High Performance Computations
FIT-VNVAcad. year: 2017/2018
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 problem to a system of differential equations. Ability to solve sophisticated systems of differential equations using simulation language TKSL.
Ability to create parallel and quasiparallel computations of large tasks.
There are no prerequisites
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, MATLAB, Simulink) 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
Study evaluation is based on marks obtained for specified items. Minimimum number of marks to pass is 50.
Language of instruction
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 high-order 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.
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
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.
Classification of course in study plans
- Programme IT-MGR-2 Master's
branch MBI , any year of study, summer semester, 5 credits, elective
branch MPV , any year of study, summer semester, 5 credits, elective
branch MGM , any year of study, summer semester, 5 credits, compulsory-optional
branch MSK , any year of study, summer semester, 5 credits, elective
branch MIS , any year of study, summer semester, 5 credits, elective
branch MBS , any year of study, summer semester, 5 credits, elective
branch MIN , any year of study, summer semester, 5 credits, compulsory-optional
branch MMI , any year of study, summer semester, 5 credits, elective
branch MMM , any year of study, summer semester, 5 credits, compulsory