NUCLREN 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
Designation:
Elective
General Education Course:
(N/A)
Cross-Listings:
Cross-listed in MechEng.
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 MechEng 6507.
Course Goals / Objectives:
Apply finite-difference methods to solution of elliptic, parabolic, and hyperbolic partial differential equations
Calculate, analyze, and reduce errors in numerical solution
Check if concurrence sought:
No
Contact Hours:
| Topic | LEC | REC | LAB | LAB Inst |
|---|---|---|---|---|
| Classification of PDEs, general discussion of methods for solving PDEs, types of meshes used etc. | 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 |
| 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 |
| Treatment of non-linearity, Newton’s method for simultaneous non-linear equations | 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 |
| Convergence analysis, spectral radius of convergence, Fourier analysis of errors | 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 |
| Higher-order methods (in space), improvement in accuracy | 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 |
| Irregular geometries: coordinate transformation, cylindrical coordinates | 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 |
| Finite-Volume discretization on unstructured mesh | 0.0 | 0.0 | 0.0 | 0 |
| Introduction to the Navier-Stokes equation | 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 |
| Total | 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:
Attachments:
(N/A)
Additional Notes or Comments:
(N/A)
Basic Course Overview:
NUCLREN_6507_basic.pdf
(11 KB)