Course details

High Performance Computations

VNV Acad. year 2006/2007 Summer semester 5 credits

Current academic year

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.

Guarantor

Kunovský Jiří, doc. Ing., CSc.

Language of instruction

Czech, English

Completion

Examination

Time span

  • 26 hrs lectures
  • 26 hrs pc labs

Department

Department of Intelligent Systems (UITS)

Subject specific learning outcomes and competences

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

Ability to create parallel and quasiparallel computations of large tasks.

Learning objectives

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

Prerequisite knowledge and skills

There are no prerequisites

Study literature

  • Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II, vol. Stiff And Differential-Algebraic Problems. Springer-Verlag Berlin Heidelberg, 1996.
  • Source codes (TKSL, MATLAB) of all computer laboratories

Fundamental literature

  • 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.
  • Šebesta, V.: Systémy, procesy a signály I. VUTIUM, Brno, 2001.

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 parallel FFT
  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

Progress assessment

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

Controlled instruction

  • Evaluated computer laboratories
  • Mid-term written examination
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