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Biography Matthew Lasater was born on June 4th, 1980 in Gastonia, NC. He continued to live there until 1996, when he left to attend the North Carolina School of Science and Mathematics in Durham, NC. After graduating from NCSSM in May of 1998, he moved to Raleigh, NC to begin college at North Carolina State University. Being as fickle as he is, Matthew switched majors constantly during his time as an undergrad- uate, starting out as a computer science major, moving on to physics, then statistics, to finally graduating in June 2001 with his bachelors in applied mathematics. He started graduate school the following August at NCSU in applied mathematics with the intention of getting his masters in applied mathematics but was swayed by his numerical analysis teacher (and soon-to-be advisor) to complete a Ph.D. program instead. Earning his bachelors in physics with a minor in statistics in May 2002, Matthew is pressing on to finish his Ph.D. in computational mathematics by the fall of 2005, after which he will start his job at M.I.T. Lincoln Laboratory as a member of the technical staff. ii
Acknowledgments First and foremost, I want to thank my advisor Tim Kelley. I appreciate his guidance, candor, knowledge, and patience without which I would not have finished this thesis. I am grateful for all he has done for me. I also want to thank some other members of the research project from which this work derives: Dwight Woolard, Peiji Zhao, and Greg Recine. They have helped me understand the application side of my research and prepared me for future work on interdisciplinary research projects. I would like to thank Pierre Gremaud, Stephen Campbell, and Ilse Ipsen for their critiques in the graduate student numerical analysis seminar and for Dr. Ipsen’s communication class. These have strengthened my ability to speak and write about mathematical topics and gave me a better appreciation of the pedagogical value found in these tasks. I am extremely thankful for the opportunity to intern at Sandia National Lab- oratories for two summers, and I want to thank Andy Salinger, Eric Phipps, Roger Pawlowski, Todd Coffey, Heidi Thornquist, and Robert Hoekstra for all their help at iii
Page 1 and 2: Numerical Methods for the Wigner-Po
Page 3: NUMERICAL METHODS FOR THE WIGNER-PO
Page 7 and 8: Table of Contents List of Tables ix
Page 9 and 10: 4.3 ApplicationofSchauder’sFixedP
Page 11 and 12: List of Tables 1.1 PhysicalConstant
Page 13 and 14: 3.11 I-V Curve with 30 Percent Redu
Page 15 and 16: CHAPTER 1. OVERVIEW 2 being heavily
Page 17 and 18: CHAPTER 1. OVERVIEW 4 Doping Spacer
Page 19 and 20: CHAPTER 1. OVERVIEW 6 and identfyin
Page 21 and 22: 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
Page 27 and 28: CHAPTER 1. OVERVIEW 14 But because
Page 29 and 30: CHAPTER 1. OVERVIEW 16 = h 2π ,we
Page 31 and 32: 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)
Page 37 and 38: 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 42
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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
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CHAPTER 4. THEORY 94 Since un → u
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CHAPTER 4. THEORY 96 thereexistsaco
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CHAPTER 4. THEORY 98 For 0
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CHAPTER 4. THEORY 100 denote this d
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CHAPTER 4. THEORY 102 Now, we can t
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CHAPTER 4. THEORY 104 operator. 4.2
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CHAPTER 4. THEORY 106 we have at th
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CHAPTER 4. THEORY 108 we have at th
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CHAPTER 4. THEORY 110 4.3 Applicati
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CHAPTER 4. THEORY 112 We need to fi
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Chapter 5 Conclusion In this work,
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CHAPTER 5. CONCLUSION 116 • Findi
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REFERENCES 118 ODE solver. Technica
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REFERENCES 120 [21] C. T. Kelley an
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REFERENCES 122 [37] Homer F. Walker
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APPENDIX A. NOTATION 124 ˜B Genera
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APPENDIX A. NOTATION 126 k Wave num
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APPENDIX A. NOTATION 128 ∆t Incre
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APPENDIX A. NOTATION 130 ɛc ɛk ɛ
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APPENDIX B. TRILINOS 132 user-given
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APPENDIX B. TRILINOS 134 Trilinos,
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APPENDIX B. TRILINOS 136 Minimum Re
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APPENDIX B. TRILINOS 138 A very use
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Appendix C Guide to RTD Simulation
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APPENDIX C. GUIDE TO RTD SIMULATION
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Appendix D GMRES and Arnoldi Iterat
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APPENDIX D. GMRES AND ARNOLDI ITERA
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APPENDIX D. GMRES AND ARNOLDI ITERA
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