| Course Unit Code | 470-8341/01 |
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| Number of ECTS Credits Allocated | 5 ECTS credits |
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| Type of Course Unit * | Compulsory |
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| Level of Course Unit * | Second Cycle |
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| Year of Study * | First Year |
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| Semester when the Course Unit is delivered | Summer Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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| Name of Lecturer(s) | Personal ID | Name |
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| LUK76 | doc. Ing. Dalibor Lukáš, Ph.D. |
| HOR33 | doc. Ing. David Horák, Ph.D. |
| Summary |
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| Successful solution of the problems arising in engineering requires anunderstanding of relevant mathematics. The students will learn about basic tools and their applications for the solution of such problems. |
| Learning Outcomes of the Course Unit |
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| Student will understand model partial differential equations, basic methods of approximation of the solution of the boundary value problems, variational equalities and inequalities, their abstract structure and methods of solution. He/she will understand the role of these conceps in applications. |
| Course Contents |
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Boundary value problems for ordinary differential equations of the 2nd order.
Finite difference discretization and boundary conditions.
Problems with non-smooth soefficients and/or right hand side.
Variational formulation of the boundary value problems.
Discretization based on variational formulation. Collocation, Ritz method, Galerkin method, finite element method.
Propertis and direct methods of solution of the discretized systems.
Conjugate gradient method with preconditioning.
Domain decomposition and multilevel methods.
Variational inequalities and their discretization.
Numerical solution of variational inequalities.
Boundary integral equations.
Bouhary element method for a model problem.
Software.
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| Recommended or Required Reading |
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| Required Reading: |
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| K. Rektorys, Variational Methods in Mathematics, Science and Engineering. Reidel, Dordrecht, 1980 |
| K.Rektorys: Variační metody v inženýrských problémech a v problémech matematické fyziky. Academia, Praha 1999. ISBN: 80-200-0714-8 |
| Recommended Reading: |
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G. Strang, Introduction to Applied Mathematics. Wellesley-Cambridge Press, 1986.
ISBN-13: 9780961408800 |
| S. Míka, A. Kufner, Parciální diferenciální rovnice I, SNTL, Praha, 1983 |
| Planned learning activities and teaching methods |
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| Lectures, Tutorials |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Exercises evaluation and Examination | Credit and Examination | 100 (100) | 51 |
| Exercises evaluation | Credit | 30 | 15 |
| Examination | Examination | 70 | 21 |