Course detail

High Performance Computations

FIT-VNVAcad. year: 2017/2018

The course is aimed at practical methods of solving sophisticated problems encountered in science and engineering. Serial and parallel computations are compared with respect to a stability of a numerical computation. A special methodology of parallel computations based on differential equations is presented. A new original method based on direct use of Taylor series is used for numerical solution of differential equations. There is the TKSL simulation language with an equation input of the analysed problem at disposal. A close relationship between equation and block representation is presented. The course also includes design of special architectures for the numerical solution of differential equations.

Language of instruction

Czech

Number of ECTS credits

Mode of study

Not applicable.

Guarantor

doc. Ing. Jiří Kunovský, CSc.

Department

Department of Intelligent Systems (UITS)

Learning outcomes of the course unit

Ability to transform a sophisticated technical problem to a system of differential equations. Ability to solve sophisticated systems of differential equations using simulation language TKSL.

Ability to create parallel and quasiparallel computations of large tasks.

Prerequisites

There are no prerequisites

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Study evaluation is based on marks obtained for specified items. Minimimum number of marks to pass is 50.

Course curriculum

    Syllabus of lectures:
    1. Methodology of sequential and parallel computation (feedback stability of parallel computations)
    2. Extremely precise solutions of differential equations by the Taylor series method
    3. Parallel properties of the Taylor series method
    4. Basic programming of specialised parallel problems by methods using the calculus (close relationship of equation and block description)
    5. Parallel solutions of ordinary differential equations with constant coefficients, library subroutines for precise computations
    6. Adjunct differential operators and parallel solutions of differential equations with variable coefficients
    7. Methods of solution of large systems of algebraic equations by transforming them into ordinary differential equations
    8. The Bairstow method for finding the roots of high-order algebraic equations
    9. Fourier series and finite integrals
    10. Simulation of electric circuits
    11. Solution of practical problems described by partial differential equations
    12. Control circuits
    13. Conception of the elementary processor of a specialised parallel computation system.

    Syllabus of computer exercises:
    1. Simulation system TKSL
    2. Exponential functions test examples
    3. First order homogenous differential equation
    4. Second order homogenous differential equation
    5. Time function generation
    6. Arbitrary variable function generation
    7. Adjoint differential operators
    8. Systems of linear algebraic equations
    9. Electronic circuits modeling
    10. Heat conduction equation
    11. Wave equation
    12. Laplace equation
    13. Control circuits

    Syllabus - others, projects and individual work of students:
    Elaborating of all computer laboratories results.

Work placements

Not applicable.

Aims

To provide overview and basics of practical use of parallel and quasiparallel methods for numerical solutions of sophisticated problems encountered in science and engineering.

Specification of controlled education, way of implementation and compensation for absences

Half Term Exam and Term Exam. The minimal number of points which can be obtained from the final exam is 29. Otherwise, no points will be assigned to a student.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Hairer, E., Norsett, S. P., Wanner, G.: Solving Ordinary Differential Equations I, vol. Nonstiff Problems. Springer-Verlag Berlin Heidelberg, 1987.
Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II, vol. Stiff And Differential-Algebraic Problems. Springer-Verlag Berlin Heidelberg, 1996.
Kunovský, J.: Modern Taylor Series Method, habilitation thesis, VUT Brno, 1995
Press, W. H.: Numerical recipes : the art of scientific computing, Cambridge University Press, 2007
Šebesta, V.: Systémy, procesy a signály I. VUTIUM, Brno, 2001.
Vavřín, P.: Teorie automatického řízení I (Lineární spojité a diskrétní systémy). VUT, Brno, 1991. (CS)

Recommended reading

Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II, vol. Stiff And Differential-Algebraic Problems. Springer-Verlag Berlin Heidelberg, 1996. (EN)
Lecture notes in PDF format (EN)
Přednášky ve formátu PDF (CS)
Source codes (TKSL, MATLAB) of all computer laboratories (EN)
Vitásek, E.: Základy teorie numerických metod pro řešení diferenciálních rovnic. Academia, Praha 1994. (CS)
Zdrojové programy (TKSL, MATLAB, Simulink) jednotlivých počítačových cvičení (CS)

Classification of course in study plans

  • Programme IT-MSC-2 Master's

    branch MMI , 0 year of study, summer semester, elective
    branch MBI , 0 year of study, summer semester, elective
    branch MSK , 0 year of study, summer semester, elective
    branch MMM , 0 year of study, summer semester, compulsory
    branch MBS , 0 year of study, summer semester, elective
    branch MPV , 0 year of study, summer semester, elective
    branch MIS , 0 year of study, summer semester, elective
    branch MIN , 0 year of study, summer semester, compulsory-optional
    branch MGM , 0 year of study, summer semester, compulsory-optional