[1] He Y, Wei T F. Computer Simulation Method for Semiconductor Device. Beijing:Scicence Press, 1989
[2] Shi M. Physics of modern semiconductor device. Beijing:Science Press, 2002
[3] Yuan Y R. Theory and Application of Reservoir Numerical Simulation, Chapter 7, Numercial Method of Transient Behavior of Semiconductor Device. Beijing:Science Press, 2013
[4] Yuan Y R. Recent progress in numerical methods for semiconductor devices. Chin J Comput Phy, 2009, 26(3):317-324
[5] Bank R E, Fichtner, W M, Rose, D J, et al. Transient simulation of sillcon devices and circuits. IEEE Computer-Aided Design, 1985, 6:436-451
[6] Jerome J W. Mathematical Theory and Approximation of Semiconductor Models. Philadelphia:SIAM, 1994
[7] Douglas Jr J, Yuan Y R. Finite difference methods for transient behavior of a semiconductor device. Mat Apli Comp, 1987, 6(1):25-38
[8] Yuan Y R. Finite element method and analysis of numerical simulation of semiconductor device. Acta Math Sci, 1993, 13(3):241-251
[9] Yuan Y R. Finite difference method and analysis for three-dimensional semiconductor device of heat conduction. Sci China Math, 1996, 39(11):1140-1151
[10] Gummel H K. A self-consistent iterative scheme for one-dimensional steady-state transistor calculation. IEEE Trans:Electron Device, 1964, 11:455-465
[11] Yuan Y R, Ding L Y, Yang H. A new method and theoretical analysis of numerical analog of semiconductor. Chin Sci Bull, 1982, 27(7):790-795
[12] Yuan Y R. Characteristics method with mixed finite element for transient behavior of semiconductor device. Chin Sci Bull, 1991, 36(17):1356-1357
[13] Yuan Y R. The approximation of the electronic potential by a mixed method in the simulation of semiconductor. J Systems Sci Math Sci, 1991, 11(2):117-120
[14] Lou Y. On basic semiconductor equation with heat conduction. J Partial Diff Eqs, 1995, 1:43-54
[15] Sun C W, Lu Q S, Fan Z X. Laser Irradiation Effect. Beijing:National Defence Industry Press, 2002
[16] Yuan Y R. Characteristic finite difference fractional step methods for three-dimensional semiconductor device of heat conduction. Chin Sci Bull, 2000, 45(2):123-131
[17] Yuan Y R. Finite difference fractional step method for transient behavior of a semiconductor device. Acta Math Sci, 2005, 25B(3):427-438
[18] Yuan Y R. Modification of upwind finite difference fractional step methods by the transient state of the semiconductor device. Numer Meth Part D E, 2008, 24(2):400-417
[19] Sun T J, Yuan Y R. An approximation of incompressible miscible displacment in porous media by mixed finite element method and characteristics-mixed finite element methd. J Comp Appl Math, 2009, 228:391-411
[20] Yang Q, Yuan Y R. An approximation of semiconductor device by mixed finite element method and characteristics-mixed finite element method. Appl Math Comput, 2013, 225:407-424
[21] Yang Q, Yuan Y R. An approximation of three-dimensional semiconductor device by mixed finite element method and characteristics-mixed finite element method. Numer Math-Theory ME, to appear
[22] Yang Q, Yuan Y R. An approximation of semiconductor device of heat conduction by mixed finite element method characteristics-mixed finite element method. Appl Numer Math, 2013, 70:42-57
[23] Ewing R E, Lazarov R D, Vassilev A T. Finite difference scheme for parabolic problems on a composite grids with refinement in time and space. SIAM J Numer Anal, 1994, 31(6):1605-1622
[24] Lazarov R D, Mischev I D, Vassilevski P S. Finite volume methods for convection-diffusion problems. SIAM J Numer Anal, 1996, 33(1):31-55
[25] Ewing R E. The Mathematics of Reservoir Simulation. Philadelphia:SIAM, 1983
[26] Douglas Jr J, Gunn J E. Two order correct difference analogues for the equation of multidimensional heat flow. Math Comp, 1963, 17(81):71-80
[27] Douglas Jr J, Gunn J E. A general formulation of alternating direction methods, part I, parabolic and hyperbolic problems. Numer Math, 1964, 6(5):428-453
[28] Douglas Jr J, Ewing R E, Wheeler M F. Approximation of the pressure by a mixed method in the simulation of miscible displacement. RAIRO Anal Numer, 1983, 17(1):17-33
[29] Douglas Jr J, Yuan Y R. Numerical simulation of immiscible flow in porous media based on combining the method of characteristics with mixed finite element procedure//Numerical Simulation in Oil Recovery. New York:Springer-Verlag, 1986:119-132
[30] Yang Q. Mixed covolume-upwind finite volume methods for semiconductor device. J Systems Sci Math Sci, 2011, 31(1):65-79
[31] Russll T F. Rigorous Block-Centered Discritizations on Irregular Grids:Improved Simulation of Complex Reservoir Systems. Project Report, Tulsa:Research Corporation, 1995
[32] Weiser A, Wheeler M F. On convergence of block-centered finite difference for elliptic problems. SIAM J Numer Anal, 1988, 25(2):351-375
[33] Jones J E. A Mixed Finite Volume Method for Accurate Computation of Fluid Velocities in Porous Media[D]. University of Colorado, 1995
[34] Nitsche J. Linear splint-funktioncn and dic methoden von Ritz for elliptishce randwert probleme. Arch Rational Mech Anal, 1968, 36:348-355
[35] Jiang L S, Pang Z Y. Finite Element Method and Its Theory. Beijing:People's Education Press, 1979
[36] Rui H X, Pan H A. A block-centered finite difference method for the Darcy-Forchheimer model. SIAM J Numer Anal, 2012, 50(5):2612-2631
[37] Yuan Y R. Time stepping along characteristics for the finite element approximation of compressible miscible displacement in porous media. Math Numer Sinica, 1992, 14(4):385-400
[38] Yuan Y R. Finite difference methods for a compressible miscible displacement problem in porous media. Math Numer Sinica, 1993, 15(1):16-28
[39] Douglas Jr J. Simulation of miscible displacement in porous media by a modified method of characteristics procedure//Numerical Analysis, Dundee, 1981, Lecture Note in Mathematics 912. Berlin:Springer-Verlag, 1982 |