Course details

High Performance Computations

VNV Acad. year 2010/2011 Summer semester 5 credits

Current academic year

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)

Study literature

  • Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II, vol. Stiff And Differential-Algebraic Problems. Springer-Verlag Berlin Heidelberg, 1996.
  • Lecture notes in PDF format
  • 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.
  • Press, W. H.: Numerical recipes : the art of scientific computing, Cambridge University Press, 2007
  • 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

Course inclusion in study plans

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