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TAM 470: Computational Mechanics, Fall 2018

  • Class Time: 12:30 - 13:50 on Tuesdays and Thursdays
  • Class Location: Room 253, Mechanical Engineering Building
  • Instructor: Paul Fischer, fischerp@illinois.edu
    • Office Hours: Wednesday, 1-3 PM, 4320 Siebel Center
  • TA: Kento Kaneko, kaneko2@illinois.edu
    • Office Hours: Monday & Thursday, 9-10 AM, 28 MEB
  • Syllabus

About the Course

The course objective is to give students insight and skills with computational methods as a means of investigating problems in mechanical engineering. While much of the course is based on numerical methods for differential equations, the examples and homeworks will be mechanics based, so that students can understand the deep connections between the behavior of mechanical systems and their numerical counterparts. Topics will include numerical solution of multidimensional boundary value problems (e.g., the heat equation, advection-diffusion, and Stokes) and initial value problems (e.g., unsteady variants of the same). By the end of the course, students will be able to identify potential sources of error and instability and be able to estimate computational costs/feasibility for these schemes. Finally, they should be able write and test (!) code to solve computational mechanics problems.

Resources

  • Text: P. Moin, Fundamentals of Engineering Numerical Analysis, 2nd E., Cambridge, 2010. Additional notes will be posted online.
  • W.H. Press et al., Numerical Recipes (Fortran, C, C++), Cambridge.
  • Deville, Fischer, and Mund, High Order Methods for Fluid Flow, Cambridge, 2002.
  • Past Exams

Grading Policy

-  5% Quizzes
- 50% Homework
- 25% Two exams at CBTF
- 20% Final exam
  • Midterm Exam 1: 10/1 - 10/3 (CBTF)
  • Midterm Exam 2: 11/5 - 11/7 (CBTF)
  • Final Exam: TBD

Course Schedule

date topic homework quiz files
Tu 8/28 Lecture 1: Course Introduction
Th 8/30 Lecture 2: Euler Methods
Tu 9/04 Lecture 3: Numerical Interpolation, Differentiation, and Integration
We 9/05 Quiz 1 due at 5 PM
Th 9/06 Lecture 4: Interpolation Applications zwgll.m
Tu 9/11 Lecture 5: Multi-dimensional Interpolation Quiz 2 due at 5 PM quik.m
Th 9/13 Lecture 6: Alternative Interpolators rfft.m, irfft.m
Tu 9/18 Lecture 7: Norms and Approximation Spaces Quiz 3 due at 5 PM
We 9/19 Homework 1 due at 5 PM
Th 9/20 Lecture 8: Weighted Residual
Tu 9/25 Quiz 4 due at 5 PM
Th 9/27 Lecture 9: Boundary Conditions
Fr 9/28 Quiz 5 due at 5 PM
Mo 10/01 Homework 2 due at 5 PM galerkin, lin_fem
Mo 10/08 Quiz 6 due at 5 PM
Th 10/11 fem2d
We 10/17 Homework 3 Part I due at 5 PM
Th 10/18 Lecture 15: Time-Dependence
Tu 10/23 Lecture 16: Heat Equation
Fr 10/26 Homework 3 Part II & III due at 5 PM
Fr 11/01 bdfext.m
Tu 11/27 Multigrid
Th 11/29 Homework 4 due at 5 PM demo_fd.m
Th 12/06 Projection Methods, Conjugate Gradient
Tu 12/11 Homework 5 due at 5 PM mgrid_v.m, lin_interp_mat.m
We 12/19 Final Exam due at 5 PM Starter Script

Additional Notes

Quizzes

In-Class Quiz Solutions

In-Class Quiz Solutions

Homework

Exams