Title:

Higly Sophisticated Computations

Code:VND
Ac.Year:2003/2004
Term:Summer
Language of Instruction:Czech
Completion:examination (written)
Type of
instruction:
Hour/semLecturesSeminar
Exercises
Laboratory
Exercises
Computer
Exercises
Other
Hours:390000
ExamsTestsExercisesLaboratoriesOther
Points:00000
Guarantor:Kunovský Jiří, doc. Ing., CSc. (DITS)
Lecturer:Kunovský Jiří, doc. Ing., CSc. (DITS)
Faculty:Faculty of Information Technology BUT

Learning objectives:
To provide overview and basics of practical use of selected methods for numerical solutions of differential equations (based on the Taylor Series Method) for extremely exact and fast solutions of sophisticated problems.
Description:
The course is aimed at practical methods of solving problems encountered in science and engineering: large systems of differential equations, algebraic equations, partial differential equations,stiff systems, problems in automatic control, electric circuits, mechanical systems, electrostatic and electromagnetic fields. An original method based on a direct use of Taylor series is used to solve the problems numerically. The course also includes analysis of parallel algorithms and design of special architectures for the numerical solution of differential equations. A special simulation language TKSL is available implemented on one-processor systems (PC486, Pentium) and on multi-processor systems.
Learning outcomes and competences:
Ability to analyse the selected methods for numerical solutions of differential equations (based on the Taylor Series Method) for extremely exact and fast solutions of sophisticated problems.
Syllabus of lectures:

1. Methodology of sequential and parallel computation (feedback stability of parallel computations)
2. Extremely precise solutions of differential equations by the Taylor series method
3. Parallel properties of the Taylor series method
4. Basic programming of specialised parallel problems by methods using the calculus (close relationship of equation and block description)
5. Parallel solutions of ordinary differential equations with constant coefficients
6. Adjunct differential operators and parallel solutions of differential equations with variable coefficients
7. Methods of solution of large systems of algebraic equations by transforming them into ordinary differential equations
8. Parallel applications of the Bairstow method for finding the roots of high-order algebraic equations
9. Fourier series and parallel FFT
10. Simulation of electric circuits
11. Solution of practical problems described by partial differential equations (investigating potentials, weather forecasting models)
12. Library subroutines for precise computations
13. Conception of the elementary processor of a specialised parallel computation system.
Fundamental literature:

1. Hennessy, J. L., Patterson, D.A.: Computer Architecture: a Quantitative Approach, Morgan Kaufmann Publishers, Inc., 1990, San Mateo, California
2. Kunovský, J.: Modern Taylor Series Method, habilitační práce, VUT Brno, 1995