Numerical Modelling of Geodynamic Processes
A.Y. 2023/2024
Learning objectives
The course aims to provide the students with the basic tools for numerical modeling of simple geological problems, using, in particular, the finite element method.
Expected learning outcomes
Ability to critically use sophisticated numerical algorithms already implemented.
Ability to independently develop simple numerical algorithms for solving complex problems.
Ability to independently develop simple numerical algorithms for solving complex problems.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
THEORY: Introduction to some methods used for the numerical resolution of geodynamic problems (Finite Difference Method, Finite Volume Method, Spectral Method, Finite Element Method). Properties of Consistency, Stability, Conservation, Limits and Accuracy of a numerical method.
Finite element method: Introduction to discrete systems. Discretization of a continuum into a set of finite elements. Reference to a simple elastic system to introduce the concepts of Nodal Forces, Nodal Displacement, Stiffness Matrix.
Generalization of the Finite Element Method. Shape functions and their properties. Integral form equivalent to a differential equation. Weak Integral Form. Weighted residue method. Galerkin method. Overview of some methods of numerical integration (Quadrature 1D. Newton-Cotes Quadrature. Gaussian Quadrature).
LABORATORY: Elements of programming (Fortran language) aimed at writing a numerical algorithm. Galerkin formulation applied to a specific problem.
Finite element method: Introduction to discrete systems. Discretization of a continuum into a set of finite elements. Reference to a simple elastic system to introduce the concepts of Nodal Forces, Nodal Displacement, Stiffness Matrix.
Generalization of the Finite Element Method. Shape functions and their properties. Integral form equivalent to a differential equation. Weak Integral Form. Weighted residue method. Galerkin method. Overview of some methods of numerical integration (Quadrature 1D. Newton-Cotes Quadrature. Gaussian Quadrature).
LABORATORY: Elements of programming (Fortran language) aimed at writing a numerical algorithm. Galerkin formulation applied to a specific problem.
Prerequisites for admission
Basic knowledge of programming, integral calculus and linear systems.
Teaching methods
Few traditional lessons on the blackboard. Frequent use of PowerPoint projections. For practical lessons, each student will have a computer at disposal to implement, with the support of the teacher, a numerical algorithm for solving a simple problem.
Teaching Resources
After each lesson on theoretical topics, a pdf file, which contains a resume of the issues covered during the lesson, is made available on the teaching web page accessible through the ARIEL portal.
Texts for further information:
Zienkiewich, The Finite Element Methods. Vol. I, any edition.
Some copies of the texts are available in the library of the Department of Earth Sciences "A. Desio".
Texts for further information:
Zienkiewich, The Finite Element Methods. Vol. I, any edition.
Some copies of the texts are available in the library of the Department of Earth Sciences "A. Desio".
Assessment methods and Criteria
The exam consists of a written test that aims to verify the knowledge of the arguments covered during the lessons.
The test lasts 3 hours and consists in a) a series of questions on theoretical topics (an open answer) and b) the modification of the numerical algorithm implemented during the practical lessons and in the discussion of the new results.
The test lasts 3 hours and consists in a) a series of questions on theoretical topics (an open answer) and b) the modification of the numerical algorithm implemented during the practical lessons and in the discussion of the new results.
GEO/10 - SOLID EARTH GEOPHYSICS - University credits: 6
Practicals: 48 hours
Lessons: 16 hours
Lessons: 16 hours
Professor:
Marotta Anna Maria
Educational website(s)
Professor(s)
Reception:
every day, by appointment via e-mail
Office - Botticelli 23 - R054