W.F. Ames, Numerical Methods for Partial Differential Equations, 3Ed, Academic Press, 1992.
 G. Bester, A. Zunger, Cylindrically shaped zinc-blende semiconductor quantum dots do not have cylindrical symmetry: Atomistic symmetry, atomic relaxation, and piezoelectric effects, Physical Review B, 71(4) 2005, 045318.
 C. Bose, Binding energy of impurity states in spherical quantum dots with parabolic confinement, Journal of Applied Physics, 83(6) 1998, 3089-3091.
 D. Braess, Finite Elements, Theory, Fast Solvers, and Applications in Elasticity Theory, Cambridge Univ. Press, 2007.
 S. Brenner, R. Scott, The Mathematical Theory of Finite Element Methods, Springer, 2007.
 P.K. Chattopadhyay, Mathematical Physics, New Age Int. (P) Ltd., 1990.
 D.M. Cunha, F.L. Souza, Facile synthetic route for producing one-dimensional zinc oxide nanoflowers and characterization of their optical properties, Journal of Alloys and Compounds, 577 2013, 158-164.
 A. Deyasi, S. Bhattacharyya, N.R. Das, Computation of intersubband transition energy in normal and inverted core-shell quantum dots using finite difference technique, Superlattices and Microstructures, 60 2013, 414-425.
 M. El-Said, Spectroscopic structure of two interacting electrons in a quantum dot by the shifted 1/N expansion method, Physical Review B, 61(19) 2000, 13026.
 T.F. Fang, S.J. Wang, Cross correlations and shot noise in a Y-shaped quantum dot, Journal of Physics: Condensed Matter, 19(2) 2006, 026204.
 B.A. Finlayson, The Method of Weighted Residuals and Variational Principles, with application in fluid mechanics, heat and mass transfer, Academic Press, 1972.
 T. García, Francisco Manuel Gómez-Campos, and Salvador Rodríguez-Bolívar, Influence on miniband structure of size variations in regimented InAs/GaAs quantum dots arrays, Journal of Applied Physics, 114 2013, 064311.
 M. Ghorbani, Diffuse Element Kansa Method, Applied Mathematical Sciences, 4(12) 2010, 583-594.
 V. Golubnychiy, H. Baumgartner, M. Bonitz, A. Filinov and H. Fehske, Screened Coulomb balls-structural properties and melting behavior, Journal of Physics A: Mathematical and General, 39(17) 2006, 4527.
 M. Governale, M. Macucci, G. Iannaccone, C. Ungarelli, and J. Martorell, Modeling and manufacturability assessment of bistable quantum-dot cells Journal of applied physics, 85(5) 1999, 2962-2971.
 A.D. Gu¨c¸lu¨, Q.F. Sun, H. Guo, R. Harris, Geometric blockade in a quantum dot: Transport properties by exact diagonalization, Physical Review B, 66(19) 2002, 195327.
 A.D. Güçlü, C.J. Umrigar, Maximum-density droplet to lower-density droplet transition in quantum dots, Physical Review B 72(4) 2005, 045309.
 T.M. Hwang, W. Wei Lin, W.C. Wang, Weichung Wang, Numerical simulation of three dimensional pyramid quantum dot, Journal of Computational Physics, 196(1) 2004, 208.
 S.M. Ikhdair, M. Hamzavi, A quantum pseudodot system with two-dimensional pseudoharmonic oscillator in external magnetic and Aharonov-Bohm fields, Physica B: Condensed Matter, 407(21) 2012, 4198-4207.
 R. Khordad, H. Bahramiyan, Impurity position effect on optical properties of various quantum dots, Physica E: Low-dimensional Systems and Nanostructures, 66 2015, 107-115.
 Y.J. Kim, J. Yoo, B.H. Kwon, Y.J. Hong, C.H. Lee and G.C. Yi, Position-controlled ZnO nanoflower arrays grown on glass substrates for electron emitter application, Nanotechnology 19(31) 2008, 315202.
 M. Mardaania, A. Shokri, K. Esfarjani, Analytical results on coherent conductance in a general periodic quantum dot: Transfer matrix method, Physica E: Low-dimensional Systems and Nanostructures, 28(2) 2005, 150-161.
 J.T. Marti, Introduction to Sobolev spaces and finite element solution of elliptic boundary value problems, Academic Press, 1986.
 R.V.N. Melnik, M. Willatzen, Bandstructures of conical quantum dots with wetting layers, Nanotechnology, 15(1) 2004.
 A.R. Mitchell, R. Wait, Finite Element Analysis and Applications, John Wiley, 1985.
 M.A. Naser, M.J. Deen, D.A. Thompson, Spectral function and responsivity of resonant tunneling and superlattice quantum dot infrared photodetectors using Green’s function, Journal of Applied Physics, 102(8) 2007, 083108.
 A.V. Nenashev, and A. V. Dvurechenskii, Variational method of energy level calculation in pyramidal quantum dots, Journal of Applied Physics, 127(15) 2020, 154301.
 S. Nomura, Y. Aoyagi, Density of states of a quantum dot array probed by photoluminescence spectra, Surface science, 529(1-2) 2003, 171-179.
 J.N. Reddy, An Introduction to the Finite Element Method, Mc Graw-Hill, 2005.
 A.H. Rodrıguez, H.Y. Ramırez, Analytical calculation of eigen-energies for lens-shaped quantum dot with finite barriers, The European Physical Journal B, 66(2) 2008, 235-238.
 E. Sadeghi, F. Vahdatnejad, M. Moradi LM, Effect of polarization charges on impurity binding energy in elliptical quantum wire, Superlattices and Microstructures, 58 2013, 165-170.
 V.A. Shuvayev, L.I. Deych, I.V. Ponomarev, A.A. Lisyansky, Self-consistent Hartree method for calculations of exciton binding energy in quantum wells, Superlattices and Microstructures, 40(2) 2006, 77-92.
 P. Solín, Partial Differential Equations and the Finite Element Method, 2005, John Wiley & Sons.
 L. Song, A. Lukianov, D. Butenko, H. Li, J. Zhang, M. Feng, L. Liu, D. Chen and N.I. Klyui, Facile Synthesis of Hierarchical Tin Oxide Nanoflowers with Ultra-High Methanol Gas Sensing at Low Working Temperature, Nanoscale Research Letters, 14(1) 2019, 1-11.
 O. Stier, M. Grundmann, D. Bimberg, Electronic and optical properties of strained quantum dots modeled by 8-band k.p theory, Physical Review B, 59(8) 1999, 5688.
 R. Wei, W. Xie, Optical absorption of a hydrogenic impurity in a disc-shaped quantum dot, Current Applied Physics, 10(3) 2010, 757-760.
 B.H. Wu, J.C. Cao, Interference of conductance and shot noise properties of photon-assisted transport through a T-shaped double quantum dot, Physical Review B, 73(20) 2006, 205318.
 G. Zhou and Y. Li, Electromagnetic-field-induced resonant structures for an open rectangular quantum dot, The European Physical Journal B-Condensed Matter and Complex Systems, 46(1) 2005, 127-132.