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REFERENCES 121 [29] Michael Pernice and Homer F. Walker. NITSOL: A Newton iterative solver for nonlinear systems. SIAM Journal of Scientific Computing, 19(1):302–318, 1998. [30] Alfio Quarteroni, Riccardo Sacco, and Fausto Saleri. Numerical Mathematics, volume 37 of Texts in Applied Mathematics. Springer-Verlag, New York, 2000. [31] Christian Ringhofer. A spectral method for the numerical simulation of quantum tunneling phenomena. SIAM J. Numer. Anal., 27:32–50, 1991. [32] Christian Ringhofer. A spectral collocation technique for the solution. SIAM J. Numer. Anal., 29:679–700, 1992. [33] Andrew G. Salinger, Nawaf M. Bou-Rabee, Roger P. Pawlowski, Edward D. Wilkes, Elizabeth A. Burroughs, Richard B. Lehoucq, and Louis A. Romero. LOCA 1.0 library of continuation algorithms: Theory and implementation man- ual. Technical Report SAND2002-0396, Sandia National Laboratory, March 2002. [34] D. R. Smart. Fixed Point Theorems. Cambridge University Press, London, 1974. [35] T.C.L.G. Sollner, W.D. Goodhue, P.E. Tannenwald, C.D. Parker, and D.D. Peck. Resonant tunneling through quantum wells at frequencies up to 2.5 THz. Appl. Phys. Lett., 43:588–590, 1983. [36] T.C.L.G. Sollner, P.E. Tannenwald, D.D. Peck, and W.D. Goodhue. Quantum well oscillators. Appl. Phys. Lett., 45:1319–1321, 1984.
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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
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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
Page 23 and 24:
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
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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 83 and 84: CHAPTER 3. BIFURCATION ANALYSIS 70
Page 85 and 86: CHAPTER 3. BIFURCATION ANALYSIS 72
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 and 132: REFERENCES 118 ODE solver. Technica
Page 133: REFERENCES 120 [21] C. T. Kelley an
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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