Approach to numerical implementation of drift-diffusion model of field effects induced by moving source
An approach to the numerical implementation of the diffusion-drift model in the application to the problem of estimating field effects induced in an object by a concentrated moving source is presented. The mathematical model is formalized using the initial boundary-value problem for a multidimensional evolution equation of the type “convection-reaction-diffusion”. The computational algorithm is based on a modification of the “predictor-corrector” scheme for solving the diffusion problem and approximating the drift component according to the Roberts-Weiss scheme. The software implementation of the mathematical model in the matlab checkpoint was carried out. The results of computational experiments with varying values of the control parameters of the model are presented.
Keywords
диффузионно-дрейфовая модель,
движущийся источник,
процесс «конвекция - реакция - диффузия»,
уравнение с частными производными параболического типа,
схема «предиктор - корректор»,
схема Робертса - Вейсса,
drift-diffusion model,
moving source,
convection-reaction-diffusion process,
finite difference predictor-corrector scheme,
Roberts-Weiss schemeAuthors
| Pavelchuk A.V. | Amur State University | ap.9.04@mail.ru |
| Maslovskaya A.G. | Amur State University | maslovskayaag@mail.ru |
Всего: 2
References
Hundsdorfer W. and Verwer J.G. Numerical Solution of Time-Dependent Advection-Diffusion Reaction Equations Series. - Berlin: Springer, 2003. - 495 p.
Otten D. Mathematical Models of Reaction Diffusion Systems, their Numerical Solutions and the Freezing Method with Comsol Multiphysics. - Bielefeld: Bielefeld University (Germany), 2000. - 77 p.
Drake J.B. Climate Modeling for Scientists and Engineers. - Knoxville, Tennessee: University of Tennessee, 2014. - 47 p.
Montecinos G.I. Numerical methods for advection-diffusion-reaction equations and medical applications: PhD thesis. - University of Trento, 2014. - 161 p.
Tan X. // Electron J. Prorab. - 2013. - No. 145. - P. 1-24.
Kadanoff L.P. Statistical Physics: Statics, Dynamics and Renormalization. - London: World Scientific Publ., 2000. - 484 p.
Patankar S.V. Numerical Heat Transfer and Fluid Flow. - Washington: Hemisphere Publ. Corp., 1980. - 195 p.
Самарский А.А., Вабищевич П.Н. Численные методы решения задач конвекции-диффузии. - М.: Эдиториал УРСС, 1999. - 248 с.
Jin Y.F., Jiang J., Hou C.M., and Guan D.H. // J. Inform. Comput. Sci. - 2012. - V. 18. - P. 5579- 5586.
Шишкина О.В. // Сибирский математический журн. - 2007. - Т. 48. - № 6. - C. 1422-1428.
Афанасьева Н.М., Вабищевич П.Н., Васильева М.В. // Изв. вузов. Математика. - 2013. - № 3. - С. 3-15.
Krukier L.A., Pichugina O.A., and Krukier B.L. // Int. Conf. Computational Science (ICCS). - 2013. - V. 18. - P. 2095-2100.
Buckova Z., Ehrhardt M., and Gunther M. Alternating direction explicit methods for convection diffusion equations // Bergische Universitat Wuppertal Fachbereich Mathematik und Naturwissenschaften, IMACM. 2015. - P. 309-325.
Cazaux J. // Microscopy and Microanalysis. - 2004. - V. 10. - No. 6. - P. 670-680.
Kotera M., Yamaguchi K., and Suga H. // Jpn. J. Appl. Phys. - 1999. - V. 38. - No. 12. - P. 7176- 7179.
Raftari B., Budko N.V., and Vuik C. // J. Appl. Phys. - 2015. - V. 118. - P. 204101.
Chezganov D.S., Kuznetsov D.K., and Shur V.Ya. // Ferroelectrics. - 2016. - V. 496. - P. 70-78.
Maslovskaya A. and Pavelchuk A. // Ferroelectrics. - 2015. - V. 476. - P. 157-167.
Pavelchuk A.V. and Maslovskaya A.G. // Proc. IOP Conf. Series: J. Phys.: Conf. Series. - 2019. - P. 012009 (6 p.).
