Domenico Lahaye
Biography of Domenico Lahaye
University:
TUDelft
Date:
January 2026
Expected Duration:
1–3 Months
Format:
Hybrid
Level:
Advanced
Language of Instruction:
English
Registration Deadline:
TBC
Price:
TBC
Course Overview
1) Block 1 (Week 1 and Week 2):
In this block, the finite difference method for the Poisson equation on the interval (Week 1) and the square (Week 2) will be discussed. The differential equation and the boundary conditions will be discretized on a mesh by a finite difference scheme. This will result in linear equations for the grid unknowns. A stencil notation for these linear equations will be introduced. A linear system will be formed and solved. The discrete solution will be visualized on the mesh. Properties of the discretization method and the linear system will be discussed.
2) Block 2 (Week 3 and Week 4):
In this block, the Galerkin finite element method for the one-dimensional (Week 3) and two-dimensional (Week 4) Poisson problem will be introduced. The problem in so-called strong form will be transformed into the problem in so-called weak or variational form. The problem in weak form will then be discretized in space using Lagrangian basis or shape functions. A linear system represents the Poisson equation on a discrete level will be assembled and solved. The finite difference and finite element solution methods will be compared.
3) Block 3 (Week 5, Week 6 and Week 7):
In this block, the application of the finite element will be extended to treat more complex problems. Partial differential equations for the scalar and vector potential for the magnetic flux or field will be derived from the Maxwell equations. More complex geometries that represent transformers, actuators or rotating extrical machines will be meshed using unstructured triangular meshes. The Maxwell equations will be discretized on these meshes. The discrete linear system will be assembled by a element-by-element procedure and solved. The computed vector potential solution will be processed to compute the magnetic flux and the magnetic field.
Main Goal
The main goal of the course is to apply the finite difference and finite element method to solve boundary value problems on a scale of problems of increasing complexity in electrical engineering applications.
Skills To Be Gained
Gain the skills to apply finite difference and the finite element method in software.
Practical Notes
To be updated
Requirements
- We expect the following prior knowledge 1) linear algebra: concepts of vector, matrix, matrix-vector multiplication, solving linear systems, computing eigenvalues and eigenvectors of a matrix; 2) calculus of functions of single variable: concepts of derivative of a function, finite difference approximation, integral of a function, quadrature, ordinary differential equations; 3) calculus of functions of more variables: concepts of partial derivative of a function, surface and line integral, quadrature, partial differential equations; 4) electric and magnetic fields: concepts of electric field, magnetic field, Maxwell equations, electrical machines and transformers.
Teaching And Assessment
Weekly lectures will be complemented by weekly practical lab sessions and three home work assignments. During the lab sessions, algorithms discussed in the lectures will be implemented, tested and further refined. Each homework assignment will correspond to a course block. The set of three assignment will form a portfolio. During the course, the student will build a portfolio of three home work assignments, each correspond to a block in the course. This portfolio will be assessed during the oral examination. During this examination, the student will be assessed on the theoretical foundation of finite difference and finite element method, on the application of these methods and their implementation in software.
Course Staff
Frequently Asked Questions
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