Thesis
Finite element methods for 2D induction heating problems
- Creator
- Rights statement
- Awarding institution
- University of Strathclyde
- Date of award
- 2026
- Thesis identifier
- T17594
- Person Identifier (Local)
- 202175209
- Qualification Level
- Qualification Name
- Department, School or Faculty
- Abstract
- Numerical modelling of induction heating is a challenge for many reasons. For instance, there are difficulties in defining the functional setting, resolving non-linear material properties, and capturing steep boundary layers. More specifically, for example, in a simplified 2D domain, the variational formulation is not necessarily well-defined due to a term in the heat equation belonging to L1(Ω) only. In this Thesis, we have two main focuses: conducting mathematical analysis on this 2D induction heating problem that deals with the irregular right-hand side, and building code to simulate realistic induction heating processes. In our analysis, by showing that the coupling leads to a right-hand side that is more regular than L1(Ω), we prove existence of solutions in a setup that is more general than the existing literature. Under strict assumptions on the shape of the mesh, we prove convergence of the standard Galerkin finite element method. The main new result we present is a proof of convergence of a recently developed finite element method to a decoupled problem under no assumptions on the mesh. The fact that this method has no conditions on the mesh allows the resolution of boundary layers in more complicated geometries. We also implement the standard finite element method and this new method using the Python software FEniCSx. We study two different 2D models, and show that these codes produce results that are comparable to experimental data, and also improve upon some results from finite element codes used by industry. We conclude by running the model of induction heating over an irregular mesh, and explicitly demonstrate the results we have proven, that the newly developed method is robust over irregular meshes.
- Advisor / supervisor
- Barrenechea, Gabriel R.
- Resource Type
- DOI
- Date Created
- 2025
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