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REFERENCES 119 [13] Lawrence C. Evans. Partial Differential Equations, volume19ofGraduate Stud- ies in Mathematics. AMS, Providence, Rhode Island, 1999. [14] William R. Frensley. Transient response of a tunneling device obtained from the Wigner function. Phys. Rev. Letters, 57:2853–2856, 1986. [15] William R. Frensley. Wigner-function model of a resonant tunneling semicon- ductor device. Phys. Rev. B, 36:1570–1580, 1987. [16] W. J. F. Govaerts. Numerical Methods for Bifurcations of Dynamical Equilibria. SIAM, Philadelphia, 2000. [17] Michael Heroux, Roscoe Bartlett, Vicki Howle Robert Hoekstra, Jonathan Hu, Tamara Kolda, Richard Lehoucq, Kevin Long, Roger Pawlowski, Eric Phipps, Andrew Salinger, Heidi Thornquist, Ray Tuminaro, James Willenbring, and Alan Williams. An Overview of Trilinos. Technical Report SAND2003-2927, Sandia National Laboratories, 2003. [18] H. B. Keller. Lectures on Numerical Methods in Bifurcation Problems. Springer- Verlag, New York, 1987. [19] C. T. Kelley. Iterative Methods for Linear and Nonlinear Equations, volume16of Frontiers in Applied Mathematics. SIAM, Philadelphia, PA, first edition, 1995. [20] C. T. Kelley. Iterative Methods for Optimization. Frontiers in Applied Mathe- matics. SIAM, Philadelphia, PA, first edition, 1999.
REFERENCES 120 [21] C. T. Kelley and Z. Q. Xue. GMRES and integral operators. SIAM Journal on Scientific Computing, 17(1):217–226, 1996. [22] N.C. Kluksdahl, A.M. Kriman, D.K. Ferry, and C. Ringhofer. Self-consistent study of the resonant-tunneling diode. Phys. Rev. B, 39:7720–7735, 1989. [23] Erwin Kreyszig. Introductory Functional Analysis with Applications. John Wiley and Sons, New York, 1978. [24] Yuri A. Kuznetsov. Elements of Applied Bifurcation Theory, volume 112 of Applied Mathematics Sciences. Springer-Verlag, New York, second edition, 1998. [25] R. B. Lehoucq, D. C. Sorensen, and C. Yang. ARPACK users’ guide: Solution of large scale eigenvalue pro blems with implicitly restarted arnoldi methods. Technical report, 1997. [26] Jerrold E. Marsden and Michael J. Hoffman. Elementary Classical Analysis. W.H. Freeman and Company, New York, 1993. [27] K. Meerbergen, A. Spence, and D. Roose. Shift-invert and Cayley transforms for detection of rightmost eigenvalues of nonsymmetric matrices. BIT, 34:409–423, 1994. [28] Carl D. Meyer. Matrix Analysis and Applied Linear Algebra. SIAM, Philadephia, PA, 2000.
Page 1 and 2:
Numerical Methods for the Wigner-Po
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NUMERICAL METHODS FOR THE WIGNER-PO
Page 5 and 6:
Acknowledgments First and foremost,
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Table of Contents List of Tables ix
Page 9 and 10:
4.3 ApplicationofSchauder’sFixedP
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List of Tables 1.1 PhysicalConstant
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3.11 I-V Curve with 30 Percent Redu
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CHAPTER 1. OVERVIEW 2 being heavily
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CHAPTER 1. OVERVIEW 4 Doping Spacer
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CHAPTER 1. OVERVIEW 6 and identfyin
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CHAPTER 1. OVERVIEW 8 for predictin
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CHAPTER 1. OVERVIEW 10 by Schrödin
Page 25 and 26:
CHAPTER 1. OVERVIEW 12 ranging term
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CHAPTER 1. OVERVIEW 14 But because
Page 29 and 30:
CHAPTER 1. OVERVIEW 16 = h 2π ,we
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CHAPTER 1. OVERVIEW 18 Table 1.1: P
Page 33 and 34:
CHAPTER 1. OVERVIEW 20 where q is t
Page 35 and 36:
CHAPTER 1. OVERVIEW 22 get K(f)
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CHAPTER 1. OVERVIEW 24 rule. The pr
Page 39 and 40:
CHAPTER 1. OVERVIEW 26 The weights
Page 41 and 42:
Chapter 2 Temporal Integration 2.1
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CHAPTER 2. TEMPORAL INTEGRATION 30
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Chapter 3 Bifurcation Analysis 3.1
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CHAPTER 3. BIFURCATION ANALYSIS 46
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Page 81 and 82: CHAPTER 3. BIFURCATION ANALYSIS 68
Page 87 and 88: Chapter 4 Theory 4.1 Steady-State T
Page 89 and 90: CHAPTER 4. THEORY 76 If we write ou
Page 91 and 92: CHAPTER 4. THEORY 78 So if we write
Page 93 and 94: CHAPTER 4. THEORY 80 Combining Equa
Page 95 and 96: CHAPTER 4. THEORY 82 We now estimat
Page 97 and 98: CHAPTER 4. THEORY 84 pendent of x,
Page 99 and 100: CHAPTER 4. THEORY 86 interval we ha
Page 101 and 102: CHAPTER 4. THEORY 88 So an estimate
Page 103 and 104: CHAPTER 4. THEORY 90 We want to cho
Page 105 and 106: CHAPTER 4. THEORY 92 The exact same
Page 107 and 108: CHAPTER 4. THEORY 94 Since un → u
Page 109 and 110: CHAPTER 4. THEORY 96 thereexistsaco
Page 111 and 112: CHAPTER 4. THEORY 98 For 0
Page 113 and 114: CHAPTER 4. THEORY 100 denote this d
Page 115 and 116: CHAPTER 4. THEORY 102 Now, we can t
Page 117 and 118: CHAPTER 4. THEORY 104 operator. 4.2
Page 119 and 120: CHAPTER 4. THEORY 106 we have at th
Page 121 and 122: CHAPTER 4. THEORY 108 we have at th
Page 123 and 124: CHAPTER 4. THEORY 110 4.3 Applicati
Page 125 and 126: CHAPTER 4. THEORY 112 We need to fi
Page 127 and 128: Chapter 5 Conclusion In this work,
Page 129 and 130: CHAPTER 5. CONCLUSION 116 • Findi
Page 131: REFERENCES 118 ODE solver. Technica
Page 135 and 136: REFERENCES 122 [37] Homer F. Walker
Page 137 and 138: APPENDIX A. NOTATION 124 ˜B Genera
Page 139 and 140: APPENDIX A. NOTATION 126 k Wave num
Page 141 and 142: APPENDIX A. NOTATION 128 ∆t Incre
Page 143 and 144: APPENDIX A. NOTATION 130 ɛc ɛk ɛ
Page 145 and 146: APPENDIX B. TRILINOS 132 user-given
Page 147 and 148: APPENDIX B. TRILINOS 134 Trilinos,
Page 149 and 150: APPENDIX B. TRILINOS 136 Minimum Re
Page 151 and 152: APPENDIX B. TRILINOS 138 A very use
Page 153 and 154: Appendix C Guide to RTD Simulation
Page 155 and 156: APPENDIX C. GUIDE TO RTD SIMULATION
Page 163 and 164: Appendix D GMRES and Arnoldi Iterat
Page 165 and 166: APPENDIX D. GMRES AND ARNOLDI ITERA
Page 167 and 168: APPENDIX D. GMRES AND ARNOLDI ITERA
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