Course Meeting Times
This course meets for the first half of the semester.
Lectures: 2 sessions / week, 1.5 hours / session
Recitations: 1 session / week, 0.5 hour / session
Final exam period is 3 hours long.
Prerequisites
12.010 Computational Methods of Scientific Programming or permission of instructor.
Educational Objectives
Students who complete this module will
- Become familiar with computational engineering and its mathematical foundations, at an elementary level.
- Deepen their understanding of the basic equations governing the phenomena in Nuclear Science and Engineering.
- Understand the methods by which physical problems can be solved using computation.
- Develop experience, confidence, and good critical judgment in the application of numerical methods to the solution of physical problems.
- Strengthen their ability to use computation in theoretical analysis and experimental data interpretation.
Grading
| ACTIVITIES | PERCENTAGES |
|---|---|
| Homework exercises (best 5 of 9 scores) | 20% |
| Class interaction | 5% |
| Final exam | 75% |
The homework evaluation will count only the best five assignment scores. However, it should be noted that some exercises build on earlier ones. Therefore students should recognize that it is not generally possible simply to omit early assignments. Moreover, the exercises are designed to develop understanding and skill with the material that will be valuable for the final exam.
Lecture Notes and Bibliography
Detailed lecture notes are provided.
Students who lack specific mathematics or science background in the areas discussed may be advised to supplement the lectures with extra reading.
Reference Books
| BOOKS | COMMENTARIES |
|---|---|
| Press, W. H., B. P. Flannery, et al. Numerical Recipes. Cambridge University Press, 1989. ISBN: 9780521383301. | This is an outstanding, readable, and practical introduction to numerical methods in science and engineering. It covers more than this course, but is the number one book recommendation. |
| Jardin, Stephen. Computational Methods in Plasma Physics. CRC Press, 2010. ISBN: 9781439810217. [Preview with Google Books] | Although focused on plasma physics, this book gives excellent introductions to finite difference PDE equations and the methods for solving them, across the spectrum of equation types. |
| Nakamura, Shoichi. Computational Methods in Engineering and Science with applications to Fluid Dynamics and Nuclear Systems. John Wiley & Sons Inc, 1977. ISBN: 9780471018001. | This book covers numerical methods in the nuclear reactor context, and therefore has some useful specialist topics. However, its mathematics is not, in my opinion, clearly written, and it is hard to learn from because of it. |
| Hebert, Alain. Applied Reactor Physics. Ecole Polytechnique De Montreal, 2009. ISBN: 9782553014369. [Preview with Google Books] | This modern reactor physics text book has numerical methods liberally sprinkled in its development and a useful appendix addressing them directly. Naturally its reactor physics goes far beyond what we will cover. |
|
Smith, G. D. Numerical Solution of Partial Differential Equations. Clarendon Press, 1965. Forsythe, George E., and Wolfgang R. Wasow. Finite Difference Methods for Partial Differential Equations. Literary Licensing, 2013. ISBN: 9781258664152. Mitchell, A. R., and D. F. Griffiths. The Finite Difference Method in Partial Differential Equations. Wiley-Blackwell, 1980. ISBN: 9780471276418. |
These are three examples of the large selection of text books that address how to solve partial differential equations numerically. |
| Hockney, R. W., and J. W. Eastwood. Computer Simulation Using Particles. CRC Press, 1988. ISBN: 9780852743928. [Preview with Google Books] | This is a classic on particle simulation, especially plasma PIC approaches, but has a lot of additional material on other topics of the course. |
| NIST / SEMATECH e-Handbook of Statistical Methods | A good resource about data fitting. |
Calendar
| LEC # | TOPICS | KEY DATES |
|---|---|---|
| 1 | Numerical fitting of data | Exercise 1 out |
| 2 | Ordinary differential equations (ODEs) | Exercise 2 out |
| 3 | Two–point boundary conditions |
Exercise 3 out Exercise 1 due |
| 4 | Partial differential equations (PDEs) |
Exercise 4 out Exercise 2 due |
| 5 | Diffusion; parabolic PDEs |
Exercise 5 out Exercise 3 due |
| 6 | Elliptic problems and iterative matrix solution |
Exercise 6 out Exercise 4 due |
| 7 | Fluid dynamics and hyperbolic equations |
Exercise 7 out Exercise 5 due |
| 8 | Boltzmann’s equation and its solution |
Exercise 8 out Exercise 6 due |
| 9 | Neutron transport |
Exercise 9 out Exercise 7 due |
| 10 | Atomistic and particle-in-cell methods | Exercise 8 due |
| 11 | Monte Carlo techniques | |
| 12 | Monte Carlo radiation transport | Exercise 9 due |
| 13 | Next steps, e.g. finite elements | |
| 14 | Final exam (3 hour period) |
