It is common practice to classify meshes into two main types: structured and unstructured. In Part 3 of the Meshing in FEA blog series we will discuss the advantages and disadvantages of each type and when to use them.
Structured meshes
Structured meshes are meshes with implicit connectivity whose structure allows for easy identification of elements and nodes. Often structured meshes have orthogonal quadrilateral (2D) or hexahedral (3D) elements.
Structured meshes allow programmers to enumerate the nodes in such a way that any adjacent elements or nodes can be called upon without knowing any connectivity information. It is also possible to access coordinates easily because the size of each element does not vary element to element.
Unstructured meshes
Unstructured meshes are meshes with general connectivity (GCON) whose structure is arbitrary and therefore the connectivity of elements must be defined and stored. GCON element types are non-orthogonal, such as triangles (2D) and tetrahedra (3D).
Unstructured meshes require programmers to map more data to each node, such as adjacency lists and coordinate lists.
Structured vs GCON
OnScale primarily uses structured Cartesian meshes because they are ideal for time-domain simulations and are optimal for most applications, but there are also benefits to unstructured meshes.
When to use each mesh typeThere are a couple of questions you should ask yourself when considering what mesh type to use.
- Do you have a complex geometry in which the geometric shape is key to the design?
- Do you have localized regions of your model that require a higher resolution mesh?
If the answer to either of these questions is yes, you may want to consider using an unstructured mesh as the biggest advantage is the ability to conform to any desired geometry with localized resolutions. If you do not require any of this functionality, however, then an unstructured mesh will not be necessary and you can reduce computation time and memory requirement using a structured grid.In summary the best choice of mesh depends on many factors: ease of generation, memory requirements, computation time, numerical accuracy, and suitability for the application.
Structured mesh advantages
- Memory efficient
- Fast to Solve
Unstructured mesh advantages
- Complex geometries easier to mesh
- Arbitrary positions
Structured mesh disadvantages
- Angled and curved geometries are approximated (leads to stair stepping)
Unstructured mesh disadvantages
- Greater memory requirement
- slower to solve
When to use each mesh type
There are a couple of questions you should ask yourself when considering what mesh type to use.
- Do you have a complex geometry in which the geometric shape is key to the design?
- Do you have localized regions of your model that require a higher resolution mesh?
If the answer to either of these questions is yes, you may want to consider using an unstructured mesh as the biggest advantage is the ability to conform to any desired geometry with localized resolutions. If you do not require any of this functionality, however, then an unstructured mesh will not be necessary and you can reduce computation time and memory requirement using a structured grid.
In summary the best choice of mesh depends on many factors: ease of generation, memory requirements, computation time, numerical accuracy, and suitability for the application.
