Course Unit

Catalogue

Parallel computing

  • Unit Coordinator: Antonio Cicone
  • ECTS Credits: 3
  • Semester: 2
  • Year: 1
  • Campus: University of L'Aquila
  • Language: English
  • Aims:

    Learning Objectives

    The aim of this course is to provide the student with knowledge of
    Parallel Computing and the ability to analyze theoretical properties and
    design mathematical software for high-performance computation.

    Learning Outcomes

    On successful completion of this module, the student should:
    - have profound knowledge and understanding of the most relevant
    numerical methods for numerical computation and the design of accurate
    and highly performant mathematical software;
    - demonstrate skills in choosing the most suitable numerical method to
    be implemented depending on the problem to be solved. Furthermore,
    they should demonstrate ability in developing mathematical software and
    in providing its theoretical analysis;
    - demonstrate the ability to read and understand other texts on related
    topics.

  • Content:

    NUMERICAL INTEGRATION
    Quadrature Formulae, The Midpoint or Rectangle Formula, The
    Trapezoidal Formula, The Cavalieri-Simpson Formula.
    FOURIER TRANSFORM
    Orthogonal Polynomials in Approximation Theory, Fourier Trigonometric
    Polynomials, The Fast Fourier Transform.
    NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS
    The Cauchy Problem, One-Step Numerical Methods, Analysis of One-Step Methods, The Zero-Stability, Convergence Analysis, The Absolute
    Stability, Difference Equations, Runge-Kutta Methods, Derivation of an
    Explicit RK Method, Systems of ODEs.

  • Pre-requisites:

    Basic Numerical Analysis and Linear Algebra.
    Contents

  • Reading list:

    A. Quarteroni, R. Sacco, F. Saleri, P. Gervasio, Numerical Mathematics,
    Springer (2014).
    The book in pdf is available for all students of the University at
    https://link-springer-com.univaq.clas.cineca.it/book/10.1007/978-0-387-22750-4

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