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| MATL7920 | Boundary Elements Methods and Applications | 3+0+0 | ECTS:7.5 | | Year / Semester | Spring Semester | | Level of Course | Third Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Doç. Dr. Pelin ŞENEL | | Co-Lecturer | Prof. Dr. Selçuk Han Aydın | | Language of instruction | | | Professional practise ( internship ) | None | | | | The aim of the course: | | The aim of the course is to introduce boundary elements method (BEM) for the discretization of the two-dimensional partial differential equations (PDEs). Application of the dual reciprocity boundary element method (DRBEM) for equations containing convective and time dependent terms will also be given. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | Derive boundary integral equations for two-dimensional PDEs. | | 1,3, | | PO - 2 : | Apply BEM to Laplace and Poisson equations. | | 1,3, | | PO - 3 : | Apply DRBEM to time dependent problems. | | 1,3, | | PO - 4 : | Make computer implementation of DRBEM to basic two-dimensional PDEs | | 1,3, | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome | | |
| Poisson's equation, approximate solutions, weighted residual techniques, weak formulations. Boundary and domain solutions, boundary integral equations and the boundary element method (BEM). BEM for the Laplace equation. Constant and linear elements discretization, evaluation of BEM integrals, BEM formulation for the Poisson equation, evaluation of domain integrals. Dual reciprocity boundary element method (DRBEM), radial basis functions. Application of DRBEM to the Poisson, Helmholtz equations and equations containing convective terms. Time dependent equations and time discretization schemes. Application of DRBEM to time dependent equations. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Poisson's equation, approximate solutions | | | Week 2 | Weighted residual techniques | | | Week 3 | Weak formulations, boundary and domain solutions | | | Week 4 | Boundary integral equations and the boundary element method (BEM) | | | Week 5 | BEM for the Laplace equation | | | Week 6 | Constant and linear elements discretization | | | Week 7 | Evaluation of BEM integrals | | | Week 8 | BEM formulation for the Poisson equation, evaluation of domain integrals | | | Week 9 | Midterm Exam | | | Week 10 | Dual reciprocity boundary element method (DRBEM), radial basis functions | | | Week 11 | Application of DRBEM to the Poisson equation | | | Week 12 | Application of DRBEM to the Helmholtz equation | | | Week 13 | Application of DRBEM to equations containing convection terms | | | Week 14 | Time dependent equations and time discretization schemes | | | Week 15 | Application of DRBEM to time dependent equations | | | Week 16 | Final Exam | | | |
| 1 | Partridge, P.W., Brebbia, C.A., Wrobel, L.C. 1992; The Dual Reiprocity Boundary Element Method, Computational Mechanics Publications, Southampton Boston. | | | |
| 1 | Brebbia, C.A., Dominguez, J. 1992; Boundary Elements an Introductory Course, WIT Press, Southampton, Boston. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 6 | 26/04/2023 | 48 | 30 | | Homework/Assignment/Term-paper | 9 | 17/05/2023 | 240 | 20 | | End-of-term exam | 16 | 20/06/2023 | 240 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 3 | 14 | 42 | | Sınıf dışı çalışma | 4 | 14 | 56 | | Arasınav için hazırlık | 6 | 2 | 12 | | Arasınav | 2 | 1 | 2 | | Ödev | 5 | 2 | 10 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 124 |
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