# Tag Info

Accepted

### Algorithm to find boundary faces of mesh

First, create a list of faces in the mesh. From there you should be able to create a map from faces to tets, as each face must belong to either one or two tets. The faces that belong to only one tet ...
• 1,031

### What is a common file/data format for a mesh (for FEM)?

The short answer is no, there is not a standard format. But there are some common ones, like Gmsh for input/output and VTK for output. Before making a decision you need to find out what do you want ...
• 8,524

### Mesh ordering algorithms used by COMSOL Multiphysics

The idea of "ordering the nodes" in a finite element mesh to improve the computational time of the sparse solver originated in the large structural analysis FE codes of the 70's. Those codes typically ...
• 6,144
Accepted

### 3D contour mesh computation

I think you could use the "marching cubes" algorithm. If memory serves, it requires a grid of samples as input, so at the very least you should be able to sample your function and run the algorithm as-...
• 4,936
Accepted

### Is mesh orthogonality important for FEM?

Yes. The constants that appear in the interpolation estimates upon which finite element error estimates are based contain minimum and maximum angles of triangles/tetrahedra (or similar geometric ...
• 55.7k

### How to "smoothen" (not just refine) a 2D/3D polygonal mesh

To complement the two answers from Daniel Shapero and Nicoguaro: Basically, there are two ways of smoothing a mesh, subdivision (generate new vertices) and smoothing (move the points in such a way ...
• 2,315

### Solving PDEs in parallel

Domain decomposition was developed in the late 1990s and early 2000s because it allowed the re-use of sequential PDE solvers: You only have to write a wrapper around it that sends the computed ...
• 55.7k
Accepted

### Unreasonably large deviation in calculations of mean curvature in different algorithms

First of all remember that curvatures, being 2nd order values, can be really sensitive to even very small variations. Moreover, we are speaking about computing differential values in a discrete ...
• 176

### How to "smoothen" (not just refine) a 2D/3D polygonal mesh

As mentioned in the answer by @DanielShapero, you can follow an approach based on local approximations of the curvature for your nodes. In the post he suggest, there is an article by Desbrun. I would ...
• 8,524

### Barycentric interpolation equivalent for irregular hexahedra

A hexahedron with straight edges is the image of the unit cube under a trilinear mapping. So, if you have values on the eight vertices of a hexahedron, and you are asking to interpolate between them ...
• 55.7k

### Commonly-used metrics to quantify the irregularity of a triangular mesh

I do not think that there exists an answer to this question in general, because it all depends on the intended use for the mesh. For instance, if you are doing computational fluid dynamics, you may ...
• 2,315
Accepted

### Commonly-used metrics to quantify the irregularity of a triangular mesh

As @Nicoguaro and @Paul have said in the comments to the question post, there are a great many ways to do this kind of thing, and I'm not sure if there is a single "best" approach. From a review ...
Accepted

• 11.4k

### Effect of mesh size on solution curves for a 1D problem

What you're looking for is an a-posteriori error estimate for your mesh study. Normally, these quantitative measures are line/area/volume- and/or time- averaged nodal or element quantities (e.g. avg. ...
• 570

### What are the best ways to interpolate a vector field inside (convex) polygons?

Let me try and break the problem down into two steps. Step 1: You have a polygon (one cell of your mesh) and you have scalar data $d_i$ associated with each vertex $\mathbf x_i$ of that polygon. You ...
• 55.7k
Accepted

### How to efficiently get mesh cell/face connectivity?

I'm answering this question because it's basic meshing knowledge that should be available and I believe neither answer is satisfactory: @Francler In an unstructured mesh, there is no theoretical ...
• 378

### Elements on a triangle (FEM)

You can rather easily write Lagrange bases over any dimension simplices. Define a $k$-simplex as the convex combinations of $k+1$ points, e.g. a triangle is a $2$-simplex. Definition As a triangle $K$ ...
• 378
Accepted

### How to refine $h$ and $\Delta t$ for convergence tests on evolution PDE

Here are a few solutions that you could explore to determine the orders in space and time. 1) Separate study of time error You can use a given spatial mesh, and perform multiple simulations with finer ...
• 1,943

### What is a common file/data format for a mesh (for FEM)?

The number of file formats for FEM is ridiculous, partly due to the fact that every software package implemented its own format in the past. (From xkcd.) I've created meshio to alleviate the pain of ...
• 3,126

### What is a common file/data format for a mesh (for FEM)?

There is actually a standard for this: ISO/TS 10303 (start with parts 1380 to 1386). Prior to being hijacked by ISO, this initiative, which began back in the 1980s, was known as PDES/STEP. See https:...
• 311

### Getting adjacent cells map for an unstructured polyhedral mesh

Using a hash map adds a log(n) complexity to all accesses (then traversing the whole mesh will cost n log(n) in general), so clearly it is not the best solution. Now your question is how you can ...
• 2,315