Gurantor department | Department of Applied Mathematics | Credits | 5 |

Subject guarantor | prof. RNDr. Radim Blaheta, CSc. | Subject version guarantor | prof. RNDr. Radim Blaheta, CSc. |

Study level | undergraduate or graduate | Requirement | Compulsory |

Year | 1 | Semester | summer |

Study language | Czech | ||

Year of introduction | 2010/2011 | Year of cancellation | |

Intended for the faculties | USP | Intended for study types | Follow-up Master |

Instruction secured by | |||
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Login | Name | Tuitor | Teacher giving lectures |

DOM0015 | Ing. Simona Domesová | ||

LUK76 | doc. Ing. Dalibor Lukáš, Ph.D. |

Extent of instruction for forms of study | ||
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Form of study | Way of compl. | Extent |

Full-time | Credit and Examination | 3+1 |

Combined | Credit and Examination | 15+5 |

Students will be able to formulate the boundary value problems arising in mathematical modeling of heat conduction, elasticity, and other phenomena (diffusion, electro and magnetostatics, etc.). It will also be able to derive the differential and variational formulation of the task and numerical solution of the finite element method. They will know the principles of proper use of mathematical models for solving engineering problems.

Lectures

Tutorials

The course should prepare the students to be able to formulate the boundary value problems arising in mathematical modelling of heat conduction, elasticity and other physical processes. The students should be also able to derive differential and variational formulation of these problems and understand the mathematical principles of their numerical solution, especially by the finite element method. The course will also touch the principles of proper use of mathematical modelling methods for solving engineering problems.

R. D. Cook: Finite element modelling for stress analysis, J. Wiley, New
York, 1995.
C. Johnson: Numerical solution of partial differential equations by the
finite element method, Cambridge Univ. Press, 1995

R. D. Cook: Finite element modelling for stress analysis, J. Wiley, New York, 1995.
C. Johnson: Numerical solution of partial differential equations by the finite element method, Cambridge Univ. Press, 1995

Additional requirements for students are not.

Subject has no prerequisities.

Subject has no co-requisities.

Mathematical modeling. Purpose and general principles of modeling. Benefits
mathematical modeling. Proper use of mathematical models.
Differential formulation of mathematical models. One-dimensional heat conduction problem and its mathematical formulation. Generalizing the model. The input linearity,
existence and uniqueness of solutions. Discrete input data. One-dimensional task
flexibility and other models. Multivariate models.
Variational formulation of boundary problems. Weak formulation of boundary problems and its relationship to the classical solutions. Energy and energy functional formulation.
Coercivity and boundedness. Uniqueness, continuous dependence of solutions
input data. Existence and smoothness of the solution.
Ritz - Galerkin (RG) method. RG method. Konenčných element method (FEM)
as a special case of the RG method. History MLP.
Algorithm finite element method. Assembling the stiffness matrix and vector
load. Taking into account the boundary conditions. Numerical solution of linear systems algebraic equations. Different types of finite elements.
The accuracy of finite element solutions. Priori estimate of the discretization error.
Convergence, h-and p-version FEM. Posteriori estimates. Network design for MLP
adaptive technology and optimal network.
FEM software and its use for MM. Preprocessing and postprocessing. Commercial
software systems. Solutions particularly difficult and special problems. Principles
Mathematical modeling using FEM.

Task name | Type of task | Max. number of points
(act. for subtasks) | Min. number of points |
---|---|---|---|

Exercises evaluation and Examination | Credit and Examination | 100 (100) | 51 |

Exercises evaluation | Credit | 30 | 15 |

Examination | Examination | 70 | 21 |

Show history

Academic year | Programme | Field of study | Spec. | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
---|---|---|---|---|---|---|---|---|---|---|---|

2019/2020 | (N3942) Nanotechnology | (3942T001) Nanotechnology | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2018/2019 | (N3942) Nanotechnology | (3942T001) Nanotechnology | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2017/2018 | (N3942) Nanotechnology | (3942T001) Nanotechnology | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2016/2017 | (N3942) Nanotechnology | (3942T001) Nanotechnology | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2015/2016 | (N3942) Nanotechnology | (3942T001) Nanotechnology | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2014/2015 | (N3942) Nanotechnology | (3942T001) Nanotechnology | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2014/2015 | (N3942) Nanotechnology | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2013/2014 | (N3942) Nanotechnology | (3942T001) Nanotechnology | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2012/2013 | (N3942) Nanotechnology | (3942T001) Nanotechnology | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2011/2012 | (N3942) Nanotechnology | (3942T001) Nanotechnology | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2010/2011 | (N3942) Nanotechnology | (3942T001) Nanotechnology | P | Czech | Ostrava | 1 | Compulsory | study plan |

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