High Performance Computations
VNV Acad. year 2018/2019 Summer semester 5 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. 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.
Language of instruction
Subject specific learning outcomes and competences
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 competences
Ability to create parallel and quasiparallel computations of large tasks.
To provide overview and basics of practical use of parallel and quasiparallel methods for numerical solutions of sophisticated problems encountered in science and engineering.
- Hairer, E., Norsett, S. P., Wanner, G.: Solving Ordinary Differenatial Equations II. Springer-Verlag Berlin Heidelberg 1996.
- Lecture notes written in PDF format,
- Source codes (TKSL) of all computer laboratories
- 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.
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.
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.
During the semester, there will be evaluated computer laboratories. Any laboratory should be replaced in the final weeks of the semester.
Course inclusion in study plans
- Programme IT-MSC-2, field MBI, MBS, MIS, MMI, MPV, MSK, any year of study, Elective
- Programme IT-MSC-2, field MGM, any year of study, Compulsory-Elective group M
- Programme IT-MSC-2, field MIN, any year of study, Compulsory-Elective group B
- Programme IT-MSC-2, field MMM, any year of study, Compulsory