Introduction to modeling and simulation

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Department of Mechanics

Synopsis:

The aim is to provide PhD students with a basic orientation and overview of concepts, models and methods applicable to the theoretical description and numerical simulation of physical and other processes relevant to engineering applications. The teaching will be tailored to the prior knowledge and anticipated needs of the enrolled participants, who will be directed to other sources of information, specialized courses, appropriate textbooks, etc., according to their abilities and interests. Topics covered may include basic computational and visualization tools, model classification, tensor notation, continuum mechanics, dimensional analysis and its applications, numerical methods for discretization of continuous problems, Fourier transform and its applications, optimization problems and methods, or applied machine learning.

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Syllabus of lectures:

Basic tools for calculations and visualization - python (or matlab), graphical libraries [Václav Nežerka]

Types of models - discrete and continuous, types of differential equations and their properties, boundary and initial conditions [Milan Jirásek]

Tensors and tensor operations, tensor notation and its advantages [Martin Horák]

Description of a continuum under large displacements, Lagrangian and Eulerian approach [Martin Horák]

Basic concepts of thermodynamics of continuous media [Milan Jirásek]

Balance equations - mass, momentum, angular momentum, energy, entropy. Difference between balance equation and constitutive relation [Milan Jirásek]

Dimensional analysis, similarity, scaling, conversion to dimensionless form, size effect [Milan Jirásek]

Heterogeneous materials, homogenization methods, multilevel approach [Jan Zeman]

Fourier transform [Jan Zeman]

Numerical methods for discretization of continuous problems - finite elements, finite differences, boundary elements, Fast Fourier Transform [Bořek Patzák, Jan Zeman FFT]

Optimization problems and methods, their use for model calibration, verification and validation, prediction [Anna Kučerová]

Machine learning and its use in engineering tasks [Anna Kučerová]

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Further information:

https://moodle-vyuka.cvut.cz/course/view.php?id=13574

No time-table has been prepared for this course

The course is a part of the following study plans: