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64 views

Signed cell adjacency matrices (boundary operators)

In How to obtain the cell-adjacency graph of a mesh? there are some great answers that show how to obtain the cell adjacency matrix of a mesh. How would one generalize these to incorporate the ...
135 views

Adjacent faces in a discrete mesh

I have a MeshRegion R and I want to extract all pairs of adjacent faces efficiently. The way that I've been computing this is demonstrated below: ...
349 views

Picking mesh elements that are not on the border of the mesh

As an example, let's say I use a set of random points to create a Voronoi mesh pts = RandomReal[{-1, 1}, {100, 2}]; VoronoiMesh[pts, {-1, 1}] and get something ...
1k views

A geometric multigrid solver for Mathematica?

Cross posted to community.wolfram.com Mathematica ships a variety of linear solvers through the interface LinearSolve[A, b, Method -> method] the most ...
132 views

Add interpolating functions over an unstructured mesh to get a single interpolating function

In a Newton iterative FEM PDE solver I am writing, each iterative step involves updating the current solution function u by adding to it the increment function <...
1k views

How to obtain the cell-adjacency graph of a mesh?

In addition to the accepted answer, see also the answer by Chip Hurst. This functionality is built in, but not documented. Given an arbitrary mesh region, how can I efficiently obtain the graph ...
55 views

Correspondence between points and cell of their VoronoiMesh [duplicate]

It is not unreasonable to expect that the $k^\text{th}$ cell of a VoronoiMesh belongs to the $k^\text{th}$ point passed to it. However, this is not the case: <...
593 views

Improve the mesh smoothing procedure

My question is inspired by this answer about meshing with quadrilateral elements. The following functions are my (naive) try of implementing the Laplacian smoothing. I find interior nodes in the mesh ...