Title:  High Performance Computations 

Code:  VNV 

Ac.Year:  2009/2010 

Term:  Summer 

Curriculums:  

Language:  Czech, English 

Private info:  http://www.fit.vutbr.cz/study/courses/VNV/private/ 

Credits:  5 

Completion:  examination (written) 

Type of instruction:  Hour/sem  Lectures  Sem. Exercises  Lab. exercises  Comp. exercises  Other 

Hours:  26  0  0  26  0 

 Examination  Tests  Exercises  Laboratories  Other 

Points:  60  20  0  20  0 



Guarantee:  Kunovský Jiří, doc. Ing., CSc., DITS 

Lecturer:  Kunovský Jiří, doc. Ing., CSc., DITS 
Instructor:  Sehnalová Pavla, Ing., DITS 

Faculty:  Faculty of Information Technology BUT 

Department:  Department of Intelligent Systems FIT BUT 


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. 
Description: 

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. 
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. 
Generic learning outcomes and competences: 

Ability to create parallel and quasiparallel computations of large tasks. 
Syllabus of lectures: 

 Methodology of sequential and parallel computation (feedback stability of parallel computations)
 Extremely precise solutions of differential equations by the Taylor series method
 Parallel properties of the Taylor series method
 Basic programming of specialised parallel problems by methods using the calculus (close relationship of equation and block description)
 Parallel solutions of ordinary differential equations with constant coefficients, library subroutines for precise computations
 Adjunct differential operators and parallel solutions of differential equations with variable coefficients
 Methods of solution of large systems of algebraic equations by transforming them into ordinary differential equations
 The Bairstow method for finding the roots of highorder algebraic equations
 Fourier series and parallel FFT
 Simulation of electric circuits
 Solution of practical problems described by partial differential equations
 Control circuits
 Conception of the elementary processor of a specialised parallel computation system.

Syllabus of computer exercises: 

 Simulation system TKSL
 Exponential functions test examples
 First order homogenous differential equation
 Second order homogenous differential equation
 Time function generation
 Arbitrary variable function generation
 Adjoint differential operators
 Systems of linear algebraic equations
 Electronic circuits modeling
 Heat conduction equation
 Wave equation
 Laplace equation
 Control circuits

Syllabus  others, projects and individual work of students: 

Elaborating of all computer laboratories results. 
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. SpringerVerlag Berlin Heidelberg, 1987.
 Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II, vol. Stiff And DifferentialAlgebraic Problems. SpringerVerlag Berlin Heidelberg, 1996.
 Vlach, J., Singhal, K.: Computer Methods for Circuit Analysis and Design. Van Nostrand Reinhold, 1993.

Study literature: 

 Hairer, E., Norsett, S. P., Wanner, G.: Solving Ordinary Differenatial Equations II. SpringerVerlag Berlin Heidelberg 1996.
 Lecture notes written in PDF format,
 Source codes (TKSL) of all computer laboratories

Progress assessment: 

Exam. 
