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APPENDIX B. TRILINOS 133 and a group of methods that can manipulate this data. To understand this better, we will consider a contrived example. Suppose we want to create a program for a supermarket that handles the grocery inventory and tracks sales. One class that would be needed is Food. TheclassFood would have data associated with it, just as its name, its price, number in stock, etc., and it would have methods associated with it to alter its name, increase or decrease its price, etc. An object is a specific instance of a class. In the main program, the user would construct these objects, use their methods to manipulate their data, and then return needed information. While this seems similar to the procedural paradigm, the object-oriented paradigm allows for a higher level of abstraction. For example, inheritence is possible with object-oriented programming. The idea of inheritence is that new types of classes can be derived from older types. Returning to our supermarket example, consider a class called Fruit. While Fruit will want to have all the data and methods associated with Food, it will also need more, such as an expiration date and a way to alter this date. So through inheritence, Fruit can be a type of Food, but then it can have additional functionality by adding in new data and methods. Furthermore, multiple inheritence is also possible. This is where a new class is created which combines the data and methods of several previously created classes while adding in new data and methods. The level of abstraction available from object-oriented programming greatly ben- efits Trilinos. While the basic skeleton of numerical algorithms are written up in
APPENDIX B. TRILINOS 134 Trilinos, the concrete implementation (the specific data type, linear solver, etc.) is left up to the user. Trilinos provides the user with the option of concrete implementations that are inherited from the abstract implementations, but, for example, if the user has spent time and effort in creating his own highly efficient linear solver, the user can still make use of all the parts of Trilinos without being forced to use Trilinos’s linear solvers. B.3 Trilinos Packages B.3.1 Epetra Epetra is a data structure used by other Trilinos software packages. While each package has an abstract implementation of the numerical algorithms, these algorithms have concrete implementations in an Epetra environment. Some examples of Epetra objects are vectors and matrices. Epetra can be (and is) used in a distributed memory environment as well. For example, if a Epetra vector is spread across several processor, the object knows how many element each processor owns and where each element is in memory. Epetra is also used for communication among processors, where a user can use Epetra commands to export and import data from each processor.
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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
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 and 144: APPENDIX A. NOTATION 130 ɛc ɛk ɛ
Page 145: APPENDIX B. TRILINOS 132 user-given
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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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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