Lesson 5: Mesh Generation with Gmsh (Part 1: Fundamentals)

Welcome to the exciting world of mesh generation! In this lesson and the next, we'll tackle meshing using Gmsh, a powerful open-source software dedicated to creating high-quality meshes for various scientific simulations, including FDTD in our case.

What is Meshing?

Meshing refers to the process of discretizing your CAD model – essentially, dividing it into smaller, simpler elements. These elements, typically triangles or tetrahedra in 2D and 3D simulations respectively, form the computational grid on which your FDTD code will solve Maxwell's equations.

Why is Meshing Important?

The accuracy and efficiency of your FDTD simulations heavily rely on a well-designed mesh. Here's why:

• Accuracy: A finer mesh with smaller elements captures more geometrical details and leads to more accurate results. However, excessively fine meshes can also increase computational cost.
• Convergence: For reliable solutions, the FDTD code needs to converge – meaning the results become stable as the mesh is refined. A good mesh facilitates convergence.
• Computational Cost: Finer meshes require more computations. Finding the right balance between accuracy and computational efficiency is crucial.

Mesh Elements in Gmsh:

https://gmsh.info/

https://www.youtube.com/playlist?list=PLvkU6i2iQ2frFlpCPgXQO8ReyhNxmwpn_

UPDATE: Here is another interesting video I found: gmsh + python: how to

access mesh information from scripts: https://www.youtube.com/watch?v=cQwYmk3bMSo

Gmsh offers various mesh element types, but for FDTD simulations, we'll primarily focus on:

• 2D Triangles: These are the most common elements for 2D simulations (e.g., waveguides with uniform cross-sections).
• 3D Tetrahedra: These form the building blocks of 3D meshes used for complex geometries like antennas or cavities.

Structured vs. Unstructured Meshes:

Gmsh allows generating both structured and unstructured meshes:

• Structured Meshes: These meshes have a regular, ordered pattern, like a grid of squares or cubes. They are efficient for simple geometries but become cumbersome for complex shapes.
• Unstructured Meshes: These offer more flexibility, allowing for irregular element shapes and adapting to intricate geometries. They are the preferred choice for most FDTD simulations.

Gmsh Interface:

Gmsh has a graphical user interface (GUI) and a command-line interface (CLI). We'll primarily use the GUI for a user-friendly experience:

1. Geometry Definition: You can import your CAD model (e.g., in STEP or IGES format) or directly define simple geometries (points, lines, surfaces) within Gmsh.
2. Meshing Parameters: Here you specify the desired element size (controls mesh fineness) and other meshing options.
3. Mesh Generation: Once parameters are set, Gmsh generates the mesh, which can be visualized and exported for use in your FDTD code.

Next Steps:

In the next lesson (Lesson 6: Mesh Generation with Gmsh – Part 2: Refinement and Advanced Techniques), we'll delve deeper into meshing with Gmsh. We'll explore mesh refinement strategies to improve accuracy in critical regions and discuss advanced techniques for handling complex geometries. Remember, mastering meshing is an essential skill for obtaining reliable results from your FDTD simulations.