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CME306 / CS205B
Mathematical Methods for Fluids, Solids and Interfaces (Spring 2009)





COURSE ANNOUNCEMENTS

Date                      Contents 2009-6-6All homework assignments have been
graded. 2009-5-26Office hours have moved to the adjacent office Gates 210.
2009-5-19Homework 8 has received a few corrections. 2009-5-19Homework 8 is
posted. 2009-5-19Homework 6 is graded, and grades for 4 and 5 were emailed out.
2009-5-12Homework 7 is posted. 2009-5-12Lecture 12 is posted. 2009-5-8The final
project description is now available through a link below. It will be due at the
end of the last day of finals week or two days before final grades are required,
whichever is earlier. 2009-5-7Lectures 10 and 11 are posted. 2009-5-5Homework 6
is posted. 2009-5-3A short document for Homework 5 is posted. It basically just
restates the email describing this assignment, so that it can be found on the
website. 2009-4-28Homework 3 is graded. 2009-4-28Lecture 9 is posted.
2009-4-24Homework 4 test cases posted here. 2009-4-21Homework 4 is posted.
2009-4-20Lectures 7 and 8 are posted. 2009-4-17Homework 2 is graded.
2009-4-16Lecture 6 is posted. 2009-4-14Homework 3 is posted. 2009-4-14Lecture 5
is posted. 2009-4-9Homework 1 is graded. 2009-4-9Lecture 4 is posted.
2009-4-7Homework 2 is posted. 2009-4-7Lecture 3 is posted. 2009-4-2Lecture 2 is
posted. 2009-3-31Lecture 1 is posted. 2009-3-31First homework is posted, due
April 7. 2009-3-31Website is live.


SUMMARY

Overview of numerical methods for the simulation of problems involving solid
mechanics and fluid dynamics. The focus is on practical tools needed for
simulation, as well as the necessary continuous mathematics involving nonlinear
hyperbolic partial differential equations. Possible topics include the finite
element method, highly deformable elastic bodies, plasticity, fracture, the
level set method, Burgers' equation, compressible and incompressible
Navier-Stokes equations, smoke, water and solid-fluid coupling.


STAFF

 * Instructor
   * Ron Fedkiw (fedkiw@cs.stanford.edu)
     * Office hours: After class (10:45AM-11:45AM), Gates 207
 * Course Assistants
   * Jón Tómas Grétarsson (jontg@stanford.edu)
     * Office Hour: Tuesday (12:00PM - 1:00PM), Gates 207, beginning 4-7-2009,
     * Office Hour: Friday (3:00PM - 5:00PM), Gates 200
   * Craig Schroeder (cas43@cs.stanford.edu)
     * Office hours: Tuesday, Friday (1:00PM - 2:00PM), Gates 200 or 210

Please refer all questions about course material and practices to the CAs before
contacting Professor Fedkiw. If you have a question for the CAs, please make
sure that it isn't answered on this webpage before contacting them. Also, please
do not show up outside of scheduled office hours without first making an
appointment. When emailing the CAs, make sure to include "CME306" or "CS205B"
somewhere in the subject of your message.


MEETING TIMES

 * Class: Tuesday and Thursday, 9:30AM-10:45AM in 260-113
 * Theoretical Section: Wednesday, 5:15PM-6:15PM in Gates 104
 * Applied Section: Thursday, 5:00PM-6:00PM in Gates 463a


USEFUL TEXTS

 * Finite Volume Methods for Hyperbolic Problems, by Randall J. LeVeque,
   Cambridge University Press 2002.
 * Finite Difference Schemes and Partial Differential Equations (2nd ed.), by
   John C. Strikwerda, SIAM 2004.
   
   The first chapter of this book is available on the SIAM website, and is on
   permanent reserve at the Mathematical and Computer Science Library.

 * Level Set Methods and Dynamic Implicit Surfaces, by Stanley Osher and Ronald
   Fedkiw, Springer 2003.
 * Mathematical Models: Mechanical Vibrations, Population Dynamics and Traffic
   Flow, by Richard Haberman, SIAM 1998


CLASS NOTES

ClassDescription Lecture 1 Introduction, Simulation of Materials Lecture 2
Conservation of Mass, Smoothed Particle Hydrodynamics Lecture 3 Smoothed
Particle Hydrodynamics, Forces, Linearized System Lecture 4 Ordinary
Differential Equations, Stability, Newmark Methods Lecture 5 Springs Lecture 6
Springs Lecture 7 Finite Element Method Lecture 8 Finite Element Method, Rigid
Bodies Lecture 9 Advection, Runge-Kutta, Hamilton-Jacobi ENO, Semi-Lagrangian
Advection Lecture 10 Hyperbolic Conservation Laws, Shoks, Rarefactions Lecture
11 Discrete Conservation Form, ENO-Roe, ENO-LLF Lecture 12 Discrete Conservation
Form, ENO-Roe, ENO-LLF Lecture 13 Multiple Dimensions, Systems Lecture 14
Systems, Discretization, Shallow Water Lecture 15 Incompressible Flow Equations
Lecture 16 Incompressible Flow: Poisson Equation Lecture 17 Incompressible Flow:
Discretization, Semi-Lagrangian Advection Lecture 18 Heat Equation Lecture 19
Viscosity, Vorticity

The lecture notes are also available in the form of a single cumulative
document.


ASSIGNMENTS

There will be a problem set assigned each week, which will be posted on Tuesday
at 11:00AM. Homework will be graded on a scale from 0 to 10 points. There are no
examinations for this course.

There are two separate tracks of homework: theory (which involves more
qualifying exam preparation), and application (which involves a mixture of
theory and programming). If you are taking the iCME qualifying exams, you are
strongly encouraged to take the theoretical track, which is described on the CME
306 page. The theoretical track is also recommended for those that are not
comfortable programming in C++, as it will not include programming projects
(extra credit Matlab assignments are possible, though).

This page covers the applied track. This homework track is also mostly
theoretical, but it will include a final project and smaller programming tasks
along the way.

The final project will consist of writing a simulator in C++ to simulate one of
the main types of phenomena discussed in the course. The project will be due on
the last day of finals. More details on the project will be posted later in the
term.

You may collaborate on homework assignments provided each student writes up his
or her own solutions and clearly lists the names of all the students in the
group.

AppliedDue DateSolutions Homework 1(tex) 2009-4-7 (solution) Homework 2(tex)
2009-4-14 (solution) Homework 3(tex) 2009-4-21 (solution) Homework 4(tex)
2009-4-28 (solution) Homework 5(tex) 2009-5-5 (solution) Homework 6(tex)
2009-5-12 (solution) Homework 7(tex) 2009-5-19 (solution) Homework 8(tex)
2009-5-26 (solution) Homework 9(tex) 2009-6-2 (solution)

Homework must be submitted physically either in class or in the bin outside
Gates 210 by 11 AM. Graded homework will be available for pickup in the Gates
377 filing cabinets.


FINAL PROJECT

Information about the project is available here.


EXTRA CREDIT

Depending on class performance on homework and exams, there will be a small
number of optional extra credit assignments. These assignments will require you
to implement some of the numerical schemes discussed during the course. Extra
credit projects do not have a set point value; rather, they will be taken into
account at the end of the quarter when determining your final letter grade.

Please note that you are free to do, as extra credit, the homework from the
theory track.


GRADING

The final grade will be calculated based on the highest score between your
theoretical and applied homework. The lower of the two will be counted towards
extra credit. You should complete either all of the theoretical or all of the
applied homework, not a mix of the two.