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APPENDIX C. GUIDE TO RTD SIMULATION CODE 143 • printSolution - a routine that postprocesses the computed steady-state distri- bution, such as computing the current output and the potential energy within the RTD. These post-processing routines are written in Fortran 77. • applyMassMatrix - a routine that applies the left preconditioner ˜ M =(K − 1 τ I)−1 . C.2.2 RTDProblemInterfaceParallel.C This is the concrete implementation of the routines defined within RTDProblemInter- face.H. These routines are written in the accompanying Fortran 77 code, and they are wrapped to interface with the C++ code at the top of the file. C.2.3 RTDContinuationParallel.C This is the driver of the continuation run. The various parameters for the nonlinear solver (inexact-Newton’s Method), the corresponding linear solver (GMRES), and eigensolver (Arnoldi) are set in this code. These include: • Continuation Run – ”Continuation Method” - Selects which continuation method is used. Cur- rently set to ”Householder Arc Length”. – ”Initial Value” - Sets the initial voltage parameter in the continuation run.
APPENDIX C. GUIDE TO RTD SIMULATION CODE 144 – ”Max Value” - Sets the upper bound on the voltage parameter for the continuation run. – ”Min Value” - Sets the lower bound on the voltage parameter for the continuation run. – ”Max Steps” - Sets the maximum number of continutation steps attempted in the run. – ”Initial Step Size” - Sets the initial step to take in the voltage parameter in the continuation run. – ”Aggressiveness” - Value chosen in (0, 1] that determines how drastically LOCA increases the step size in the continuation parameter after success- fully converging the previous value of the continuation parameter. This is currently set to 0.5. To generate a smoother I-V curve over a specified voltage range, one can lower the aggressiveness value. • Nonlinear Solver – Convergence criteria - The nonlinear iteration terminates when the nonlinear residual norm is less than a specified tolerance (currently 10 −9 )or after a maximum number of iterations (currently 7). • Linear Solver – ”Max Iterations” - Maximum number of iterations GMRES will take to solve linear system. This is currently set to 500.
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Numerical Methods for the Wigner-Po
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NUMERICAL METHODS FOR THE WIGNER-PO
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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
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CHAPTER 1. OVERVIEW 10 by Schrödin
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CHAPTER 1. OVERVIEW 12 ranging term
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CHAPTER 1. OVERVIEW 14 But because
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CHAPTER 1. OVERVIEW 16 = h 2π ,we
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CHAPTER 1. OVERVIEW 18 Table 1.1: P
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CHAPTER 1. OVERVIEW 20 where q is t
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CHAPTER 1. OVERVIEW 22 get K(f)
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CHAPTER 1. OVERVIEW 24 rule. The pr
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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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Chapter 4 Theory 4.1 Steady-State T
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CHAPTER 4. THEORY 76 If we write ou
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CHAPTER 4. THEORY 78 So if we write
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CHAPTER 4. THEORY 80 Combining Equa
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CHAPTER 4. THEORY 82 We now estimat
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CHAPTER 4. THEORY 84 pendent of x,
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CHAPTER 4. THEORY 86 interval we ha
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CHAPTER 4. THEORY 88 So an estimate
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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 and 134: REFERENCES 120 [21] C. T. Kelley an
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
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