Title:  High Performance Computations 

Code:  VNV 

Ac.Year:  2019/2020 

Sem:  Summer 

Curriculums:  

Language of Instruction:  Czech 

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

Credits:  5 

Completion:  examination (written) 

Type of instruction:  Hour/sem  Lectures  Seminar Exercises  Laboratory Exercises  Computer Exercises  Other 

Hours:  26  0  0  26  0 

 Exams  Tests  Exercises  Laboratories  Other 

Points:  60  20  0  20  0 



Guarantor:  Zbořil František V., doc. Ing., CSc. (DITS) 

Deputy guarantor:  Šátek Václav, Ing., Ph.D. (DITS) 

Lecturer:  Šátek Václav, Ing., Ph.D. (DITS) 
Instructor:  Šátek Václav, Ing., Ph.D. (DITS) Veigend Petr, Ing. (DITS) 

Faculty:  Faculty of Information Technology BUT 

Department:  Department of Intelligent Systems FIT BUT 

Schedule: 

  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 competencies: 

  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.  Generic learning outcomes and competencies: 

  Ability to create parallel and quasiparallel computations of large tasks.  Why is the course taught: 

  Supercomputers are often used to solve large technical and scientific problems. Before writing the first line of code, the user should perfectly understand the problem, that is being solved.
The goal of this course is to familiarize the students with the physics behind the problems, that are often solved in practice. To be able to see connection between the equations that govern the problem (and then solve it using differential calculus) and the real system. The students should also understand the numerical methods that are being used in the often used software packages as "black boxes". To be able to choose a proper numerical method for a specific problem and not just pick one at random.
 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 finite integrals
 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.
 Shampine, L. F.: Numerical Solution of ordinary differential
equations, Chapman and Hall/CRC, 1994
 Strang, G.: Introduction to applied mathematics, WellesleyCambridge
Press, 1986
 Meurant, G.: Computer Solution of Large Linear System, North
Holland, 1999
 Saad, Y.: Iterative methods for sparse linear systems, Society for
Industrial and Applied Mathematics, 2003
 Burden, R. L.: Numerical analysis,
Cengage Learning, 2015
 LeVeque, R. J.: Finite Difference Methods for Ordinary and Partial
Differential Equations: SteadyState and Timedependent Problems (Classics
in Applied Mathematics), 2007
 Strikwerda, J. C.: Finite Difference Schemes and Partial
Differential Equations, Society for Industrial
and Applied Mathematics, 2004
 Golub, G. H.: Matrix computations, Hopkins Uni. Press, 2013
 Duff, I. S.: Direct Methods for Sparse Matrices (Numerical
Mathematics and Scientific Computation), Oxford University Press, 2017
 Corliss, G. F.: Automatic differentiation of algorithms, SpringerVerlag New York Inc., 2002
 Griewank, A.: Evaluating Derivatives: Principles and Techniques of
Algorithmic Differentiation, Society for Industrial and Applied
Mathematics, 2008
 Press, W. H.: Numerical recipes : the art of scientific computing, Cambridge
University Press, 2007
 Study literature: 


 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.
 Butcher, J. C.: Numerical Methods for Ordinary Differential
 Lecture notes written in PDF format,
 Source codes (TKSL) of all computer laboratories
 Controlled instruction: 

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

  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.  
