Questions tagged [mesh]

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

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5
votes
0answers
640 views

Region Intersection for MeshRegion objects embedded in 3D

How can I create a logical intersection of MeshRegion objects that are three-dimensional? The RegionIntersection function will ...
4
votes
2answers
438 views

How would I define a region with multiple holes?

I would like to define a region consisting of a polygon with eight holes in it. This is essentially a stamped piece of metal with eight holes. ...
4
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3answers
122 views

Cell-adjacency Graph of a Square Mesh

Consider the list of points pts = {{1, 1}, {1, 2}, {2, 1}, {2, 2}} I want to use them to define a 2x2 square mesh using ...
4
votes
3answers
171 views

Level sets of a parametric plot (3D)

I am having difficulty getting the level sets of a 3D parametric plot. I have a parametrized 3D surface that I suspect is self-intersecting and one way to see this visually is by plotting the level ...
4
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1answer
263 views

NMinimize fails on Mesh?

Context I want to identify the minimum of a solution of a PDE found on a mesh. Problem I do not understand why NMinimize fails on a mesh? As a test case, ...
4
votes
4answers
174 views

Volume of HexahedronElement with non-coplanar faces

Bug fixed in Version 12.0 I would like to calculate the volume of ElementMesh made of HexahedronElement. Even though ...
4
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3answers
1k 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
1answer
626 views

Transforming a region obtained with RegionPlot

I have a region r0, obtained from an interpolated function, with the use of RegionPlot. Let's call this function under the ...
4
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1answer
144 views

Multiple Boundary Conditions for NDSolve in mesh with multiple interfaces

Here is my problem: I want to solve a Laplacian equation in a 2D geometry with multiple interfaces, each interface presenting a different boundary condition. As for an example, I am working on a ring ...
4
votes
2answers
881 views

Generating Meshes with Conforming Boundaries for FEM

I would like to solve a PDE on an annulus with some boundary condition that relates the inner circle to the outer circle. (For example, periodicity along radial lines). If I use a finite element ...
4
votes
1answer
78 views

Find surrounding vertices (simplexes) of a given point for DelaunayMesh

Generating a Delaunay triangulation of some random points: pts = RandomReal[{-1, 1}, {50, 2}]; dm = DelaunayMesh[pts]; HighlightMesh[dm, Style[0, Black]] gives [...
4
votes
3answers
112 views

Forcing at least $n$ spatial steps in solving a 1D spatio-temporal PDE problem with NDSolve

I want to solve the telegraph equation with a spatial discretization forced at 200 points. I tried: ...
4
votes
2answers
302 views

Plot the solution over the deformed mesh

I'm solving a linear elasticity problem and trying to plot a displacement/stress fields over the deformed mesh instead of the undeformed one. The deformed (red) and undeformed (black) meshes look like:...
4
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3answers
1k views

Different MeshStyle for different functions

By using Plot command I want to get one curve in form of circles and other like a solid line. ...
4
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1answer
104 views

How to draw individual mesh lines in ArrayPlot

Consider the following ArrayPlot. ...
4
votes
1answer
65 views

Plotting a vector field embedded in a donut

I have the following code ...
4
votes
2answers
189 views

How to make a frustum of a cone

For finite element purposes I need a frustum of a cone with a finite wall thickness, i.e. a tapered pipe. To make a cone is easy ...
4
votes
1answer
85 views

Color a mesh using `ListDensityPlot`

I have a list of data and I plot using ListDensityPlot: ...
4
votes
1answer
216 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 ...
4
votes
1answer
1k views

Explanation about RegionFunction and MeshFunctions?

In the link, ParametricPlot3D, consider the example(Variation on the Spheres) given in the Neat Examples section. Can someone please explain how ...
4
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1answer
108 views

Adaptive Meshrefinement NDSolve&FiniteElements

In a simple example I try to solve the heat equation using NDSolve and Method->"FiniteElement". I know that NDSolve gives ...
4
votes
1answer
101 views

control FEM grid size for 1D regions

I need to manage the mesh size for finite element method solution to a differential equation, where properties change over two regions. This is for one dimension. I created a boundary mesh of three ...
4
votes
1answer
150 views

MeshRefinementFunction for region gives error

I would like to refine a mesh within a given path/volume, that is specified by the MeshRefinementFunction option given in ToElementMesh[]. For starting i took a simple 3D MeshRegion of a Tetrahedron <...
4
votes
1answer
293 views

Voronoi mesh from non-parametric surfaces for 3D printing

I am trying to make a Voronoi mesh from the Stanford Bunny surface for 3D printing, intended as a test case to make a Voronoi mesh from any arbitrary, non-parametric 3D surface. Related techniques ...
4
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1answer
103 views

mesh element id style

I need help to make the elements id visible in the meshing code ...
4
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1answer
183 views

How to get a larger triangle when we discretize a sphere?

In order to solve this problem,I want to get larger triangles (Of course less amount). But I don't know how to do this. I have tried MaxCellMeasure and ...
4
votes
1answer
98 views

Disassambling a boundary mesh into pieces and building it back again fails. Why?

I have just a misunderstanding of a sort. What I want is (1) to build a boundary mesh, (2) then to disassemble it into a list of the boundary points, and (3) to further assemble it back starting from ...
4
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1answer
62 views

Keep mesh of triangulation under complex valued transformation

I try to make a quick tool for "plotting" complex valued functions. Therefore I generate a Table of complex valued points lying in the complex plane building a ...
4
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1answer
47 views

Extra Lines in 3D ConvexHullMesh

I would like to make a picture of a truncated octahedron using ConvexHullMesh as follows: ...
4
votes
1answer
75 views

Difficulty in specifying mesh refinement

I am trying to give a region within a 3D volume a finer mesh than the rest of the volume. My problem is more complicated but here is a minimum working example. I define a 3D cuboid and try and have a ...
4
votes
1answer
81 views

VoronoiMesh with custom distance function

I'm failing at reading the documentation. Is there a way to specify the distance function used by VoronoiMesh? As a stripped down example say I have a rank-1 lattice such as: ...
4
votes
1answer
96 views

Transforming a 2D Mesh into a 3D object

So I have A 2D Mesh Region, for example ...
4
votes
1answer
334 views

Projecting 3D Mesh Region onto 2D Plane

For vizualization purposes in a beamer presentation I would like to project a 3D MeshRegion like ConvexHullMesh[RandomReal[{-1, 1}, {50, 3}]] onto a 2D plane. How ...
4
votes
1answer
244 views

How to create a neighboring list for a given triangulation and find the triangle and construct the tile?

I am new to Mathematica and I am currently in need of some help with creating a neighboring list of triangles for a given triangulation and finding the path to the triangle containing the random point ...
4
votes
1answer
99 views

duplicated vertices in mesh generation

I want to generate a MeshRegion from ParametricPlot3D, e.g. the hemisphere (the PlotPoint is used to get small numbers of vertices) ...
4
votes
2answers
319 views

Stop ListContourPlot from interpolating beyond the data points

I am using listcontourplot to show my 3D data points but It is interpolating between faraway points and it is changing the outline of the shape. this is what I want to see: and this is what I have: ...
4
votes
1answer
141 views

How can I construct the derivative matrix for an irregular domain?

I wish to construct the derivative matrix corresponding to an irregular set of points. For example, I have the following grid consisting 16 nodes in the 2D plane: ...
4
votes
1answer
147 views

How do I change nodal coordinates in a 2D mesh without changing anything else?

I have a 2D mesh that I generated via ToElementMesh. It discretizes a square domain with a small hole whose shape comes from a parametric B-spline. I now want to ...
4
votes
1answer
333 views

Writing loops for triangle elements

I'm kind of new to using Mathematica, so any help is great. I'm trying to write a program that will create a list or matrix that will give each small triangle's point numbers. For example if given ...
4
votes
1answer
70 views

Make MeshRegion/BoundaryMeshRegion work as a graphics primitive in M11

Mathematica 12 has the nice feature that MeshRegion and BoundaryMeshRegion objects render nicely when included as a primitive in ...
4
votes
1answer
118 views

Error in Mesh Region during concave hull

I have the following data: Data.csv It crates the following image: Im trying to make a concave hull so that I can create an outline of the region. I have tried to use all versions of the ...
4
votes
1answer
106 views

Speedup DiscretizePDE when InitializePDECoefficients contains Interpolation functions

I work on FEM in Mathematica and want to speed up the computation when dealing with very fined mesh (i.e., a huge number of DOF). I found that a very much longer time is consumed when the ...
4
votes
1answer
324 views

Curved mesh boundary from space curve

This is a follow-up question to an earlier question. Question: Given a general space curve xy[t_] = {x[t], y[t]}, how can a region be generated to yield a mesh ...
4
votes
2answers
964 views

Generating mesh from region - possible bug

I want to perform a calculation over a region that is an isosceles triangle with a circular segment attached to the base. The region generalises a circular sector, where the apex of the triangle is ...
4
votes
1answer
207 views

Problem with MeshOrderAlteration to create a 2nd order ElementMesh

After working on this 2D domain, I'm trying to reproduce the same ideas to create a mesh of a sphere composed of QuadElement, instead of more simple and common <...
4
votes
1answer
133 views

BooleanRegion with .stl files does not work

Im trying to use BooleanRegion[] on an .stl file. The imported .stl file is called pores and is of type MeshRegion (...
4
votes
1answer
261 views

Intersection of sphere and region below a plane-DiscretizeRegion was unable to discretize the region ImplicitRegion

I am trying to create a geometric object represented by the intersection of a sphere and the space below a plane using ImplicitRegion. When I use the sphere alone, it works. When I use the plane alone,...
4
votes
1answer
116 views

Finite element mesh coordinate lies outside solution interpolation function

I solve a finite element problem and then want to look at values at mesh nodes for further calculations. Unfortunately the solution interpolation function identifies some mesh coordinates as being ...
4
votes
1answer
134 views

ElementMesh from Tetrahedron subdivision

I would like to create a nice "structured" ElementMesh made of TetrahedronElement by dividing one larger ...
4
votes
2answers
131 views

Count number of connected regions/meshes

I want to count number of connected region. For ex I have a region below which has 2 connected region. And also, How to check whether the function ...