Physics 640: Scientific Computation and Visualization
Prof.
http://www.faculty.umb.edu/tomas_materdey/640
1. Catalogue Description.
An
introduction to scientific computation and visualization with applications to
physics, biology, chemistry, mathematics and engineering suitable for first
year graduate students and advanced undergraduates in these and related fields.
Students will have immersion experiences in computing by working on several
projects from start to finish, from developments of numerical algorithms, code
writing and debugging, to data processing and visualization. The course
provides an ideal environment to learn the fundamentals of high-performance
scientific computing and visualization. The prerequisites are introductory
physics, linear algebra and differential equations or by permission of the
instructor.
2. Course Goals and Objectives.
The goals are for students to get introduced to
and gain some confidence in doing scientific computation in all of its phases,
from numerical analysis, programming and debugging, to graphical representation
of the final results. The objectives are to provide a model
introduction, then have the students work through five assigned bi-weekly
projects under supervision, and perform a final project of their choice.
3. Course Content, Instructional
Approach, and Expectations.
Major course topics:
-Finite-Difference in the
Time-Domain (FDTD) and the numerical solution of Maxwell’s equations
-Implementation of a FDTD
code in Fortran:
-Introduction to dielectric
waveguides
-Molecular Dynamics
-Time-frequency analysis:
Wigner function and wavelets
-Introduction to Matlab
-Fast Fourier Transform (FFT)
-Numerical Projects in
Biology/Chemistry/Physics/Engineering
The instructional approach will be active-learning,
students will get introduced to scientific computation by actively performing,
with the instructor’s guidance, the assigned projects and the final project of
their choice. Students can use the bibliography to supplement class
presentations on numerical algorithms and other background information.
Projects can be worked in teams but students are required submit an individual
report for each of the five projects, and make a short presentation on the
final project during the last week of classes. The project reports will include
at least 5 sections:
1. Introduction/background information on the problem
to solve
2. Equations and numerical algorithms
3. Code/programming
4. Graphical representations
5. References and conclusion
and will follow the format of a standard
scientific/engineering journal manuscript. To ensure adequate individual
progress, a short in-class midterm will be performed during week #7 or #8
4. Evaluation of Student Performance.
The grade distribution is: 12% for each of the five
assigned biweekly projects (of which 2% from in-class performance, logbook and
presentations and 10% from the individual project report); 30% from the final
project (of which 15% from in-class performance and logbook; 5% from the final
presentation; and 10% from the final report); 10% from in-class midterms.
5. General Bibliography.
Books:
1.-
Koonin S. and Meredith D, Computational Physics Fortran Edition, Perseus Books,
2002
2.-
Taflove, A., Computational Electrodynamics: The Finite-Difference Time-Domain
Method, Artech House,
3.-
Richard E. Crandall, Projects
in Scientific Computation, Springer-Verlag (1994).
4.-
J. M. Haile, Molecular Dynamics Simulation: Elementary Methods, John Wiley
(1992).
Articles:
1.-
Ozigov, Y.I., Simulation of Quantum Dynamics via Classical Collective Behavior,
arXiv: quant-ph/0602155 v1,
2.-
Miloshevsky, G.V. et. al., Application of finite-difference methods to
membrane-mediated protein interactions and to heat and magnetic field diffusion
in plasmas, J. Comp. Phys. 212, 25-51, 2006
3.-
Kuferman R. and Tadmor, E., A fast, high resolution, second-order central
scheme for incompressible flow, Proc. Natl. Acad. Sci. USA, vol. 94,
pp.4848-4852, May 1997
4.-
Filbert, F, Convergence of a finite volume scheme for the Vlasov-Poisson
system, SIAM J. Numer. Anal., vol. 39, No. 4, pp. 1146-1169, 2001
5.-
Skarka et al., Explicit analytical solution of the nonlinear Vlasov-Poisson
system, Phys. Plasmas 1 (3), March 1994
6.-
Ciftja, O. and Faruk, M.G., Two-dimensional quantum-dot helium in a magnetic field:
variational theory, Phys. Rev. B 72, 205334, 2005
7.-
Zhu, W and Trickey, S.B., Analytical solutions for two electrons in an
oscillator potential and a magnetic field, Phys. Rev. A 72, 022501, 2005
8.-
Varshni, Y.P., Simple wavefunction for an impurity in a parabolic quantum dot,
Superlattices and Microstructures, Vol. 23, No. 1, 1998
9.-
Branis, S. et. al., Hydrogenic Impurities in quantum wires in the presence of a
magnetic field, Phys. Rev. B 47, No. 3, 1316, 1993
Plus other articles students may find useful for their projects
6. Honor Code and Disability Statement
HONOR
CODE:
For
all assignments (midterm and project reports), each student is required to sign
a short statement declaring that she/he has followed the Code of Student
Conduct (as outlined in the U Mass Boston Student Handbook) in performing the assignments and that all
work done by others has been properly cited and acknowledged.
DISABILITY
STATEMENT:
If
you have a disability and feel you will need accommodations in order to
complete course requirements, please contact the Ross Center for Disability
Services (M-1-401) at (617) 287-7430.