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APPENDIX C. GUIDE TO RTD SIMULATION CODE 145 – ”Tolerance” - Tolerance to which GMRES drives the relative residual of • Eigensolver the linear solve. This is currently set to 10 −3 . – ”Compute Eigenvalues” - Boolean variable that turns on the eigensolver if it is set to ”true”. – ”Arnoldi Size” - Maximum number of Arnoldi iterations to converge the requested number of eigenvalues/eigenvectors. – ”NEV” - Requested number of eigenvalues/eigenvectors to converge. – Tol - Tolerance to which the Arnoldi iteration drives the Schur error for the eigenvalue approximation. – ”Frequency” - The number of continuation steps taken between calls to the eigensolver to converge the requested number of eigenvalues/eigenvectors. – ”Cayley Pole” - Sets the Cayley pole parameter ¯µ. This is currently set to 0.002. – ”Cayley Zero” - Sets the Cayley zero parameter ¯σ. Thisiscurrentlyset to −0.002. C.2.4 rtdrespara.f This routine computes the preconditioned nonlinear residual ˜ MW( f), where W ( f)is the nonlinear residual and ˜ M =(K − 1 τ I)−1 is the left preconditioner.
APPENDIX C. GUIDE TO RTD SIMULATION CODE 146 C.2.5 rtdinit1.f This routine loads the initial guess for the steady-state distribution of the first value of the continuation parameter from the data file initial.out. C.2.6 rtdinit2.f This routine loads f0(x, k) from the data file sol.out, calculates physical constants, and creates the matrix representation of C.2.7 transipara.f f0(x,k) Kmax −Kmax f0(x,k ′ . )dk ′ This routine is the physics module of the RTD simulation. There are functions within that solve Poisson’s equation for the electric potential, calculates the relaxation time, defines the barrier locations and heights, etc. C.2.8 dout.f This routine post-processes computed electron distributions f(x, k) for both the time-dependent and steady-state simulations. There are functions for printing time- integration statistics and saving the electron density, current density, and electric potential to the files ele.out, cur.out, andrvstem.out.
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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
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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
Page 153 and 154: Appendix C Guide to RTD Simulation
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