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Appendix B Trilinos B.1 Introduction Trilinos is a software library currently under development by Sandia National Labo- ratories [17]. It is a set of parallel numerical solvers written in C++. A key feature of this software library is how compartmental the packages are. While Trilinos offers the user access to linear solver, nonlinear solver, eigensolvers, preconditioners, etc., the user does not need to download all of Trilinos to work. The user only needs to get which core packages they need. Another key feature of Trilinos is the separa- tion between the abstract solver layer and the data structures used in coding. If a user has a specifically tuned linear solver for his application and just wants to use the nonlinear solvers available in Trilinos, this is easy to handle. A wrapper around the data structure must be created, and then Trilinos’s nonlinear solvers can use the 131
APPENDIX B. TRILINOS 132 user-given linear solver. These features of Trilinos are possible since it is programmed in an object-oriented language. In the next section, the difference between procedural and object-oriented programming will be explained, and we will see how Trilinos benefits from the abstraction offered by object-oriented programming. B.2 Procedural and Object-Oriented Programming When most people think of computer programming, they usually think of the procedural paradigm of programming. Under this paradigm, emphasis is placed on functions and their ability to take as input a data structure, perform some computations on this data, and return as output a data structure. The highest level of abstraction available to user is the ability to write subroutines. Here, if in the main program, the user is repeatedly performing the same type of data manipulation, instead of writing the code that does this manipulation in every part of the main program that needs it, the user writes the code once in a subroutine, and then has the main program call the subroutine whenever needed. This is more efficient than rewriting the same code over and over again and makes it easier for a programmer to find his mistake in such a routine if there is only one source to look for it. This is the type of programming paradigm used to create the RTD simulator we connected to LOCA. Object-oriented programming, in constrast to procedural programming, puts the emphasis on the data structures instead of the functions that manipulate them. Under this paradigm, classes are the main components. Here, a class is a collection of data
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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
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 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: APPENDIX A. NOTATION 130 ɛc ɛk ɛ
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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