Introduction to modeling and simulation

Course guarantor:

Milan Jirásek

Lecturer:

Milan Jirásek

Tutor:

Supervisor:

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.

Requirements:

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

Tensors and tensor operations, tensor notation and its advantages

Description of a continuum under large displacements, Lagrangian and Eulerian approach

Basic concepts of thermodynamics of continuous media

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

Dimensional analysis, similarity, scaling, conversion to dimensionless form, size effect

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 [Václav Nežerka]

Syllabus of tutorials:

Study Objective:

Study materials:

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: