High-Performance Computing and High-Load Systems

Entry requirements: Basics of mathematics, natural sciences and socio-economics. Analytical skills.

Credits: 3

Course: Core

Language of the course: Russian

Objectives

  • Introduction to effective methods of solving systems of linear equations;
  • Introduction to effective methods of solving non-linear algebraic problems (optimization, non-linear equation solutions);
  • Basic methods of studying convergence and stability of iterative procedures.
  • Understanding of correlation between typical computational problems and basic models in mathematical physics;
  • Understanding of parallel productivity models;
  • OpenFOAM programming.

Students will learn:

  • To expertly use state-of-the-art professional equipment
  • To develop logic of reasoning and prepositions based on interpretation of data integrated from various fields of science and engineering
  • To master means and methods of retrieving, storing, processing and translating information with the use of state-of-the-art computer technologies, such as in global computer networks
  • To analyze professional information, to execute and present analytical reviews with well-founded conclusions and recommendations

Contents

The course structure consists of four big sections:

– Matrix and solutions of systems of linear equations
– Non-linear problems
– Linear functional operators
– Numerical solutions of partial differential equations and OpenFOAM application package

Solving many subject-oriented problems at the computational level frequently comes down to several typical problem settings. Here systems of linear equations hold a special place and are an integral part of numerical modelling based on equations of mathematical physics. Previously studied Gauss method for solving systems of linear equations is computationally ineffective, while this course studies superior methods for solving systems of linear equations.

This course covers the link between the parameters of the original subject-oriented problem and the mathematical model, and the resulting computational complexity of a corresponding algebraic problem; basic mathematical methods of studying convergence of iterative procedures. The OpenFoam program package is suggested as a superior tool for programming computational methods of solving linear and non-linear equations.

Format

Lectures and labs

Assessment

Attendance is mandatory. The final grade is based on the student performance throughout the course.