High Performance Computations (in English)
FIT-VNVeAcad. year: 2019/2020
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.
Learning outcomes of the course unit
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.
Recommended optional programme components
Recommended or required reading
Vitásek, E.: Základy teorie numerických metod pro řešení differenciálních rovnic. Academia, Praha 1994.
Přednášky ve formátu PDF
Zdrojové programy (TKSL) jednotlivých počítačových cvičení.
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.
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Half-term and Final exams.
Language of instruction
To provide overview and basics of practical use of parallel and quasiparallel methods for numerical solutions of sophisticated problems encountered in science and engineering.
Specification of controlled education, way of implementation and compensation for absences
During the semester there will be voluntary computer laboratories. Any laboratory should be replaced in the final weeks of the semester.
Type of course unit
26 hours, optionally
Teacher / Lecturer
- 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 high-order 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.
Exercise in computer lab
26 hours, compulsory
Teacher / Lecturer
- 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
eLearning: currently opened course