(in Polish) Zaawansowane metody numeryczne: solvery 1000-1S26SOL
Although numerical methods have been an actively developing field for many years, there still remains a significant amount of work to be done. In particular, when it comes to partial differential equations, standard approaches can quickly face numerous barriers, both practical and theoretical.
Our goal will be to familiarize participants with selected methods for the fast/efficient solution of large systems resulting from the discretization of such equations. We will start with classical literature on iterative methods, then move on to advanced topics concerning the theory and practice of domain decomposition methods (with and without overlap), multigrid methods and others, eventually reaching contemporary research topics. If time premits, we will also touch upon issues of computational complexity and implementation on modern supercomputers.
Course coordinators
Prerequisites (description)
Learning outcomes
Student:
- Knows selected methods for solving large systems of algebraic equations resulting from the discretization of partial differential equations.
Knows and can apply space decomposition, domain decomposition, and multigrid method paradigms to derive solvers.
Is able to analyze the properties of the learned methods based on the literature.
Is familiar with current research trends in this field.
Is able to prepare and deliver presentations of varying lengths and levels of generality.
Assessment criteria
Delivery of presentations, active participation and engagement.
Bibliography
- W. Hackbusch "Iterative Solution of Large Sparse Systems of Equations", Springer 2016
- A. Tosselli, O. Widlund "Domain Decomposition Methods - Algorithms and Theory", Springer 2005
- D. Braess "Finite elements. Theory, fast solvers, and applications in solid mechanics", Cambridge 2001
and research/survey papers presented during the course of the seminar.
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes: