Course Details for A.Y. 2018/2019

Course Objectives

Skills on numerical methods and numerical algorithms with reference to applications to problems of numerical ODE, linear algebra, solving numerical problems in a supercomputer.

Course Content

• Linux/Unix OS and tools
• HPC architecture
• System Scheduler
• Message Passing Interface
• open MP
• GPU computing
• Applications:Linear algebra, PDE , ODE.
• Basic difference schemes for ODE. The conditions of convergence. Stability and approximation properties of difference schemes.
• Numerical differentiation
• Numerical integration, numerical Fourier trasform
• Difference equations. Stability of solutions
• Boundary value problems and their applications to the calculus of variations

Learning Outcomes (Dublin Descriptors)

On successful completion of this course, the student should

Prerequisites and Learning Activities

Basic calculus of differentials of one and many variables, Integration, Basic facts from the theory of ODE, basic linear algebra, basic algebra (polynomials).

Assessment Methods and Criteria

Students individual research projects and a written theoretical exam.

Textbooks

• E.Isaacson, H.Keller, Analysis of numerical methods , J.Wiley & sons, New York. 1966.    
• A. Quarteroni, R. Sacco, F. Saleri, Matematica Numerica , Springer ­ Collana Unitext. 2000.    
• Rauber, Thomas, Rünger, Gudula, Parallel Programming for Multicore and Cluster Systems , Springer-Verlag. 2013.    

Course page updates

• A.Y. 2016/2017
• A.Y. 2017/2018
• A.Y. 2018/2019
• A.Y. 2019/2020