In this lecture, we'll cover the following:

• Why consistent node ordering is required for finite element analysis.
• Issues arising from direct mesh generation and how subdivision improves mesh quality.
• Strategy for enforcing counterclockwise node ordering.
• Identifying the top-right node using geometric reasoning and tolerances.
• Implementing an automated node reordering function.

In this lecture, we focus on ensuring that the nodes defining each element are ordered in a way that is compatible with our finite element code, specifically counterclockwise starting from the upper right node. We begin by revisiting the meshing process and highlighting how directly targeting a fine mesh size can introduce irregular regions. To address this, we instead generate a coarser mesh and subdivide it, which produces a more uniform mesh.

We then develop a function to systematically reorder element nodes. We compute each element’s centroid, determine the angle to each node, and sort these angles to guarantee a counterclockwise arrangement. From there, we identify the upper right node by considering both the maximum y-coordinate and a tolerance to handle floating-point inconsistencies, followed by a tie-break using the x-coordinate. Finally, we rotate the node ordering so that this upper right node appears first. This ensures that all elements conform to the expected format and can be reliably used within the finite element solver.

Next up

Next, we will extend the meshing capabilities by implementing openings (holes) within the mesh.