MATH595 THE BOUNDARY ELEMENT METHOD & APP.
| Course Code: | 2360595 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Prof.Dr. CANAN BOZKAYA |
| Offered Semester: | Fall Semesters. |
Course Objectives
At the end of this course, the student will:
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gain a rigorous understanding of weighted residual formulations for partial differential equations
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develop the theoretical and computational framework of the boundary element method (BEM) for Laplace and Poisson-type problems
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understand and implement the dual reciprocity boundary element method (DRBEM) for transforming domain integrals into boundary-only expressions
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acquire practical skills in coding and validating BEM/DRBEM algorithms for advanced engineering and mathematical applications
Course Content
Weighted residual methods, the boundary element method for Laplace and Poisson equations. The dual reciprocity method, computer implementation.
Course Learning Outcomes
Student, who passed the course satisfactorily will be able to:
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explain the fundamental concepts of weighted residual methods including Galerkin and collocation techniques
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apply the boundary element method (BEM) to solve Laplace and Poisson equations in engineering/mathematical problems
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implement the dual reciprocity boundary element method (DRBEM) for converting domain integrals into equivalent boundary-only formulations
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construct boundary integral formulations for given partial differential equations using appropriate fundamental solutions
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develop and test computer codes for the numerical implementation of BEM and DRBEM
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evaluate the accuracy and convergence of BEM/DRBEM solutions through benchmark problems
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interpret physical meaning and mathematical properties of boundary-only formulations in comparison to domain-based numerical methods
Program Outcomes Matrix
| Level of Contribution | |||||
| # | Program Outcomes | 0 | 1 | 2 | 3 |
| 1 | Acquires mathematical thinking skills (problem solving, generating ways of thinking, forming correspondence, generalizing etc.) and can use them in related fields. | ✔ | |||
| 2 | Gains academic maturity through self-study. | ✔ | |||
| 3 | Can design mathematics related problems, devise solution methods and apply them when appropriate. | ✔ | |||
| 4 | Carries out parts of a mathematical research program independently. | ✔ | |||
| 5 | Has a command of Turkish and English languages so that he/she can actively communicate (read, write, listen and speak). | ✔ | |||
| 6 | Contributes to solving global, environmental and social problems either individually or as being part of a social group. | ✔ | |||
| 7 | Respects ethical values and rules; applies them in professional and social issues. | ✔ | |||
| 8 | Can work cooperatively in a team and also individually. | ✔ | |||
| 9 | Gets exposed to academic culture through interaction with others. | ✔ | |||
| 10 | Comprehends necessity of knowledge, can define it and acquires it; uses knowledge effectively and shares it with others. | ✔ | |||
0: No Contribution 1: Little Contribution 2: Partial Contribution 3: Full Contribution