Faculty of Information Technology, BUT

Course details

Advanced Computer Applications

APP Acad. year 2004/2005 Summer semester 6 credits

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 - an  analysed problem is transformed to a system of differential equations. A new original method based on direct use of Taylor series is used for numerical solution of obtained system of differential equations - extremely exact and fast solution can be obtained. There is the TKSL simulation language with an equation input of the analysed problem ad disposal. A close relationship between equation and block representation is presented. Following technical problems are analysed: large systems of differential equations, algebraic equations, partial differential equations,stiff systems, problems in automatic control, electric circuits, mechanical systems, electrostatic and electromagnetic fields. The course also includes design of special architectures for the numerical solution of differential equations.

Guarantor

Language of instruction

Czech

Completion

Examination (written)

Time span

39 hrs lectures, 26 hrs pc labs

Assessment points

80 exam, 20 half-term test

Department

Lecturer

Instructor

Subject specific learning outcomes and competences

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

Generic learning outcomes and competences

Ability to create parallel and quasiparallel computations of large tasks, including stiff systems detection.

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 kwnowledge and skills

Numerical mathematics and theory of differential equations

Study literature

Lecture notes written in PDF format, source codes (TKSL) 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.
  • 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.

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. Parallel applications of 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 - others, projects and individual work of students

Home assignments for individual students.

Progress assessment

  • Mid-term written examination - 20 point
  • Final written examination - 80 points

Exam prerequisites

Submitting a project for each computer tutorial.
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