MECHENG 6507
Transcript Abbreviation:
NumMeth
Course Description:
Numerical techniques and computer algorithms to solve initial and boundary value problems relevant to engineering applications, such as heat conduction and mass diffusion.
Course Levels:
Graduate (5000-8000 level)
Designation:
Elective
General Education Course:
(N/A)
Cross-Listings:
Cross-listed in NuclrEn.
Credit Hours (Minimum if “Range”selected):
3.00
Max Credit Hours:
3.00
Select if Repeatable:
Off
Maximum Repeatable Credits:
(N/A)
Total Completions Allowed:
(N/A)
Allow Multiple Enrollments in Term:
No
Course Length:
14 weeks (autumn or spring)
12 weeks (summer only)
Off Campus:
Never
Campus Location:
Columbus
Instruction Modes:
In Person (75-100% campus; 0-24% online)
Prerequisites and Co-requisites:
Prereq: 2850, Math 2174, 2415, or 4512; or Grad standing in MechEng or AeroEng, or NuclrEng; or permission of instructor.
Electronically Enforced:
No
Exclusions:
Not open to students with credit for NuclrEn 6507.
Course Goals / Objectives:
Apply finite-difference methods to solution of elliptic, parabolic, and hyperbolic partial differential equations
Apply finite-volume methods to solution of elliptic, parabolic, and hyperbolic partial differential equations
Solve set of linear algebraic equations resulting from discretization of partial differential equations using various direct and iterative solution methods
Calculate, analyze, and reduce errors in numerical solution
Check if concurrence sought:
No
Contact Hours:
| Topic | LEC | REC out-of-class | REC in-class | Weekly LAB out-of-class | Weekly LAB in-class |
|---|---|---|---|---|---|
| Classification of PDEs, general discussion of methods for solving PDEs, types of meshes used etc. | 0.0 | 0.0 | 0 | 0.0 | 0 |
| Derivation of finite-difference equations, errors in difference approximations, application of boundary conditions | 0.0 | 0.0 | 0 | 0.0 | 0 |
| Direct Solution Techniques: tri-diagonal matrix (TDMA) inversion, LU decomposition, Gaussian elimination, incomplete LU decomposition, basics of pre-conditioning | 0.0 | 0.0 | 0 | 0.0 | 0 |
| Treatment of non-linearity, Newton’s method for simultaneous non-linear equations | 0.0 | 0.0 | 0 | 0.0 | 0 |
| Iterative solution techniques: Jacobi, Gauss-Seidel, Line-by-line (ADI), Stone’s method, conjugate gradient (CG). | 0.0 | 0.0 | 0 | 0.0 | 0 |
| Convergence analysis, spectral radius of convergence, Fourier analysis of errors | 0.0 | 0.0 | 0 | 0.0 | 0 |
| Multi-grid methods: basic philosophy and simple two-stage geometric multi-grid solution | 0.0 | 0.0 | 0 | 0.0 | 0 |
| Higher-order methods (in space), improvement in accuracy | 0.0 | 0.0 | 0 | 0.0 | 0 |
| Parabolic problems: treatment of time derivative, Euler and Crank-Nicolson, time marching methods | 0.0 | 0.0 | 0 | 0.0 | 0 |
| Irregular geometries: coordinate transformation, cylindrical coordinates | 0.0 | 0.0 | 0 | 0.0 | 0 |
| Finite-Volume method: basic philosophy and fundamental differences with finite-difference method | 0.0 | 0.0 | 0 | 0.0 | 0 |
| Finite-Volume discretization on unstructured mesh | 0.0 | 0.0 | 0 | 0.0 | 0 |
| Introduction to the Navier-Stokes equation | 0.0 | 0.0 | 0 | 0.0 | 0 |
| Hyperbolic wave equation, Euler and Burger’s equations, schemes for hyperbolic equations | 0.0 | 0.0 | 0 | 0.0 | 0 |
| Total | 0 | 0 | 0 | 0 | 0 |
Grading Plan:
Letter Grade
Course Components:
Lecture
Grade Roster Component:
Lecture
Credit by Exam (EM):
No
Grades Breakdown:
| Aspect | Percent |
|---|---|
| Weekly homework assignments and/or projects | 60% |
| Mid-term exam | 20% |
| Final exam | 20% |
Representative Textbooks and Other Course Materials:
| Title | Author | Year |
|---|---|---|
| No Textbooks and Other Course Materials Entered. | ||
ABET-CAC Criterion 3 Outcomes:
(N/A)
ABET-ETAC Criterion 3 Outcomes:
(N/A)
ABET-EAC Criterion 3 Outcomes:
(N/A)
Embedded Literacies Info: