Questions on the use and creation of meshes including the use of MeshRegion, ElementMesh, and TetGenLink.

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3
votes
2answers
79 views

Assigning Element Markers to 3D FEM Mesh

I have created a 3D graphic using GraphicsComplex and then use ToElementMesh to generate a 3D Mesh that I want to solve a PDE on, but I cannot figure out how to apply ElementMarkers to the Boundaries. ...
1
vote
0answers
33 views

Find best convex approximation of an “almost convex” function

I've got values of a function of two variables at integer points inside a rectangle, that is, a rectangular table $f(i,j)$, $1\leqslant i\leqslant m$, $1\leqslant j\leqslant n$. The function is very ...
8
votes
2answers
118 views

How to assign Element marker at boundary edges

How to assign marker at the boundary edges as 1, 2, 3, 4 respectively and set all of the inside elements of region as 0? for example: Code: ...
7
votes
0answers
78 views

Defining a MeshRegion from a list of points and Polygons with duplicate points does not work in 10.4

Bug introduced in 10.4 and persists through 10.4.1 This code produces a MeshRegion in versions 10.0 through 10.3.1, ...
12
votes
1answer
140 views

How to access FEM shape functions

A couple of days ago I asked here about surface meshes and plotting on surfaces. Now I have another question: How can I access the surface or boundary element shape functions? I would like to ...
4
votes
2answers
108 views

How to create a surface mesh embedded in 3D?

I am working on a problem where I want to optimize current densities on 2D surfaces embedded in 3D to generate magnetic fields. The current density on a surface can be written as a scalar function ...
12
votes
1answer
150 views

RegionNearest and neighborhoods

In this previous question we see that RegionNearest isn't quite as 'capable' as Nearest for some things. Similarly, I need to ...
2
votes
1answer
73 views

Plot a revolution surface, with two cross sections to show its shape

I'm having trouble plotting a revolution surface with intersections. What I have done is shown in the figure, with the help of SphericalPlot3D: . But I can't plot ...
11
votes
2answers
263 views

How to mesh a region using adaptive cubic elements

Assume a list of {x,y,z} coordinates. The coordinates are arranged in a regular fashion through a fixed raster size (called ...
1
vote
0answers
47 views

Handling Self-Intersecting Regions

I am trying to test various parametric regions of a function for membership of the origin (point {0,0}). I generate the boundary by creating four parametric boundary curves, and then use RegionMember ...
1
vote
1answer
51 views

Angles inside of Voronoi mesh cells

How can I determine the angles belonging to the vertices of each interior Voronoi mesh cell? ...
3
votes
2answers
129 views

Connecting the points surrounding the adjacent polygons

I'm trying to connect the points surrounding the adjacent polygons. I know how to find the adjacent polygons on a Voronoi mesh. However, I'm unable to adjacent of the adjacent polygons. What I'm ...
3
votes
4answers
133 views

Invalid region for small angles. To Element Mesh. Finite element method

I would like to mesh the region below in order to use it for a calculation by means of NDSolve. Could anyone help me to discretize this region for NDSolve using. Thank you very much. ...
5
votes
3answers
296 views

Removing cells from Voronoi mesh if they exceed a certain area or circumference

I start with the example in Finding the perimeter, area and number of sides of a Voronoi cell with RunnyKine's answer: ...
0
votes
0answers
25 views

Discretization of a region for NDSolve using [duplicate]

I would like to mesh the region below in order to use it for a calculation by means of NDSolve. Could anyone help me to discretize this region for NDSolve using. Thank you very much. ...
4
votes
2answers
115 views

Color code Voronoi cell areas depending on number of vertices

The following question is similar to Colouring points in a Delaunay Mesh by the number of nearest neighbours ... but I do not know how adapt this answer to my problem. I have the following image: ...
8
votes
2answers
275 views

DelaunayMesh in a specified closed region - creating a concave hull from a set of points

I have a list of discrete points wich I want to use as nodes for creating a 2D mesh. I used DelaunayMesh and it works fine. The problem that I have is that some elements/polygons are outside of the ...
0
votes
0answers
20 views

Is there a extend mesh generation program link with mathematica such as openfoam native blockmesh?

I have read the relative mesh tutorial in mathematica, and found that it mainly focused on finite element method with triangle and tetrahedron, so I wonder if it is possible to link a general extend ...
1
vote
2answers
110 views

Delete/Extract some certain data from a list?

These are some polygons for Voronoi mesh. ...
7
votes
4answers
470 views

Change appearance of ConvexHullMesh

I'm struggling to understand the behaviour of ConvexHullMesh (or rather the non-behaviour). I have a polynom p ...
2
votes
0answers
86 views

ElementMesh (rendering?) issue

The appearance of the following ElementMesh is bad as you can see for example on the inside surface of the shell. The same problem happens converting to a ...
6
votes
0answers
134 views

Possible Bug with Options in DelaunayMesh

Bug introduced in 10.2 and persisting through 10.4 Update: It turns out after some testing, none of the Options work in ...
6
votes
1answer
159 views

Making a 2D hexagonal mesh

There are a lot of answers for how to make a hexagonal mesh on a 3D surface but nothing on how to make a hexagonal mesh on a 2D surface. Can any provide code on how to do so? I am new to mathematica, ...
3
votes
2answers
126 views

How to make the mesh to rotate with a surface in Manipulate?

Here's a Manipulate code to show a particular 3D surface, rotating uniformly in time. The point of this Manipulate box is to show that the surface do indeed rotate like a solid, so I can't "cheat" ...
5
votes
1answer
35 views

How to specify the text size of a vertex index in a 3D mesh using Labeled

My code takes a list of {x, y, z} vertices and displays a convex hull with each vertex labeled by its index in the list. Here is a minimal working example of the ...
2
votes
1answer
126 views

MeshRegion: How to take out a subregion

I have this application at hand: I need to find the Voronoi Regions of a finite set of point and then i have to find the center of mass of each of these Voronoi regions for a given mass distribution. ...
2
votes
1answer
65 views

How to draw the shape of a 2D, 2nd order, element of an ElementMesh

I just want to create a drawing of the shape of 2nd order, two dimensional, finite element like a TriangleElement. Something like ...
3
votes
3answers
199 views

Create graphic object using {x,y} points, and plot a contour over it

I am trying to create a graphics object (polygon built with {x,y} points)so I can plot a contour over it. I would like the coordinates of the contour plot and graphics object be matched (ie, {0,0} in ...
1
vote
1answer
53 views

Different Mesh lines and styles in the same plot

After searching, I learned how to make "GridLines" in DensityPlot by Mesh/MeshFunctions. Here I'd like to draw an addition Mesh line at Q=6^(0.25) via Mesh/MeshFunctions or other ways and highlight ...
11
votes
1answer
193 views

How to enforce a symmetric solution with FEM?

I'm solving the laplace equation in a domain with holes, and I need to compute the integral of the gradient on the boundary of these holes. For that I define a mesh and solve the laplace equation ...
3
votes
1answer
195 views

How to calculate a Delaunay mesh nerve?

How to calculate a Delaunay mesh nerve? A Delaunay mesh nerve is a collection of triangles that surround a single triangle called the nerve nucleus. The triangles in a Delaunay mesh nerve either have ...
4
votes
2answers
109 views

MeshRefinementFunction missing points

I'm doing some FEM on a rectangular region with a spherical cavity: ...
1
vote
2answers
257 views

How to find adjacent polygons of a specific polygon in a VoronoiMesh?

I have developed a code for VoronoiMesh. I am also able to find the polygon with highest number of adjacent polygons. How do I find the indices of the adjacent ...
1
vote
1answer
77 views

change color of the face in a 2D ConvexHullMesh [duplicate]

If I say tri = ConvexHullMesh[{{0, 1}, {1, 1}, {1, 0}}] a triangle is rendered in blue. How can I change that color? An answer to an earlier question suggested ...
3
votes
3answers
221 views

Plot a vector field over a line

This seemingly simple problem is giving me some trouble. I need to plot a vector field on a line, and for that I'm following what I found here. I try to create a mesh that contains two points and just ...
4
votes
3answers
197 views

Colouring points in a Delaunay Mesh by the number of nearest neighbours

I apologise if this is a repeated question, but I've searched for a while and can't find anything. I'm doing some molecular dynamics simulations using Mathematica V10, and I've placed a ...
8
votes
0answers
269 views

How to create an ElementMesh of a Sphere

I want to create an ElementMesh of a "sphere". To reduce the computational effort I want to use HexahedronElement; the ...
6
votes
1answer
111 views

how to create a FEM mesh with “RegionPlot” where the sample points are a function of the position

I need to resolve the diffusion equation in a domain with circular sources (holes). I've tried defining the whole region with holes but the result is very mesh-dependent and not symmetric, so at the ...
6
votes
2answers
99 views

How to scale values for ColorFunction in SliceContourPlot3D?

Trying to help out in the question, Finite Elements 3D, I came across this behavior of SliceContourPlot3D: ...
6
votes
1answer
166 views

Long running ToElementMesh with very “large” domains

This is fixed in version 10.3. I'm trying to solve a system of PDE over a large domain. This doesn't means I need to have a huge amount of mesh points and mesh elements to discretize the domain. ...
9
votes
2answers
384 views

Small circles at mesh nodes

How to show the (16 X 4) mesh intersection points by a tiny red dots? ParametricPlot[v { Cos[u], Sin[u]}, {u, 0, 2 Pi},{v,1,3}, Mesh-> {15,3} ]
8
votes
2answers
649 views

Function Interpolation with Automatic / Algorithmic Values Mesh

I have an underlying function f(x,y,z) that is computationally intensive, but is smooth and continuous. I'm needing to find the function values along a line in xyz. Currently, I'm calculating f at ...
4
votes
2answers
489 views

Different MeshStyle for different functions

By using Plot command I want to get one curve in form if circles and other like a solid line. ...
1
vote
2answers
280 views

Time-dependent mesh deformation

I want to display the result of a deformation with a mesh, but I solved the deformation with a time dependency. So I have two functions: uxsol[t,x,y] and ...
10
votes
2answers
398 views

create an (almost) hexagonal mesh on an ellipsoid

EDIT I edited the question in order to take into @Kuba's comment. I want to create this figure with Mathematica (in particular an almost hexagonal mesh on an ellipsoid; thanks to @Kuba I know this ...
0
votes
0answers
27 views

How can I efficiently select certain mesh elements based on measurement criteria?

I am trying to do some mesh cleaning based on element size, but I'm having a hard time seeing how to best use the MeshRegion data structure to accomplish it without ...
0
votes
0answers
40 views

Ordering of MeshCoordinates in MeshRegion and associated BoundaryMeshRegion

When generating a MeshRegion from a BoundaryMeshRegion and vice versa it would be advantageous if the two types of objects were ...
2
votes
1answer
102 views
8
votes
1answer
150 views

ParametricPlot MeshStyle bug in v10?

Bug introduced in 10.0.1 or earlier and fixed in 10.0.2.0 Original Post The documentation gives the following code and says "Use a red mesh in the x direction and a blue mesh in the y direction:" ...