Numerical Modelling of Geodynamic Processes and Laboratory
A.Y. 2025/2026
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 simple geological 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
Course syllabus
THEORY: Outline of 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, Boundedness and Accuracy of a numerical method.
Finite Element Method: Introduction to discrete systems. Discretization method of a continuum in 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. Form Functions and their properties. Integral Form equivalent to a differential equation. Weak Integral Form. Weighted Residue Method. Galerkin Method. Outline of some numerical integration methods (1D Quadrature. Newton-Cotes Quadrature. Gauss Quadrature).
LABORATORY: Elements of programming (Fortran language) and writing of a simple finite element numerical algorithm that solves a simple process.
Finite Element Method: Introduction to discrete systems. Discretization method of a continuum in 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. Form Functions and their properties. Integral Form equivalent to a differential equation. Weak Integral Form. Weighted Residue Method. Galerkin Method. Outline of some numerical integration methods (1D Quadrature. Newton-Cotes Quadrature. Gauss Quadrature).
LABORATORY: Elements of programming (Fortran language) and writing of a simple finite element numerical algorithm that solves a simple process.
Prerequisites for admission
Basic knowledge of programming, integral calculus and linear systems.
Teaching methods
The lessons will take place in the Laboratory of Numerical Modeling of Geodynamic Processes. There will be both traditional lessons on the blackboard and lessons through the use of PowerPoint projections.
During the practical laboratory hours, students will have access to a computer where they can implement, with the support of the teacher, a numerical algorithm for the simulation of a simple process.
During the practical laboratory hours, students will have access to a computer where they can implement, with the support of the teacher, a numerical algorithm for the simulation of a simple process.
Teaching Resources
Personal notes of students.
Reference text:
Zienkiewich, The Finite Element Methods. Vol. I, any edition.
Reference text:
Zienkiewich, The Finite Element Methods. Vol. I, any edition.
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: 9
Practicals: 72 hours
Lessons: 24 hours
Lessons: 24 hours
Professors:
Marotta Anna Maria, Regorda Alessandro
Professor(s)
Reception:
every day, by appointment via e-mail
Office - Botticelli 23 - R054