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Course, academic year 2023/2024
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Shape and Material Optimisation 1 - NMNV541
Title: Tvarová a materiálová optimalizace 1
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: not taught
Language: Czech, English
Teaching methods: full-time
Teaching methods: full-time
Guarantor: prof. RNDr. Jaroslav Haslinger, DrSc.
Class: M Mgr. MOD
M Mgr. MOD > Volitelné
M Mgr. NVM
M Mgr. NVM > Povinně volitelné
Classification: Mathematics > Numerical Analysis
Incompatibility : NMOD105
Interchangeability : NMOD105
Is interchangeable with: NMOD105
Annotation -
Last update: T_KNM (14.04.2015)
The first part of this course is devoted to comprehensive introduction to the mathematical theory of optimal shape design problems. The stability of solutions to elliptic PDE’s on parameters characterizing the geometry of systems ( thickness of plates, shape of domains where state problems are formulated) will be studied. This property plays the key role in the existence analysis. This part deals not only with the continuous setting of problems but also with their discretizations (state problems by finite elements, shapes by Bezier curves) followed by the convergence analysis.
Course completion requirements -
Last update: prof. RNDr. Jaroslav Haslinger, DrSc. (07.06.2019)

Oral examination

Literature -
Last update: doc. RNDr. Václav Kučera, Ph.D. (29.10.2019)

J. Haslinger, P. Neittaanmäki: Finite Element Approximation for Optimal Shape, Material and Topology Design. 2nd edition, John Willey, 1996

J. Haslinger, R. Mäkinen: Introduction to Shape Optimization,Theory, Approximation and Computation. SIAM, 2003

Requirements to the exam -
Last update: prof. RNDr. Jaroslav Haslinger, DrSc. (08.10.2017)

The exam is only oral according to the joint syllabus.

Syllabus -
Last update: T_KNM (27.04.2015)

Abstract formulation of shape optimization problems. Existence of solutions.

Discretization of shape optimization problems- abstract formulation. Convergence analysis

Application of abstract results to particular shape optimization problems with different state relations ( Dirichlet, Neumann, mixed Stokes)

Entry requirements -
Last update: RNDr. Miloslav Vlasák, Ph.D. (17.05.2018)

Basic knowledge of functional analysis and approximation of elliptic equations by finite elements is required.

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