Course detail

High Performance Computations

FIT-VNVAcad. year: 2018/2019

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.

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

Not applicable.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

  • Vitásek, E.: Základy teorie numerických metod pro řešení differenciálních rovnic. Academia, Praha 1994.
  • Přednášky ve formátu PDF
  • Zdrojové programy (TKSL, MATLAB, Simulink) jednotlivých počítačových cvičení.

  • Kunovský, J.: Modern Taylor Series Method, habilitation thesis, VUT Brno, 1995
  • 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.
  • Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Van Nostrand Reinhold, 1993.
  • Angot, A.: Užitá matematika pro elektrotechnické inženýry. Praha, 1971.
  • Vavřín, P.: Teorie automatického řízení I (Lineární spojité a diskrétní systémy). VUT, Brno, 1991.
  • Šebesta, V.: Systémy, procesy a signály I. VUTIUM, Brno, 2001.
  • Eysselt, M.: Logické systémy I. a II. část. Brno, 1990.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

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.

Language of instruction

Czech, English

Work placements

Not applicable.

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.

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

During the semester, there will be evaluated computer laboratories. Any laboratory should be replaced in the final weeks of the semester.

Classification of course in study plans

  • Programme IT-MGR-2 Master's

    branch MBI , any year of study, summer semester, 5 credits, optional
    branch MPV , any year of study, summer semester, 5 credits, optional
    branch MGM , any year of study, summer semester, 5 credits, compulsory-optional
    branch MSK , any year of study, summer semester, 5 credits, optional
    branch MIS , any year of study, summer semester, 5 credits, optional
    branch MBS , any year of study, summer semester, 5 credits, optional
    branch MIN , any year of study, summer semester, 5 credits, compulsory-optional
    branch MMI , any year of study, summer semester, 5 credits, optional
    branch MMM , any year of study, summer semester, 5 credits, compulsory

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

Syllabus


  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.

Exercise in computer lab

26 hours, compulsory

Teacher / Lecturer

Syllabus


  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

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