M.SC. in Computer Engineering (Without Thesis)

MATH 667 | Course Introduction and Application Information

Course Name

Theory of Finite Elements

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
MATH 667	Fall/Spring	3	0	3	7.5

Prerequisites	None
Course Language	English
Course Type	Elective
Course Level	Third Cycle
Mode of Delivery	-
Teaching Methods and Techniques of the Course	-
National Occupation Classification	-
Course Coordinator	Yrd. Doç. Dr. Sevin GÜMGÜM
Course Lecturer(s)	Yrd. Doç. Dr. Sevin GÜMGÜM
Assistant(s)	Araş. Gör. Cemal Murat ÖZKUT

Course Objectives

This course aims to teach the method of finite elements which is one of the main tools for the numerical treatment of elliptic and parabolic partial differential equations. It is based on the variational formulation of the differential equation, it is much more flexible than finite difference methods and finite volume methods and thus be applied to more complicated problems.

Learning Outcomes

#	Content	PC Sub	* Contribution Level
#	Content	PC Sub	1	2	3	4	5
1	To be able to explain RayleighRitz Method.
2	To be able to explain Lagrange basis functions in one dimensional problem.
3	To be able to define the relationship between finite elements and finite difference methods.
4	To be able to explain Hermit basis functions.
5	To be able to define rectangular and triangular finite elements.
6	To be able to explain Natural coordinates.

Course Description

In this course variational formulation of boundary value problems, an introduction to Sobolev spaces and finite element concepts will be taught. Also includes classification of finite elements in onedimensional and twodimensional models.

Course Category	Core Courses
	Major Area Courses
	Supportive Courses
	Media and Management Skills Courses
	Transferable Skill Courses

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week	Subjects	Related Preparation	Learning Outcome
1	Linear Interpolation	The Finite Element Method: Its Basis and Fundamentals (Sixth edition) by O.C. Zienkiewicz, R.L.Taylor, J.Z. Zhu, 2005, Elsevier Butterworth Heinemann.
2	RayleighRitz Method	A First Course in Finite Elements by Jacob Fish, Ted Belytschko, 2007, John Wiley & Sons Ltd.
3	General scheme for the method of finite elements..	The Finite Element Method: Its Basis and Fundamentals (Sixth edition) by O.C. Zienkiewicz, R.L.Taylor, J.Z. Zhu, 2005, Elsevier Butterworth Heinemann.
4	Partial linear Lagrange basis functions in one dimensional case. Formulation of global matrix.	The Finite Element Method: Its Basis and Fundamentals (Sixth edition) by O.C. Zienkiewicz, R.L.Taylor, J.Z. Zhu, 2005, Elsevier Butterworth Heinemann.
5	Relationship between finite elements and finite difference methods.	A First Course in Finite Elements by Jacob Fish, Ted Belytschko, 2007, John Wiley & Sons Ltd.
6	Second order (kind) Lagrange basis functions. Formulation of global matrix.	A First Course in Finite Elements by Jacob Fish, Ted Belytschko, 2007, John Wiley & Sons Ltd.
7	Hermit basis functions.	The Finite Element Method: Its Basis and Fundamentals (Sixth edition) by O.C. Zienkiewicz, R.L.Taylor, J.Z. Zhu, 2005, Elsevier Butterworth Heinemann.
8	Variational formulation of Laplace Boundary Value Problem.	The Finite Element Method: Its Basis and Fundamentals (Sixth edition) by O.C. Zienkiewicz, R.L.Taylor, J.Z. Zhu, 2005, Elsevier Butterworth Heinemann..
9	First kind rectangular Lagrange finite elements.	Varyasyonel Problemler ve Sonlu Elemanlar Yöntemi, A. Hasanoğlu, Literatür Yanıncılık, İstanbul, 2001
10	First kind triangular finite element formulation.	Varyasyonel Problemler ve Sonlu Elemanlar Yöntemi, A. Hasanoğlu, Literatür Yanıncılık, İstanbul, 2001
11	Natural coordinates for one dimensional problems.	Varyasyonel Problemler ve Sonlu Elemanlar Yöntemi, A. Hasanoğlu, Literatür Yanıncılık, İstanbul, 2001
12	Natural coordinates for triangular finite elements.	Varyasyonel Problemler ve Sonlu Elemanlar Yöntemi, A. Hasanoğlu, Literatür Yanıncılık, İstanbul, 2001
13	Natural coordinates for rectangular finite elements.	Varyasyonel Problemler ve Sonlu Elemanlar Yöntemi, A. Hasanoğlu, Literatür Yanıncılık, İstanbul, 2001
14	Review of the semester
15	Review of the semester
16	Review of the semester

Course Notes/Textbooks	The extracts above and exercises will be given.
Suggested Readings/Materials	None

EVALUATION SYSTEM

Semester Activities	Number	Weighting	LO 1	LO 2	LO 3	LO 4	LO 5	LO 6
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments	2	15
Presentation / Jury
Project	2	20
Seminar / Workshop
Oral Exams
Midterm	1	25
Final Exam	1	40
Total

Weighting of Semester Activities on the Final Grade		60
Weighting of End-of-Semester Activities on the Final Grade		40
Total

ECTS / WORKLOAD TABLE

Semester Activities	Number	Duration (Hours)	Workload
Theoretical Course Hours (Including exam week: 16 x total hours)	16	3	48
Laboratory / Application Hours (Including exam week: '.16.' x total hours)	16		0
Study Hours Out of Class	15	5	75
Field Work			0
Quizzes / Studio Critiques			0
Portfolio			0
Homework / Assignments	2	10	20
Presentation / Jury			0
Project	2	15	30
Seminar / Workshop			0
Oral Exam			0
Midterms	1	20	20
Final Exam	1	32	32
		Total	225

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#	PC Sub	Program Competencies/Outcomes	* Contribution Level
#	PC Sub	Program Competencies/Outcomes	1	2	3	4	5
1	Accesses information in breadth and depth by conducting scientific research in Computer Engineering, evaluates, interprets and applies information.		-	-	-	X	-
2	Is well-informed about contemporary techniques and methods used in Computer Engineering and their limitations.		-	-	X	-	-
3	Uses scientific methods to complete and apply information from uncertain, limited or incomplete data, can combine and use information from different disciplines.		-	-	-	X	-
4	Is informed about new and upcoming applications in the field and learns them whenever necessary.		-	-	-	-	X
5	Defines and formulates problems related to Computer Engineering, develops methods to solve them and uses progressive methods in solutions.		-	-	-	-	X
6	Develops novel and/or original methods, designs complex systems or processes and develops progressive/alternative solutions in designs.		-	-	-	X	-
7	Designs and implements studies based on theory, experiments and modelling, analyses and resolves the complex problems that arise in this process.		-	-	-	X	-
8	Can work effectively in interdisciplinary teams as well as teams of the same discipline, can lead such teams and can develop approaches for resolving complex situations, can work independently and takes responsibility.		-	-	X	-	-
9	Engages in written and oral communication at least in Level B2 of the European Language Portfolio Global Scale.		-	-	X	-	-
10	Communicates the process and the results of his/her studies in national and international venues systematically, clearly and in written or oral form.		-	-	X	-	-
11	Is knowledgeable about the social, environmental, health, security and law implications of Computer Engineering applications, knows their project management and business applications, and is aware of their limitations in Computer Engineering applications.		-	-	X	-	-
12	Highly regards scientific and ethical values in data collection, interpretation, communication and in every professional activity.		-	X	-	-	-