# Boundary Element Method Programming (MDES651) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Boundary Element Method Programming MDES651 Area Elective 3 0 0 3 5
Pre-requisite Course(s)
Consent of the instructor
Course Language English Focus Course Ph.D. Face To Face Lecture. The main objective of this course is to acquaint the students with the basic concepts about the programming principles of boundary element method. The students will learn the procedures in developing a boundary element formulation for specific engineering problems and with the obtain formulation; they will be able to program specific problems to solve given tasks. The students who succeeded in this course; Students will learn the basic principles of developing a boundary element formulation for a given specific engineering problem. Students will be able to design and implement a boundary element program for a given problem. Students will be acquainted with the challenges of numerical programming, e.g., numerical evaluation of singular integrals and special techniques to evaluate the Cauchy principal and Hadamard Finite Part integrals. Students will be able to implement pre and post processors for boundary element analysis programs. Students will acquire a new insight to numerical solution of boundary value problems. Vector calculus; boundary value problems in mechanics; general outline of boundary element formulation; direct and indirect formulations; discretization-elements and integration; assembly and solution techniques; advanced techniques-dual reciprocity and multiple reciprocity, substructuring and boundary element-finite element coupling; parallel prog

### Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Mathematical introduction: Vector calculus and boundary value problems, numerical solution techniques of BVPs Related pages of the textbook and other courses
2 Boundary element method formulations Related pages of the textbook and other courses
3 Boundary element formulations – direct method Related pages of the textbook and other courses
4 Boundary element formulations – indirect method Related pages of the textbook and other courses
5 Several application problems: Laplace equation, linear Poisson equations, linear theory of elasticity Related pages of the textbook and other courses
6 Discretization of the domain – element types Related pages of the textbook and other courses
7 Discretization of the domain – integrations over elements Related pages of the textbook and other courses
8 Near singular, weakly singular integrals and integrals containing higher singularities Related pages of the textbook and other courses
9 Numerical evaluation of Cauchy principal value integrals and Hadamard Finite Part integrals Related pages of the textbook and other courses
10 Assembly and solution Related pages of the textbook and other courses
11 Pre- and post-processing of data Related pages of the textbook and other courses
12 Alternative formulations; dual reciprocity, multiple reciprocity and domain decomposition techniques Related pages of the textbook and other courses
13 Finite element – boundary element coupling Related pages of the textbook and other courses
14 Parallel programming issues in boundary element method Related pages of the textbook and other courses
15 Overall review -
16 Final exam -

### Sources

Course Book 1. [1] Beer, G., Programming the boundary element method, John Wiley &Sons, (2001). 2. [2] Gao, X. W., Davies, T. G., Boundary element programming in mechanics, Cambridge University Press, (2002). 3. [3] Brebbia C. A., Domingues, J., Boundary elements, McGraw-Hill, (1992).. 4. [4] Wrobel, L.C., The boundary element method v.1 Applications in thermo-fluids and acoustics, John Wiley and Sons Inc., (2002) 5. [5] Aliabadi, M.H., The boundary element method v.2 Applications in solids and structures, John Wiley and Sons Inc., (2002)

### Evaluation System

Attendance/Participation 1 5
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics 5 5
Homework Assignments 5 40
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 1 20
Final Exam/Final Jury 1 30
Toplam 13 100
 Percentage of Semester Work 70 30 100

### Course Category

Core Courses X

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Ability to carry out advanced research activities, both individual and as a member of a team X
2 Ability to evaluate research topics and comment with scientific reasoning X
3 Ability to initiate and create new methodologies, implement them on novel research areas and topics X
4 Ability to produce experimental and/or analytical data in systematic manner, discuss and evaluate data to lead scintific conclusions X
5 Ability to apply scientific philosophy on analysis, modelling and design of engineering systems X
6 Ability to synthesis available knowledge on his/her domain to initiate, to carry, complete and present novel research at international level X
7 Contribute scientific and technological advancements on engineering domain of his/her interest area X
8 Contribute industrial and scientific advancements to improve the society through research activities X

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours) 16 3 48
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class 16 2 32
Presentation/Seminar Prepration
Project
Report
Homework Assignments 5 5 25
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 2 8 16
Prepration of Final Exams/Final Jury 1 10 10