Numerical Modelling of Geodynamic Processes
A.Y. 2024/2025
Learning objectives
The course unit 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 geophysical problems.
Ability to independently develop simple numerical algorithms for solving complex geophysical 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 two tests:
(1) A practical test in the Laboratory (maximum duration 4 hours) during which the student will be asked to modify the numerical algorithm implemented during the lessons and to write a report with discussion of the new results.
(2) An oral test that aims to verify the knowledge of the topics covered during the lessons. Part of the oral test will consist of the discussion of the report produced during the practical test.
Passing the practical test is preparatory to the oral test.
The practical test will take place at least two weeks before the oral test and on a date to be agreed with the teachers responsible for the course.
The oral test will follow the official schedule published on the UNIMI website.
(1) A practical test in the Laboratory (maximum duration 4 hours) during which the student will be asked to modify the numerical algorithm implemented during the lessons and to write a report with discussion of the new results.
(2) An oral test that aims to verify the knowledge of the topics covered during the lessons. Part of the oral test will consist of the discussion of the report produced during the practical test.
Passing the practical test is preparatory to the oral test.
The practical test will take place at least two weeks before the oral test and on a date to be agreed with the teachers responsible for the course.
The oral test will follow the official schedule published on the UNIMI website.
GEO/10 - SOLID EARTH GEOPHYSICS - University credits: 6
Practicals with elements of theory: 36 hours
Lessons: 24 hours
Lessons: 24 hours
Professors:
Marotta Anna Maria, Regorda Alessandro
Educational website(s)
Professor(s)
Reception:
every day, by appointment via e-mail
Office - Botticelli 23 - R054