In this lecture, we'll cover the following:

• How to set up and reference the Gmsh library and its Python API.
• How to define geometry using points, lines, loops, and surfaces.
• How to implement a function to generate a finite element mesh for a polygon.
• The difference between transfinite meshing for quadrilaterals and general meshing for arbitrary shapes.
• How to extract and structure mesh data (nodes and elements) for further analysis.

In this lecture, we build our first finite element mesh using Gmsh within a Python environment. We begin by exploring the available documentation and examples, then move on to installing and initialising the Gmsh library. We define a simple rectangular geometry using corner points and develop a reusable function that can accept arbitrary polygonal inputs. The workflow in Gmsh is introduced step by step: adding points, connecting them with lines, forming a curve loop, and finally defining a surface to be meshed.

We then focus on meshing strategies, distinguishing between structured transfinite meshing for quadrilateral domains and a more flexible, option-driven approach for general polygons. We configure meshing algorithms, control mesh density, and discuss practical considerations such as mesh size and computational cost. Finally, we generate the mesh and extract key data - node coordinates and element connectivity, organising it into a structured dictionary suitable for downstream finite element analysis.

Next up

With the mesh generated, the next lecture focuses on building a visualisation function to inspect and verify the mesh.