HPC Computational Methods

Entry requirements:

Credits: 4

Course: Core

Language of the course: English

Lecturer

Andrew Svitenkov

Objectives

  • Acquaintance with advanced methods of solution of SLAE
  • Acquaintance with advanced methods of solution nonlinear problems
  • Learning of basic tools of investigation of convergence and stability of iterative procedures
  • Understanding of relation between typical computational problems and common models of mathematical physics
  • Understanding of models of parallel performance
  • Programming with OpenFoam 

Contents

Various domain-driven problems have the same mathematical formulation on the level of computational method. If problem is linear we solve a SLAE, if it is nonlinear we make it linear and solve a SLAE again. Typically studied Gaussian elimination method is extremely ineffective and more advanced solution computational methods are considered during the course.

During classes students will grasp the relation between parameters of domain-driven problem and computational complexity of final algebraic problem. Basic mathematical tools for convergence analysis of iterative procedures will be considered. OpenFoam software package will be introduced like convenient tool for programming of computational schemes for linear and nonlinear algebraic problems. 

Format

Lectures, master classes, lab works.

Assessment

Attendance is arbitrary.

Grading: 20% participation in class discussions, 20% lab work, 60% final exam. Defense of lab work is mandatory for admission to the exam.