# Computational Engineering

**Graduate Coordinator: Dr. Adrian Sescu**

Center for Advanced Vehicular Systems (CAVS)

Box 9618

Mississippi State, MS 39762

Telephone: 662-325-5431

E-mail: cme-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 HPC^{2}. Programs of study and research leading to both the Master of Science degree and the Doctor of Philosophy degree are offered on the Starkville Campus and through Distance Education. There is an increased demand by industry, academia, and government for scientists and engineers with a foundation to create tools for computational analysis and design, and with a strong domain knowledge for application of these tools to complex engineering problems. 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 HPC^{2}.

## 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 Graduate Coordinator. International students must have scored at least 550 PBT (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.

Highly qualified undergraduate students may be considered for direct admission if the following criteria are met: 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, and a competitive GRE score for applicants from a non-ABET-accredited program.

### Provisional Admission

A Master of Science applicant who has not fully met the GPA requirement stipulated by the University may be admitted on a provisional basis. Provisional admission will not be considered for Ph.D. applicants.The following identify requirements in addition to those outlined by University policy in the *Graduate Catalog*. A provisionally-admitted student is eligible for a change to regular status after receiving a 3.30 GPA on the first 9 hours of graduate courses at Mississippi State University (with no grade lower than a B). The first 9 hours of graduate courses must be within the student's program of study. Courses with an S grade, transfer credits, or credits earned while in Unclassified status cannot be used to satisfy this requirement. If a 3.30 is not attained, the provisional student **shall **be dismissed from the graduate program. Academic departments may set higher standards for students to fulfill provisional requirements; a student admitted with provisional status should contact the graduate coordinator for the program's specific requirements. While in the provisional status, a student is not eligible to hold a graduate assistantship.

## 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 data analytics. 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 program is contingent upon satisfactory performance in the courses and research and satisfactory performance toward completion of the degree. In addition to the University guidelines, satisfactory performance is achieved when all four of the following criteria are met:

- The student maintains a B average or better on: a.) all graduate courses completed
__and__b.) all graduate courses included on the program of study. - If the student registers for research credits in a given term, he/she receives a satisfactory (S) grade at the end of the term.
- The student has a major advisor and supervisory graduate committee after the first two terms of enrollment.

In addition to the University guidelines for academic dismissal in the Graduate Catalog, a graduate student in the Computational Engineering program shall be dismissed if he or she receives two unsatisfactory (U) grades on research credit hours. A student will be placed on academic probation based on University guidelines in the Graduate Catalog, or if one of the following conditions are met:

- A second C grade on the program of study
- A grade of U on research credit hours

The probationary period is defined to be one term (summer is included if the student is enrolled). A probationary period of two terms may be considered for online students with a GPA below 3.0/4.0. If at the end of the probationary period the student has not remedied his/her deficiency (i.e., has not achieved a 3.00 GPA and/or has not scheduled research credit hours and received a satisfactory (S) grade) the student may be dismissed. For students enrolled in either the M.S. or Ph.D. program, all issues related to academic probation, dismissal, and appeal will be governed by University policy, as approved by Graduate Council and the Provost and outlined by the Graduate School in the Graduate Catalog.

## Graduate Courses

Because of the interdisciplinary nature of the Computational Engineering program, courses listed under the "Courses" tab 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 Graduate Coordinator. The program of study must demonstrate the student has achieved a working knowledge of

- a Computational Engineering application area,
- high-performance computing, and
- numerical mathematics

## Master of Science in Computational Engineering - Thesis

8000-level coursework | 12 | |

Additional graduate-level coursework | 12 | |

Research/thesis | 6 | |

CME 8000 | ||

Total Hours | 30 |

## Master of Science in Computational Engineering - Non-Thesis

8000-level coursework | 15 | |

Additional graduate-level coursework | 15 | |

Research project | 3 | |

Directed Individual Study in Computational Engineering | ||

Total Hours | 33 |

## Doctor of Philosophy in Computational Engineering

A Ph.D. in Computational Engineering requires the following credit hours beyond a B.S.

8000-level graduate coursework | 24 | |

Additional graduate-level coursework | 24 | |

Research/Dissertation | 24 | |

CME 9000 | ||

Dissertation/Dissertation Research Hours in Computational Engineering | ||

Total Hours | 72 |

**Qualifying GPA credit hours from M.S. degree may be counted towards this requirement.**

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 the student must:

- 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 policies and protocols of the Graduate School.

## 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

**ASE 8423 Computational Fluid Dynamics II: 3 hours.**

(Prerequisite: ASE 8413 or equivalent). Three hours lecture. Compressible Viscous Methods; Navier-Stokes equation methods; turbulence models; incompressible methods; panel methods; finite element methods, current literature

**CE 6533 Computational Methods in Water Resources Engineering: 3 hours.**

(Prerequisite: Grade of C or better in CE 3503; or consent of major advisor). Three hours lecture. Review of relevant numerical analysis; numerical methods for kinematic wave, St. Venant, Boussinesq and dept-averaged equations; simulation of one and two dimension free-surface flows

**CE 6913 Matrix of Analysis of Structures: 3 hours.**

(Prerequisite: Grade of C or better in CE 3603, or consent of instructor; or consent of major advisor). Matrix formulation and computer analysis of structures. Linear stiffness analysis of truss and frames structures

**CE 8203 Finite Element Modeling in CEE: 3 hours.**

(Prerequisite: Consent of Major Advisor). Three hours lecture. Modern finite element methods for continuum mechanical models relevant to civil and environmental engineering, including surface and subsurface fluid flow, mass transport, and solid mechanics

**CE 8683 Finite Element Analysis in Structural Engineering: 3 hours.**

(Prerequisite: Consent of Major Advisor). 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 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

**EM 6123 An Introduction to the Finite Element Method: 3 hours.**

(Prerequisite: Consent of Instructor). Three hours lecture. Introduction to the mathematical theory, formulation, and computer implementation of the finite element method. App- lication to one-and two-dimensional problems in engineering mechanics

**EM 6143 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 ASE 4553/6553 and IE 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; formulating optimization models; simplex algorithm, duality and sensitivity analysis, integer programming; branch-and-bound algorithm; real-life applications of linear and integer programming models (Same as MA 4733/6733)

**IE 6743 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 ASE 4553/6553 and EM 4143/6143 )

**IE 6773 Systems Simulation I: 3 hours.**

(Prerequisite: Grade of C or better in IE 4934, IE 4933 or equivalent programming course, Co-requisite: IE 4623). Three hours lecture. The principles of simulating stochastic systems with an emphasis on the statistics of simulation and the use of discrete-event simulation languages

**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 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

## 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.**

(Prerequisites: Grade of C or better in CSE 3183). 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 and CSE 2813 with a grade of C or better). Three hours lecture. Study of complexity 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 1233 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 1233 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 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 problem algorithms,interger and goal programming. (Same as IE 4733/6733)

**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 4313/6313 and MA 4323/6323 or consent of the instructor). Three hours lecture. Gaussian elimination and its variants; iterative methods for linear systems; the lease-squares problem; QR factorization; singular value decomposition; principal component analysis; eigenvalue problems; iterative methods for eigenvalue problems; applications to data mining

## Scientific 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 techniques;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

## Data Analytics

**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 Fourier 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 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 Research in Computational Engineering: 1-13 hours.**

Hours and credits to be arranged