, vol. 76, no. 8, pp. 1905—1915. DOI: 10.1029/JB076i008p01905
8. Hardy R. L. Theory and applications of the multiquadric biharmonic method 20 years of discovery 1968—1988. Comput. Math. Appl., 1990, vol. 19, no. 8–9, pp. 163—208. DOI: 10.1016/0898-1221(90)90272-L
9. Kansa E. J. Multiquadrics — a scattered data approximation scheme with applications to computational fluid-dynamics. 1. Surface approximations and partial derivative estimates. Comput. Math. Appl., 1990, vol. 19, no. 8–9, pp. 127—145. DOI: 10.1016/0898-1221(90)90270-T
10. Vorob’ev D. A., Hvesyuk V. I. Calculation method for non-stationary heating of nano-structures. Science and Education of Bauman MSTU, 2013, pp. 541—550. (In Russ.). DOI: 10.7463/0913.0617255
11. Chen W. New RBF Collocation Methods and Kernel RBF with Applications. In: M. Griebel, M.A. Schweitzer (Eds.). Meshfree Methods for Partial Differential Equations. Lecture Notes in Computational Science and Engineering. Berlin; Heidelberg: Springer, 2003, vol. 26, pp. 75—86. DOI: 10.1007/978-3-642-56103-0_6
12. Benaim M. On the functional approximation with normalized Gaussian units. Neural Computation, 1994, vol. 6, no. 2, pp. 319—333. DOI: 10.1162/neco.1994.6.2.319
13. Bugmann G. Normalized Gaussian radial basis function networks. Neurocomputing, 1998, vol. 20, no. 1–3, pp. 97—110. DOI: 10.1016/S0925-2312(98)00027-7
14. Kansa E. J. Multiquadrics-a scattered data approximation scheme with applications to computational fluid dynamics-II. Solutions to hyperbolic, parabolic, and elliptic partial differential equations. Comput. Math. Appl., 1990, vol. 9, no. 8–9, pp. 147—161. DOI: 10.1016/0898-1221(90)90271-K
Review
For citations:
Abgaryan K.K., Kolbin I.S. Numerical simulation of heat transfer in semiconductor heterostructures. Izvestiya Vysshikh Uchebnykh Zavedenii. Materialy Elektronnoi Tekhniki = Materials of Electronics Engineering. 2017;20(4):256-261. https://doi.org/10.17073/1609-3577-2017-4-256-261