Mathematical Modeling in Technical Applications

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Technical Mathematics

Synopsis:

Basic principles of mathematical modeling.

Black box and white box models,

Statistical and deterministic approach, continuous and discrete models, continuum.

Role of theoretical mathematics.

Introduction to finite differences for PDE of 1st and 2nd order, consistency, stability, convergence.

Introduction to finite volumes, basic overview

Introduction to finite elements

Solution of simple problems with an open-source software packages

Postprocessing and visualization (gnuplot, Matlab, …)

Introduction to OpenFOAM software package

Examples of some problems of continuum mechanics

Presentations of individual homework

Requirements:

Syllabus of lectures:

Basic principles of mathematical modeling.

Black box and white box models,

Statistical and deterministic approach, continuous and discrete models, continuum.

Role of theoretical mathematics.

Introduction to finite differences for PDE of 1st and 2nd order, consistency, stability, convergence.

Introduction to finite volumes, basic overview

Introduction to finite elements

Solution of simple problems with an open-source software packages

Postprocessing and visualization (gnuplot, Matlab, …)

Introduction to OpenFOAM software package

Examples of some problems of continuum mechanics

Presentations of individual homework

Syllabus of tutorials:

Study Objective:

Study materials:

LEVEQUE, R J. Finite Difference Methods for Ordinary and Partial Differential Equations. 2008. ISBN 9780898716290

Bhavikatti, S.S.. Finite Element Analysis, New Age International Ltd, 2004. ProQuest Ebook Central, https://ebookcentral.proquest.com/lib/cvut/detail.action?docID=358028.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: