Computational Engineering, Ph.D.
Doctoral students must complete a minimum of 72 hours beyond the bachelor’s degree, exclusive of credit for the master’s thesis. These hours must include a minimum of 24 semester hours in doctoral research and dissertation and a minimum of 48 semester hours in other courses. The courses must include:
- A minimum of 24 semester hours of graduate coursework in engineering in courses numbered 500 and above, with at least 12 of these in computational engineering. A minimum of 6 semester hours of courses is required at the 700 level. These are exclusive of thesis or dissertation credit. The student’s supervisory committee can approve a student’s petition to replace one 700-level course with one or more 500-level course(s) that are more appropriate.
- A minimum of 12 semester hours of coursework in mathematics or computer science in courses numbered 400 and above and taken for graduate credit exclusive of a first course in ordinary differential equations. No more than 6 hours can be earned in a 400 level course.
- There are multiple pathways toward accumulating the required coursework: a) all coursework may be performed at UTC, b) credit may be earned through coursework performed within the University of Tennessee system, c) credit is normally granted for up to 24 semester hours credited toward a master’s degree at another university, and d) transfer credit may be granted for courses applicable to the program of study and accepted for graduate credit at another university.
The program of study must adequately address the following core requirements, with appropriate course content in each of three primary areas that are essential to computational engineering: 1) an engineering application area, 2)scientific supercomputing, and 3) mathematics of computation, as determined by the student’s supervisory committee and the Graduate Program Coordinator. Courses completed at the master’s level can be included to satisfy the core requirements. Required courses in the program of study can vary, based on each student’s background and goals. It is the responsibility of the student’s supervisory committee, with the approval of the Graduate Program Coordinator, to ensure the student’s adequate exposure to each area, which may involve completion of some undergraduate prerequisite courses.
The program of study must establish a primary applications focus, with additional coursework in both scientific supercomputing and mathematics of computation that logically relates to the applications focus. A Program of Study Form must be signed by the student, each committee member, and the Graduate Program Coordinator and then submitted to the UTC Graduate School for final approval. The student should file the Program of Study Form during the second semester of coursework and before completing 12 semester hours of coursework.
Typical Program of Study
Programs of study will depend on the student’s academic background and undergraduate major, as well as on the intended area of research. For a student whose undergraduate major was engineering (the most common case), a typical curriculum for one program cycle past the baccalaureate degree might include the following courses:
- ENCM 5160 - Grid Generation (3)
- MATH 5600 - Numerical Analysis I (3)
- ENCM 5100 - Computational Fluid Dynamics I (3)
- Graduate Seminar
- ENCM 5340 - Viscous Flow Theory (3)
- MATH 5610 - Numerical Analysis II (3)
- ENCM 7100 - Computational Fluid Dynamics II (3)
- ENCM 7340 - Viscous Flow Computation (3)
- MATH 5620 - Numerical Solution of Partial Differential Equations I (3)
- ENCM 5210 - Introduction to Parallel Algorithms (3)
- Graduate Seminar
- ENGR 5420 - Finite Element Analysis (4)
- MATH 4200 - Linear Algebra and Matrix Theory (3)
- MATH 5630 - Numerical Solution of Partial Differential Equations II (3)
- ENCM 7160 - Adaptive & Dynamic Grid Generation (3)
- MATH 4570 - Introductory Complex Variables (3)
- ENCM 7210 - Parallel Scientific Supercomputing (3)
- ENCM 7310 - Computational Design (3)