MathMods :: Joint MSc

Additional Info

• ECTS credits: 6
• University: University of L'Aquila
• Semester: 3
• Objectives:

   

  The aim of the course is the study of analytical, numerical and computational methods (on parallel computing structures), for the solution of partial differential equations considered as basic elements for the construction of mathematical models for natural disasters. During the course will be introduced basic concepts related to the analytical and numerical solution for wave equations, elastodynamics equations and advection-reaction-diffusion systems.
  In addition to the classical analytical and numerical approach, some basic elements for the simulation of the studied problems on parallel computing structures will be introduced, with reference to the programming of Shared Memory, Distributed Memory and/or GPU computing architectures.
  The course activities are consistent with the professional profiles proposed by the Mathematical Engineering master course in relation to the acquisition of programming skills for complex computing structures and the solution of theoretical models.
  
  Learning outcomes
  
  At the end of the course the student should be able to:
  
  1) Know the basic aspects related to the analytical and numerical solutions of the proposed models.
  2) Use parallel computing codes related to the models proposed during the course.
  3) Propose solutions related to problems similar to the models proposed during the course.
  4) Understand technical-scientific texts on related topics.

• Topics:

   

  Main Topics
  Wave equations analytical and numerical methods, elastodynamic equations analytical and numerical methods.
  Diffusion equations analytical and numerical methods.
  Advection-reaction-diffusion systems analytical and numerical methods.
  Introduction to parallel computing architectures:
  Shared memory systems, distributed memory systems and GPU computing.
  Models for performance evaluation Speedup, Efficiency and Amdahl's law.
  Introduction to Linux/Unix operating systems and scheduling for HPC applications.
  Message passing interface (MPI) programming
  MPI basic notions, point-to-point communications, collective communications

• Prerequisites:

   

  Basic knowledge of mathematical analysis, numerical analysis and scientific programming.