Physics 573 – Numerical Methods in Physics
Spring 2008
Dr. Thomas Papenbrock Lecture hours:
226
tpapenbr@utk.edu Nielsen Physics 512
Office hours: 10:0012:00 Tue/Thu, or by appointment
Course description: This course will teach basic Fortran algorithms and numerical methods that solve a variety of physics problems.
Prerequisites: The course assumes a familiarity with linear algebra and differential equations. A good working knowledge of classical mechanics, quantum mechanics and thermodynamics is of advantage to fully benefit from the physics problems that will be solved and addressed in this course.
Books: We will use information from various sources, available in books or online.
[1] M. Metcalf and J. Reid: Fortran 90/95 explained, 2^{nd}
edition, Oxford University Press (
[2] W. H. Press et al.: Numerical Recipes in Fortran 77, 2^{nd} edition, Cambridge University
Press (
[3] S. E. Koonin: Computational Physics, Benjamin/Cummings
(
Online texts:
[4] Numerical Recipes online: http://www.nrbook.com/a/
[5] P. Pacheco’s User Guide to MPI: ftp://math.usfca.edu/pub/MPI/mpi.guide.ps.Z
[6] MPI online at NERSC: http://www.nersc.gov/nusers/help/tutorials/mpi/intro/print.php
[7] W. Krauth’s
Introduction to
[8] Morten HjorthJensen’s Lecture Notes on Computational Physics
http://www.uio.no/studier/emner/matnat/fys/FYS3150/h07/undervisningsmateriale/Lecture%20Notes/lecture2007.pdf.These notes contain many interesting physics examples and projects. Recommended reading!
Academic honesty: All work submitted by a student is expected to represent their own work. Students are expected to perform all work in conformance with the University policies regarding Academic Honesty.
Computer use: Each student must obtain a Unix account at UTK. Please register for the Unix account at http://accounts.utk.edu/uact/register/ as soon as possible. Useful information for Unix users can be found at http://oit.utk.edu/usag/unixmenu.html. The UT computers unix.cas.utk.edu and moe.cas.utk.edu will be used for homework and projects.
Grading policy: The semester grade will be a weighted average of homework scores, preclass reading quiz, the semester project, the student’s participation in the inclass projects, and class attendance.
Homework will comprise
50% of the final semester grade.
Homework will consist of problems/projects that each student has to solve numerically within one week after the homework assignment. Due dates for problem sets are firm. In lieu of extensions, the lowest score on homework sets will be dropped from the average.
The semester project
will comprise 20% of the final semester grade.
During the semester, each student has to solve a scientific problem with the numerical methods of this course. The choice of the project is up to the student. Examples can be chosen from scientific articles in published journals (e.g. Physical Review Letters, Nature, Science, etc.). The following rules apply. First, the project cannot be simply related to any of the homework problems or inclass projects. Only nontrivial extensions of these problems are permitted, and the project must be considerably larger in scope than a homework problem. Second, the project must be new to you. It cannot be part of your thesis. Third, the project has to be solved individually and independently. The student’s deliverables are the Fortran90 program that solves the problem, and a short inclass presentation of the problem and its solution.
Preclass reading
quizzes will comprise 10% of the final semester grade.
It is expected that you read the relevant material before class. You should know the basic concepts and definitions, in order to maximize the benefit of the lecture. There will be regular reading quizzes: A few questions will be posed on Blackboard (http://online.utk.edu) and have to be answered no later than 40 minutes before class.
Project participation and class attendance will comprise 20% of the final semester grade.
Class attendance is required. For the inclass projects, I expect active participation from each student.
Schedule:
The class will meet 30 times. There will be 21 lectures, the final exam
(presentation of student’s projects), and eight inclass projects, where the
students will apply the material of previous lectures to solve physics problems.
The schedule below is tentative. Any
changes will be announced in class.
Week 
Date 
Lecture 
Material 

1 
10Jan 
1 
Introduction:
Motivation and course overview 

2 
15Jan 
2 
Computer
use: security, compiling, linking, graphics 


17Jan 
3 
Fortran
90: data types 
[1], [8] 
3 
22Jan 
4 
Fortran
90 cont’d: control structures 
[1], [8] 

24Jan 

Project 1: practical application of lectures 24 

4 
29Jan 
5 
Numerical
integration of functions 
[2] 

31Jan 
6 
Root
finding: NewtonRaphson 
[3] [8] 
5 
5Feb 

Project 2: practical application of lectures 56 


7Feb 
7 
Integration
of ordinary differential equations (ODE) 
[2] 
6 
12Feb 
8 
ODE
cont’d: RungeKutta method. Stability. Chaos 
[2] [3] 

14Feb 

Project 3: practical application of lectures 78 

7 
19Feb 
9 
Minimization
of functions 
[2] 

21Feb 
10 
Minimization
cont’d: simulated annealing method 
[2] 
8 
26Feb 

Project 4: practical application of lectures 910 


28Feb 
11 
Eigenvalue (EV) problems: Small oscillations 
[2] 
9 
4Mar 
12 
EV
cont’d: Schroedinger equation 
[3] chap.
3.43.5 

6Mar 
13 
EV cont’d
HartreeFock approximation 
[3] chap.
3.5 
10 
11Mar 

Project 5: practical application of lectures 1113 


13Mar 
14 
Code
optimization 

11 
18Mar 

Spring Break 


20Mar 

Spring Break 

12 
25Mar 
15 

[3] chap.
8.18.2 [7]
1.11.2 [8] chap.
8 

27Mar 
16 
MC
cont’d: Metropolis algorithm 
[3] chap.
8.3 [7]
1.21.3 [8] chap.
9 
13 
1Apr 

Project 6: practical application of lectures 1516 
[8] chap.
10, 11 

3Apr 
17 
Sorting 
[2] chap.
8.08.3 
14 
8Apr 
18 
Recursion 
[1] chap.
5.165.17 

10Apr 

Project 7: practical application of lectures 1718 

15 
15Apr 
19 
Parallelization:
Message Passing Interface (MPI) 
[5],[6],
[8] chap. 7.7 

17Apr 
20 
MPI cont’d.

[5],[6] 
16 
22Apr 
21 
MPI
cont’d. Managerworker algorithm 


24Apr 

Project 8: practical application of lectures 2021 


4/296/5 

Final Exam: Presentation of
students’ projects 
