# 470-8743/01 – Mathematical Modelling and FEM (MMMKP)

 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
DOM0015 Ing. Simona Domesová
LUK76 doc. Ing. Dalibor Lukáš, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 3+1
Part-time Credit and Examination 15+5

### Subject aims expressed by acquired skills and competences

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

### Summary

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.

### Compulsory literature:

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

### Recommended literature:

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

### Other requirements

Additional requirements for students are not.

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

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.

### Conditions for subject completion

Full-time form (validity from: 2012/2013 Winter semester)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
Exercises evaluation Credit 30  15
Examination Examination 70  21
Mandatory attendence parzicipation:

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### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType 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

### Occurrence in special blocks

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