Notes on Meshing in COMSOL Multiphysics

Importance of Meshing

• Meshing is crucial for solving problems in COMSOL Multiphysics.
• The finite element method (FEM) discretizes problems into smaller parts called elements.
• Proper meshing leads to accurate and efficient resolution of model geometry.

Key Factors to Consider While Meshing

1. Mesh Sequence Type

   • Options: Automated vs Custom mesh generation.
   • Automated meshes adapt to changes in physics and boundary conditions.

2. Order of Operations

   • Mesh operations are carried out sequentially from the top down in the mesh sequence.

3. Element Types

   • 1D: Intervals
   • 2D: Triangles or quadrilaterals (default: triangular)
   • 3D: Tetrahedra (default), hexahedra, pyramids, prisms.

4. Size and Distribution of Elements

   • Adjust globally using predefined size settings in the mesh node.

5. Element Order

   • Affects solution interpolation between nodes, especially for multiphysics problems.

6. Mesh Quality

   • Important for solver convergence and obtaining accurate approximations.

Creating Meshes

• Automated Mesh Creation: Right-click mesh node in model builder; uses default settings based on included physics.
• Custom Mesh Creation:
  • Edit a physics-controlled mesh or start from scratch.
  • Use options like adding local size sub-nodes, adjusting global size settings, or employing a free triangular mesh.

Example of Editing a Mesh

• Demonstrate customizing the mesh sequence.
• Local size sub nodes can create finer or coarser mesh based on requirement.

Example of Building a Custom Mesh

1. Delete existing mesh sequence.
2. Add a mesh generator node, such as a free triangular mesh.
3. Apply desired settings, adjust number of boundary layers, etc.

Mesh Operations and Sequence

• Each mesh operation can be modified or new sub-nodes can be added.
• Building errors may occur if the order of nodes is incorrectly adjusted.

Element Discretization Order

• Collection of nodes forms elements in the generated mesh.
• Order of discretization affects function interpolating solutions, particularly in multiphysics problems.
• Can be set in the physics settings under the discretization section.

Checking Mesh Quality

• Use manual or automatic mesh refinement studies to verify mesh quality.
• Statistics: Right-click on mesh node for various metrics (e.g. element quality histograms).

Summary of Best Practices

• Start with the most dominant mesh size.
• For complex geometries, apply finer meshes where needed (e.g., solder joints).
• Verify mesh quality and computational efficiency through refinement studies.

Conclusion

• COMSOL provides tools for both automated and manual mesh generation.
• Proper meshing is vital for accurate modeling and simulation results in COMSOL Multiphysics.

Useful Links

• Check COMSOL tutorials on mesh generation methods for further learning.