457-0309/02 – Numerical Methods II (NM2)

Gurantor departmentDepartment of Applied MathematicsCredits6
Subject guarantorprof. RNDr. Radim Blaheta, CSc.Subject version guarantorprof. RNDr. Radim Blaheta, CSc.
Study levelundergraduate or graduateRequirementChoice-compulsory
Year1Semestersummer
Study languageCzech
Year of introduction2003/2004Year of cancellation2009/2010
Intended for the facultiesFEIIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
BLA19 prof. RNDr. Radim Blaheta, CSc.
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 2+2
Part-time Credit and Examination 10+10

Subject aims expressed by acquired skills and competences

The course will introduce students to the basic principles of formulation of boundary and initial value problems and mathematical derivation of the finite element method. An attention is also paid to the computer implementation and analysis of the accuracy of the method. Theoretical foundations provide qualified assessment of the results obtained by the available software tools as well as a further development of the finite element methods.

Teaching methods

Summary

The course deals with a description of the finite element method and its use for solving boundary and initial value problems arising in mathematical modeling of physical processes, such as problems of heat conduction, elasticity etc.

Compulsory literature:

K. Rektorys:. Variational Methods in Mathematics, Science and Engineering, D. Reidel Publ. Comp, NY 1975 C. Johnson: Numerical solution of partial differential equations by the finite element method, Cambridge Univ. Press, 1995

Recommended literature:

Additional study materials

Way of continuous check of knowledge in the course of semester

E-learning

Other requirements

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Přednášky: Matematická formulace okrajových a počátečních úloh popisujících fyzikální procesy. Výhody matematického modelování a správné použití matematických modelů. Matematická formulace v případě 2D a 3D úloh. Variační (slabá) formulace úloh. Energetický funkcionál a energetická formulace. Existence a hladkost řešení. Ritzova - Galerkinova (RG) metoda. Metoda konečných prvků pro 1D úlohy. Metoda konečných prvků pro 2D a 3D úlohy. Počítačová realizace MKP. Technika referenčního prvku. Izoparametrické konečné prvky. Přesnost řešení metodou konečných prvků. Apriorní odhad diskretizační chyby. Aposteriorní odhady. Návrh sítě pro MKP, adaptivní techniky a optimální sítě. Nekonformní a smíšené techniky. Nelineární úlohy. Cvičení: Odvození matematické formulace okrajových a počátečních úloh popisujících různé fyzikální procesy. Variační (slabá) formulace úloh. Využití Ritzovy - Galerkinovy metody. Metoda konečných prvků - elementární formulace. Metoda konečných prvků - algoritmizace. Počítačová realizace, pre a postprocessing. Řešení vybraných úloh a sledování diskretizační chyby. Použití komerčního software. Projekty: Projekty zadávané studentům obsahují sady jednoduchých problémů, jejichž řešení umožní samostatné využití probírané látky. Projekty mohou obsahovat počítačovou realizaci a využití MKP programů.

Conditions for subject completion

Part-time form (validity from: 1960/1961 Summer semester, validity until: 2008/2009 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Exercises evaluation and Examination Credit and Examination 100 (145) 51 3
        Examination Examination 100  0 3
        Exercises evaluation Credit 45  0 3
Mandatory attendence participation:

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Conditions for subject completion and attendance at the exercises within ISP:

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Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2009/2010 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Choice-compulsory study plan
2009/2010 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Choice-compulsory study plan
2008/2009 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Choice-compulsory study plan
2008/2009 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Choice-compulsory study plan
2007/2008 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Choice-compulsory study plan
2007/2008 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Choice-compulsory study plan
2005/2006 (N2646) Information Technology (1103T021) Computational Mathematics P Czech Ostrava 2 Compulsory study plan
2005/2006 (N2646) Information Technology (1103T021) Computational Mathematics K Czech Ostrava 2 Compulsory study plan
2004/2005 (N2646) Information Technology (1103T021) Computational Mathematics P Czech Ostrava 2 Compulsory study plan
2004/2005 (N2646) Information Technology (1103T021) Computational Mathematics K Czech Ostrava 2 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction



2009/2010 Summer