Computational Engineering
Graduate Coordinator: Dr. Pasquale "PC" Cinnella
Center for Advanced Vehicular Systems (CAVS)
Box 9618
Mississippi State, MS 39762
Telephone: 662-325-5431
E-mail: grad-coordinator@hpc.msstate.edu
An Interdisciplinary Curriculum
The Computational Engineering graduate program is interdisciplinary, with faculty drawn from the academic departments of the College of Engineering and the College of Arts and Sciences, as well as the research faculty of the HPC2. Programs of study and research leading to both the Master of Science degree and the Doctor of Philosophy degree are available. There is an increased demand by industry, academia, and government for scientists and engineers with a better knowledge of the skills necessary to create new technologies and improve upon existing ones through simulation tools. Such programs come with curricula covering a large range of subjects, so that they can produce scientists and engineers with broad backgrounds and viewpoints. These scientists and engineers can then be expected to understand the basic approaches to solving analytical problems and also using mathematical and computational tools required to arrive at solutions. The program is open to students with undergraduate degrees in engineering, computer science, mathematics, or a physical science. Research assistantships are available through research projects in the HPC2.
Admission Criteria
To be admitted, the student must meet the admission requirements of the Office of the Graduate School and receive a positive recommendation from the Computational Engineering screening committee. International students must have scored at least 550 PBT (213 CBT or 79 iBT) on the Test of English as a Foreign Language (TOEFL) or 6.5 on the International English Language Testing System (IELTS). Students with a degree from a program that is not EAC/ABET accredited must have a satisfactory performance on the GRE.
In addition, highly qualified undergraduate students, with a minimum equivalent GPA of 3.50/4.00 on the last 60 credit hours of undergraduate courses, or a first class with distinction degree classification for students from institutions where no GPA is reported, or a satisfactory performance on the GRE for students from a non-ABET-accredited program, can be directly admitted to the Ph.D. program.
Provisional Admission
Because of the interdisciplinary nature of the Computational Engineering program, virtually all students are required to take some prerequisite courses. Nevertheless, all students admitted to the program are granted regular admission. Provisional admission is not approved.
Program of Study
The specific requirements for the degrees are governed by the requirements of the Office of the Graduate School, the College of Engineering, and by the student’s graduate committee. The committee must include at least one Computational Engineering faculty member from each of the following areas:
- a Computational Engineering application area,
- high-performance computing, and
- numerical mathematics.
The graduate committee will ensure that the student’s program of study adequately addresses each of the three primary cross-disciplinary areas (an application area, high-performance computing, and numerical mathematics), and students are encouraged to include one or more courses in scientific visualization or graphics. The composition of the graduate committee and the student’s program of study must be approved by the Computational Engineering Graduate Coordinator.
Academic Performance
Continued enrollment in the graduate program in Computational Engineering is dependent upon satisfactory performance in the courses and satisfactory progress toward completion of the degree. To achieve satisfactory performance, a student must
- maintain a B average on:
- all undergraduate prerequisite courses;
- all graduate courses completed after admission to the program;
- all graduate courses included on the student’s program of study;
- have no more than one grade less than C;
- have a major advisor and a supervisory committee (after the first two semesters of enrollment).
Should a student’s cumulative grade point average (in any of the three categories above) be less than 3.00 at the end of a term, the student will be placed on “probation” and will be given one semester to earn a cumulative grade point average of 3.00 or greater. If at the end of the probationary term the student’s cumulative grade point average (in any of the three categories above) is less than 3.00, the student’s program of study will be terminated immediately. If the student enrolls in the summer term, it will count as one term.
Should a student earn a second grade less than a C, the student’s program of study will be terminated immediately. Should a student who is beyond his/her second period of study not have a major advisor and supervisory committee, the student will be placed on probation and given one semester to form a committee. Should the student not be able to form a committee, his/her program of study will be terminated. A student may appeal termination of his/her study to the Computational Engineering Supervisory Committee.
Graduate Courses
Because of the interdisciplinary nature of the Computational Engineering program, courses listed below are typical of those used to assemble a program of study. Courses not listed can be used for graduate credit with the approval of the student’s supervisory committee and the Computational Engineering Program Coordinator .
Master of Science in Computational Engineering - Thesis
| 8000-level coursework | 12 | |
| Additional graduate-level coursework | 12 | |
| Research/thesis | 6 | |
| Total Hours | 30 | |
Master of Science in Computational Engineering - Non-Thesis
| 8000-level coursework | 15 | |
| Additional graduate-level coursework | 15 | |
| Research project | 3 | |
| Total Hours | 33 | |
Doctor of Philosophy in Computational Engineering
The Doctor of Philosophy in Computational Engineering, in addition to the coursework and research hours, includes a comprehensive examination, a dissertation, and dissertation defense. Each candidate for the doctoral degree must conduct research and in their dissertation defense on that research
- demonstrate a mastery of the techniques of research and
- make a very distinct contribution to the field of Computational Engineering.
The dissertation must conform to the rules of the Office of the Graduate School.
For direct-admit Ph.D. students, 72 credit hours beyond the B.S. are required (48 credit hours of coursework and 24 credit hours of dissertation research).
Computational Engineering Applications
ASE 6423 Introduction to Computational Fluid Dynamics: 3 hours.
(Prerequisite: Consent of instructor). Three hours lecture. Elementary aspects of computational fluid dynamics (CFD); review of numerical analysis and fluid mechanics as pertinent to CFD; numerical solution to selected fluid dynamic problems
ASE 6433 Fundamentals of Numerical Grid Generation: 3 hours.
(Prerequisite: Consent of instructor). Three hours lecture. Grid Generation strategies; effects of grid quality on discetization errors; structured and unstructured grid generation algorithms; solution adaptive grid generation; surface grid generation
ASE 6553 Engineering Design Optimization: 3 hours.
(Prerequisite:Consent of Instructor).Three hours lecture. Introduction to optimality criteria and optimization techniques for solving constrained or unconstrained optimization problems. Sensitivity analysis and approximation. Computer application in optimization. Introduction to MDO. (Same as EM 4143/6143 and IE 4743/6743)
ASE 8363 Computational Heat Transfer: 3 hours.
(Prerequisite: Consent of Instructor). Three hours lecture. Application of numerical techniques to elliptic and parabolic problems in engineering heat transfer and fluid flow. Discretization techniques; linearization; stability analysis. (Same as ME 8363)
ASE 8413 Computational Fluid Dynamics I: 3 hours.
(Prerequisite: Consent of instructor). Three hours lecture. Review of relevant numerical analysis; one dimensional methods; compressible inviscid methods, Euler Equation methods, inviscid-viscous interaction methods; current literature
CE 8683 Finite Element Analysis in Structural Engineering: 3 hours.
(Prerequisite: CE 4663/66630). Three hours lecture. Energy and elasticity principles. Development of planar three-dimensional and curved elements. Applications to plates and shells. Use of computer programs
CHE 8113 Advanced Chemical Engineering Thermodynamics: 3 hours.
(Prerequisites: CHE 3123 and CHE 4113 or equivalent). Three hours lecture. Advanced study of fundamental laws of thermodynamics as applied to unit operations, nonideal fluids and solutions, chemical equilibria, electrochemistry and similar topics
CHE 8123 Chemical Kinetics and Dynamics: 3 hours.
(Prerequisite: consent of instructor). Three hours lecture. Theory and interrelations of phenomemological chemical kinetics and molecular reaction dynamics
CHE 8223 Advanced Process Computations: 3 hours.
(Prerequisite: CHE 3223). Three hours lecture. Numerical methods. Numerical solution of ordinary and partial differential equations for process applications. Use of algebraic and matrix methods. Digital computer applications
CHE 8523 Advanced Transport Phenomena: 3 hours.
Three hours lecture. (Prerequisite: Graduate standing). Fundamental principles in momentum, heat, and mass transport. Conservation equations. Continuity, motion, energy equations, and multicomponent mass equation of change
EM 6213 Advanced Mechanics of Materials: 3 hours.
(Prerequisite: EM 3213). Three hours lecture. Stress, strain, stress-strain relationships, strain energy, failure theories, curved beams, unsymmetrical bending, shear center, torsion of noncircular sections, energy principles, Castigliano's theorem, inelastic behavior
EM 8203 Applied Elasticity: 3 hours.
Three hours lecture. Analysis of stress and strain; stress-strain relations; bending and torsion of beams; stress functions; strain energy
IE 6113 Human Factors Engineering: 3 hours.
(Prerequisite: Junior standing in engineering). Two hours lecture. Three hours laboratory. Human capabilities and limitations affecting communications and responses in man-machine systems. Emphasis on physiological and psychological fundamentals
IE 6123 Psychology of Human-Computer Interaction: 3 hours.
(Prerequisite: PSY 3713 or CS 4663/6663 or IE 4113/6113 or consent of instructor). Two hours lecture. Two hours laboratory. Exploration of psychological factors that interact with computer interface usability. Interface design techniques and usability evaluation methods are emphasized. (Same as CS 4673/6673 and PSY 4743/6743)
IE 6713 Operations Research I: 3 hours.
(Prerequisites: IE 4613). Mathematical techniques of decision making, queuing, networks, simulation and dynamic programming
IE 6733 Linear Programming: 3 hours.
(Prerequisites: MA 3113).Three hours lecture.Theory and application of linear programming;simplex algorithm, revised simplex algorithm,duality and sensitivity analysis,transportation and assignment problems algorithms, integer and goal programming. (Same as MA 4733/6733)
IE 6753 Systems Engineering and Analysis: 3 hours.
(Prerequisite: Grade of C or better in IE 3913 and IE 4613). Three hours lecture. Systems concepts, methodologies, models and tools for analyzing, designing, and improving new and existing human-made systems
IE 6773 Systems Simulation I: 3 hours.
(Prerequisite: Grade of C or better in IE 4934 or equivalent programming course and grade of C or better in IE 4613). Three hours lecture. The principles of simulating stochastic systems with an emphasis on the statistics of simulation and the use of discreet-even simulation languages
IE 8153 Cognitive Engineering: 3 hours.
Three hours lecture. Implications of human perceputal, cognitive, and psycho-motor capabilities on the design of systems for effective, efficient and safe human-machine performance
IE 8723 Operations Research II: 3 hours.
(Prerequisite: IE 4713). Problem formulation, general inventory theory, restricted inventory models. Markovian and queuing processes, sequencing and coordination, game theory, search problems
IE 8743 Nonlinear Programming I: 3 hours.
(Prerequisite: IE 4733 or MA 4733). Three hours lecture. Optimization of nonlinear functions; quadratic programming, gradient methods, integer programming; Lagrange multipliers and Kuhn-Tucker theory
IE 8753 Network Flows and Dynamic Programming: 3 hours.
(Prerequisites:MA 2733 and IE 4613).Three hours lecture. Applications of network optimization problems and simplex algorithm;and dynamic programming to industrial/ management problems. Study of serial/non-serial multistage deterministic and stochastic systems. Principles of optimality
IE 8773 Systems Simulation II: 3 hours.
(Prerequisite: IE 4773/6773 ). Three hours lecture. Continuation of IE 4773. Includes: Advanced theory and practice of simulation, the statistics of simulation, simulation languages, and continuous simulations
ME 8243 Finite Elements in Mechanical Engineering: 3 hours.
(Prerequisites: ME 4403 and EM 3213). Three hours lecture. Concepts and applications of finite element analysis in mechanical engineering problems
ME 8223 Inelasticity: 3 hours.
(Prerequisite:EM 8113 and EM 8203 ) Three hours lecture. This course covers plasticity, creep, viscoelasticity, and inelastic behavior in relation to microstructure-property relations, constitutive modeling at different length scales, and computational simulations.(Same as CE 8323)
ME 8813 Viscous Flow I: 3 hours.
Three hours lecture. Fundamental laws of motion for a viscous fluid; classical solutions of the Navier-Stokes equations; inviscid flow solutions; laminar boundary layers; stability criteria
ME 8823 Viscous Flow II: 3 hours.
(Prerequisite: ME 8813 or equivalent). Three hours lecture. Numerical solution techniques for viscous flow equations. Turbulence and turbulence modeling. Current literature and topics
ME 8843 Unstructured Grid Technology: 3 hours.
(Prerequisites: ASE 8413, proficiency in computer programming, and consent of instructor). Three hours lecture. Unstructured grid generation based on Delaunay, Advancing-Front, Iterative Point Placement, and Local- Reconnection techniques. Implementation of unstructured Finite-Element/Volume methods for engineering applications
PH 6213 Intermediate Mechanics I: 3 hours.
(Prerequisites: PH 1133 or PH 2233 and MA 2733). Three hours lecture. Plane statics and dynamics of particles and systems of particles with emphasis on both derivation and application of principles involved
PH 6323 Electromagnetic Fields I: 3 hours.
(Prerequisites: PH 1133 or PH 2233 and MA 2743). Three hours lecture. Electrostatics, dielectrics, electric current, magnetostatics, electromagnetic induction, magnetic properties of matter
PH 6413 Thermal Physics: 3 hours.
(Prerequisites: PH 3613 and MA 2743). Three hours lecture. Thermodynamics, kinetic theory, classical and quantum statistical mechanics. Applications to low temperature physics, solid-state physics and plasma physics
PH 6433 Computational Physics: 3 hours.
(Prerequisites:PH 3613 and MA 3253).Three hours lecture. An Introduction to modern methods of computational physics including topics such as:solution of differential equations, numerical matrix methods, and Monte Carlo simulation
PH 6713 Introduction to Quantum Mechanics: 3 hours.
(Prerequisites: PH 3613 and MA 3253). Three hours lecture. Principles of quantum mechanics, Heisenberg uncertainty principle, angular momentum; the Schrodinger wave equation in one and three dimensions; the one-electron atom
PH 6813 Introduction to Solid State Physics: 3 hours.
(Prerequisite: PH 3613). Three hours lecture. Crystal structure, crystal diffraction and the reciprocal lattice, crystal binding, free electron gas, energy bands, and semiconductors
PH 8213 Mechanics: 3 hours.
(Prerequisite: A good undergraduate training in physics and mathematics consent of instructor). Coordinate systems and transformations, tensors, and matrices. Particle dynamics, variational principles, Lagrange's and Hamilton's equations, rigid body motion, special relativity in mechanics
PH 8313 Electromagnetic Theory: 3 hours.
(Prerequisite: PH 4333 or equivalent). Maxwell's theory of electromagnetism. Boundary value problems in electrostatics, static multipole moments, theory of dielectrics, magnetostatics, plane electromagnetic waves, simple radiating systems. (Same as ECE 8313)
PH 8513 Statistical Mechanics: 3 hours.
(Prerequisites: PH 4713 and PH 4413 ). Classical and quantum statistical mechanics and statistical interpretation of thermodynamic quantities
PH 8743 Quantum Mechanics I: 3 hours.
(Prerequisites: PH 4723 and MA 3313). Schrodinger theory, spherically symmetric systems, matrix mechanics, angular momentum and spin, time-independent perturbation theory
High Performance Computing
CME 8113 Computational Geometry: 3 hours.
(Prerequisite: consent of instructor). Three hours lecture. Computer aided geometric design techniques and their applications in engineering and general computational field simulation
CSE 6163 Designing Parallel Algorithms: 3 hours.
(Prerequisities:Grade of C or better in CSE 3324 or CSE 4733/6733). Three hours lecture. Techniques for designing algorithms to take advantage efficiently of different parallel architectures. Includes techniques for parallelizing sequential algorithms and techniques for matching algorithms to architectures
CSE 6214 Introduction to Software Engineering: 4 hours.
(Prerequisite: CSE 2383 with a grade of C or better). Three hours lecture. Two hours laboratory. Introduction to software engineering; planning, requirements, analysis and specification, design; testing; debugging; maintenance; documentation. Alternative design methods, software metrics, software projecet management, reuse, and reengineering
CSE 6233 Software Architecture and Design Paradigms: 3 hours.
(Prerequisite: Grade of C or better in CSE 4214/6214). Three hours lecture. Topics include software architectures, methodologies, model representations, component-based design ,patterns,frameworks, CASE-based designs, and case studies
CSE 6283 Software Testing and Quality Assurance: 3 hours.
(Prerequisite:Grade of C or better in CSE 4214/6214). Three hour lecture. Topics include methods of testing, verification and validation, quality assurance processes and techniques, methods and types of testing, and ISO 9000/SEI CMM process evaluation
CSE 6753 Foundations in Computation: 3 hours.
(Prerequisite: CSE 1213 or CSE 1233 or CSE 1273 or CSE 1284 with a grade of C or better, or permission of instructor). Three hours lecture. Foundational concepts of computational algorithm design and analysis. (No credit for student in Computer Science, Computer Engineering, or Software Engineering degree programs)
CSE 6833 Introduction to Analysis of Algorithms: 3 hours.
(Prerequisites:CSE 2383,CSE 2813, and MA 2733 with a grade of C or better). Three hours lecture. Study of compexity of algorithms and algorithm design. Tools for analyzing efficiency; design of algorithms, including recurrence,divide-and-conquer, dynamic programming and greedy algorithms
CSE 8273 Software Requirements Engineering: 3 hours.
(Prerequisites:CSE 4214/6214 with grade of C or better). Three hours lecture. An in-depth study of current research and practice in requirements elicitation, requirements analysis, requirements specification, requirements verification and validation, and requirements management
CSE 8833 Algorithms: 3 hours.
(Prerequisites: CSE 4833/6833).Three hours lecture. Advanced techniques for designing and analyzing algorithms, advanced data structures, case studies, NP-completeness including reductions, approximation algorithms
CSE 8843 Complexity of Sequential and Parallel Algorithms: 3 hours.
(Prerequisite:CSE 4833/6833 ).Three hours lecture. Complexity of sequential algorithms, theory of complexity, parallel algorithms
CSE 9133 Topics in High Performance Computing: 3 hours.
(Prerequisite:Consent of Instructor). Three hours lecture. Reading and study of current work related to the area of high performance computing. Intended for doctoral students. ( May be taken for credit more than once)
ECE 6713 Computer Architecture: 3 hours.
(Prerequisites:Grade of C or better in ECE 3724). Three hours lecture. Detailed design and implementation of a stored-program digital computer system. Designs for the CPU, I/O subsystems, and memory organizations. ALU design and computer arithmetic
ECE 8063 Parallel Computer Arch I: 3 hours.
(Prerequisite: ECE 4713/6713/ CS 4113/6113). Three hours lecture. Study of hardware structures relevant to concurrent computing; evaluation and design methods associated with memory, pipelining, and multiple processors
Numerical Mathematics
MA 6313 Numerical Analysis I: 3 hours.
(Prerequisites: CSE 1213 or equivalent, MA 3113, and MA 2743). Three hours lecture. Matrix operations; error analysis; norms of vectors and matrices; transformations; matrix functions; numerical solutions of systems of linear equations; stability; matrix inversion; eigen value problems; approximations
MA 6323 Numerical Analysis II: 3 hours.
(Prerequisites: CSE 1213 or equivalent. MA 3113 and MA 3253) Three hours lecture. Numerical solution of equations; error analysis; finite difference methods; numerical differentiation and integration; series expansions; difference equations; numerical solution of differential equations
MA 8203 Foundations of Applied Mathematics I: 3 hours.
(Prerequisites: MA 3113, MA 3253 or consent of instructor.) Three hours lecture. Principles of applied mathematics including topics from perturbation theory, calculus of variations, and partial differential equations. Emphasis of applications from heat transfer, mechanics, fluids
MA 8213 Foundations of Applied Mathematics II: 3 hours.
(Prerequisite: MA 8203). Three hours lecture. A continuation of MA 8203 including topics from wave propagation, stability, and similarity methods
MA 8363 Numerical Solution of Systems of Nonlinear Equations: 3 hours.
(Prerequisites: MA 4313/6313 and MA 4323/6323). Three hours lecture. Basic concepts in the numerical solution of systems of nonlinear equations with applications to unconstrained optimization
MA 8383 Numerical Solution of Ordinary Differential Equations I: 3 hours.
(Prerequisites: MA 4313/6313 and MA 4323/6323). Three hours lecture. General single-step, multistep, multivalue, and extrapolation methods for systems of nonlinear equations; convergence; error bounds; error estimates; stability; methods for stiff systems; current literature
MA 8443 Numerical Solution of Partial Differential Equations I: 3 hours.
(Prerequisites: MA 4313/6313, MA 4323/6323, and MA 4373/6373 or consent of instructor). Three hours lecture. Basic concepts in the finite difference and finite element methods; methods for parabolic equations; analysis of stability and convergence
MA 8453 Numerical Solution of Partial Differential Equations II: 3 hours.
(Prerequisite: MA 8443). Three hours lecture. Methods for elliptic equations; iterative procedures; integral equation methods; methods for hyperbolic equations; stability; dissipation and dispersion
MA 8463 Numerical Linear Algebra: 3 hours.
(Prerequisite: MA 4323/6323). Three hours lecture. Basic concepts of numerical linear algebra
Graphics and Visualization
CSE 6413 Principles of Computer Graphics: 3 hours.
(Prerequisities:MA 3113 and grade of C or better in CSE 2383). Three hours lecture. Graphics hardware; algorithms,graphics primitives, windowing and clipping , transformations,3D graphics, shading,hidden surfaces; standards
CSE 8413 Visualization: 3 hours.
(Prerequisites:CSE 4413/6413).Three hours lecture. Essential algorithms for three-dimensional rendering and modeling teechniques;viewing transformations, illumination,surface modeling; methodologies for visualization of scalar and vector fields in three dimensions
CSE 8433 Advanced Computer Graphics: 3 hours.
(Prerequisites:CSE 4413/6413 ). Three hours lecture. Realistic, three-dimensional image generation; modeling techniques for complex three-dimensional scenes; advanced illumination techniques; fractal surface modeling; modeling and rendering of natural phenomena
ECE 6413 Digital Signal Processing: 3 hours.
(Prerequisite:Grade of C or better in ECE 3443). Three hours lecture. Discrete time signals, Z-Transform, Discrete Fouier Transform, digital filter design including IIR, FIR, and FFT synthesis
ECE 8423 Adaptive Signal Processing: 3 hours.
(Prerequisites: ECE 3443 or consent of instructor). Three hours lecture. Adaptive filtering, theoretical foundation, algorithms, structures, and implementations. Applications are included
ECE 8433 Statical Signal Processing: 3 hours.
(Prerequisite: MA 4533/6533 or consent of instructor). Three hours lecture. Detection theory and design, statistical decisions, Bayes and Neyman-Pearson detection, asymptotic performance, signal processing applications
ECE 8443 Pattern Recognition: 3 hours.
(Prerequisite: MA 4533/6533 or consent of instructor). Three hours lecture. Classification description, and structure of pattern recognition, patterns and feature extractions, engineering approaches including statistical and syntactic, and signal processing applications
ECE 8453 Introduction to Wavelets: 3 hours.
(Prerequisite: ECE 3443 or consent of instructor). Three hours lecture. Wavelet-expansion systems, discrete wavelet transform, multiresolution analysis, time-frequency anaylsis, filter banks and the discrete wavelet transform, wavelet transform, wavelet design, wavelet-based applications
ECE 8473 Digital Image Processing: 3 hours.
(Prerequisites: CS 1233, CS 1284 or equivalent, ECE 4413/ 6413 ). Three hours lecture. A study of digital image processing principles, concepts, and algorithms; mathematical models; image perception; image sampling and quantization, transforms, image coding
ECE 8483 Image and Video Coding: 3 hours.
(Prerequisite: ECE 8473 or consent of instructor). Three hours lecture. Intraframe predictive coding, intraframe transform coding, still-image coding standards, motion compensation, video-coding standards, image transmission and error control
Special Topics, Individual Study, Thesis and Dissertation Research
CME 6990 Special Topics in Computational Engineering: 1-9 hours.
Credit and title to be arranged. This course is to be used on a limited basis to offer developing subject matter areas not covered in existing courses. (Courses limited to two offerings under one title within two academic years)
CME 7000 Directed Individual Study in Computational Engineering: 1-6 hours.
Hours and credits to be arranged
CME 8000 Thesis Research/ Thesis in Computational Engineering: 1-13 hours.
Hours and credits to be arranged
CME 8990 Special Topics in Computational Engineering: 1-9 hours.
Credit and title to be arranged. This course is to be used on a limited basis to offer developing subject matter areas not covered in existing courses. (Courses limited to two offerings under one title within two academic years)
CME 9000 Dissertation Research/ Dissertation in Computational Engineering: 1-13 hours.
Hours and credits to be arranged