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# Questions tagged [mesh-generation]

The generation of a set of interconnected geometric objects that approximate a desired domain or region in euclidean space.

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### (Isoparametric) Mapping of physical coordinates to their equivalent parametric coordinates on a reference element

I have some experiece with finite element methods (FEM), in general. However, I mainly worked with Cartesian grids -- i.e. using orthogonal (non-curved) elements. Recently, I became interested in a ...
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### Finding neighboring cells using Gmsh API

I am creating a simple mesh on a square domain, $[-5,5]\times[-5,5]$ using the following .geo file ...
• 183
1 vote
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### Best way to find the meshing with lowest number of elements allowing a max error of 1%?

So, I have a reference simulation meshing that's 100% reliable but it's costly in terms of time so I'm looking for optimizing it by finding the minimum mesh allowing at most 1% of error with respect ...
104 views

### Generating unstructured finite volume mesh

I want to generate a triangular mesh over a rectangle domain in order to solve Euler equations. Most mesh generator generate a mesh while providing node connectivity for each element. This is ...
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1 vote
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### How to generate mesh for space-time FEM method in FEniCS?

suppose that I have a region called $\Omega$,suppose that this is a 2D or 3D region, how to generate the corresponding space-time mesh by using FEniCS? and how to extract the boundary and implement ...
• 193
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### uniform refinement is not working in gmsh

I get 0 node and elements when I use -refine command line flag in gmsh. Explicitly writing RefineMesh; in the script produces the original mesh and not a refined one. Am I missing something while ...
• 11
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### Gmsh problems in Google Colab, visualize mesh

I'm trying to implement mesh in Google colab from gmesh tutorials. I have an error: Exception: Fltk not available My code is: ...
49 views

### Meshing inconsistency

New to Gmsh. I am trying to create a very simple mesh that is essentially two cylinders merging into one. So I added two parallel cylinders first (a bit farther from each other). Then I extruded (...
68 views

### Algebraic Grid Generation

I am new to the topic " Algebraic Grid Generation". I want to find a simple example where we solve the host equation, let us say the heat equation, numerically in the computational domain ...
140 views

### AMR-Capable meshing software that is not based on quad/octrees

I am looking for AMR/re-meshing software (structured grids would suffice) that is NOT based on quad-octrees, i.e., a fixed refinement rate of 2 but (ideally) something user defined, i.e., ratios of 1....
• 1,093
1 vote
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### Wall refinement of a tetraheadral Complex Geometry using Gmsh without a Geo file

I have an msh file, which is generated from a third party software(Pointwise). The geometry is a complex cylindrical pipe like structure with lot of branches. I need to refine the mesh further only on ...
• 359
1 vote
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### Could you recommend some books on FEM that explain various data-structures in FEM?

I want to understand the data structure of elements, elements around elements, and so on, and various other data structures in FEM, could you please recommend some books?
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### Delaunay-based isosurface extraction vs marching cubes

I recently tried the isosurface extraction algorithm provided by the C++ library CGAL. This is new to me. It is based on Delaunay triangulations. I have some experience with the marching cubes, I ...
182 views

### snappyHexMesh not meshing correct region

I created a simple model of cylindrical container to perform heat transfer simulation using FreeCAD for CAD modelling. I exported the model in stl format along with domain boundaries and faces. I have ...
193 views

### Gmsh Python: Specify mesh regularity conditons

I am using python API of Gmsh to generate a mesh for a rectangular domain. I am really new at this. My code looks like this, ...
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### Choice of grid generation for FDM discretisation methods

I'm currently revisiting some FDM schemes for convection-diffusion equations in 1D, 2D and 3D and getting up to speed with the industry-standard methods again. The application is derivatives pricing, ...
122 views

### Open source implementations of the medial axis transform for vector shapes

Are there any open source implementations of the medial axis transform for vector shapes? I have searched without finding any useful results. It seems that CGAL library doesn't have it implemented nor ...
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1 vote
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### Unreasonably large deviation in calculations of mean curvature in different algorithms

for my work I am currently trying compare the mean curvature of different meshes. I have the following scheme. I have a ground truth mesh and a comparison mesh, which I want to compare it too. I am ...
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### Interpolation of 1D solution from an original grid to a new grid

I have a solution of a 1D wave on a grid (tangent hyperbolic variation) and now I want to interpolate the obtained solution to a new grid with the same number of points as the previous grid but the ...
• 121
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### Node connectivity for regular structured meshes

Consider a regular rectangular 2D $r$-$z$ mesh with constant spacing $\Delta r$ along the $r$-axis with $n$ points and spacing $\Delta z$ along the $z$-axis with $m$ points. I thought it would be a ...
• 111
398 views

### How to create random, unstructured mesh of surface

I am working on a supersonic boundary element method (https://github.com/usuaero/MachLine). In order to test its sensitivity to the boundary discretization, I'd like to be able to create "random&...
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1 vote
152 views

### From 3D to 2D with a STL file

I would like to do a 2D projection from a 3D geometry saved in a stl file and know the distance between the two projected planes. In order to explain better the concept I will start with an almost ...
• 109
1 vote
2k views

### CFD in Python: Mesh Generation

I am trying to set up a 3D CFD scheme for thermal and flow modelling in Python using the finite volume method. The first concern is to build the geometry and an accompanying mesh that is efficient for ...
712 views

### Which algorithms exist to create a tetrahedral volume mesh from an STL file?

Basically just that. I am trying to write a C++ program that reads in an STL and should compute an unstructured tetrahedral volume mesh based on the surface triangulation given by the STL file. I ...
162 views

### Connectivity of octree as grid

What is the algorithm which transforms the octree/quadtree into a grid? i.e, getting the adjacency or connectivity between the cells in order to be able to perform interpolation, gradient,...etc. I am ...
151 views

### Is there any reliable free/open source tool for structured mesh smoothing?

I have been using Pointwise for grid generation and found the quality of smoothed grids to be stunning. I am not aware of any free/open source alteranative that offers the same capabilities for ...
880 views

### Convolute a gaussian kernel with a large array of off-grid centroids without looping? (how to make "A Thousand (Gaussian) Points of Light" )

For a finite object size diffraction simulator, I need to generate arrays which are the sum of thousands of instances of a Gaussian (or other) 2D kernel at centroids that will not fall in any ...
• 1,068
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### Finite Volume on Cubed Sphere

The US weather model uses an uncommon (?) discretization called 'Finite Volume on Cubed Sphere'. To avoid the singularities that occur at the poles when using lat/lon discretization, they instead ...
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### Mesh aspect ratio issue with adaptive mesh refinement (AMR)

I am working on implementation of AMR for my finite volume code. Let me use a 2-D mesh to describe my question. Starting with SINGLE initial cell (let the mesh refine level k = 0) as a root of a quad-...
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### Parametric surface in 3D

I want to create a mesh for a 3D surface with coordinates defined by a parametric function. Is it possible to define this mesh using Gmsh? If it is not possible, what free software do you recommend me?...
• 515
1 vote
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### Renumbering the nodes for quadratic basis functions for a 2D domain

I have a simple triangulation for a 2D domain, described by the connectivity matrix $T$ and by the point matrix $P$. For didactic purposes, I assembled the stiffness matrix for $-\Delta u = f$ by ...
• 405
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### Visualize a mesh from list of 3D point and faces

I have a list of vertices and faces. Now, I want to create a mesh using the given points and faces list and visualize it. Also, I want to play with the mesh by adding an extra point on the faces. Can ...
• 111
1 vote
1k views

### Open-source Hexahedral meshing tools

I'm looking for an open-source automatic meshing tool or library able to generate full or dominant hexahedral mesh starting from a provided arbitrary model i.e. a surface triangular mesh stored in STL ...
• 11
664 views

### Meshing surface of a sphere with a subdomain

I am trying to build a triangle mesh of the surface of a sphere which also includes a subdomain defined by a 'polygon'. Here is a successful example (subdomain defined by the red dots): Note that the ...
54 views

### Hi I am trying to model a 2D Lug angle using Gmsh 4.6. How can I combine transfinite quad and regular full quad meshes in the following geo file?

I need transfinite mesh a small section of the bolt hole to insert a crack. However, The transfinite mesh and regular full quad mesh seem being incompatible and throwing errors. How can I combine ...
365 views

### For traditional FEM and FVM, why can't we use mesh to represent geometry and use the mesh which represent the geometry to do the computation directly?

Isogeometric analysis [1] has the advantage of integrating geometric and mesh models using NURBS or Spline. At the same time, I would like to ask a question to my friends: for traditional FEM and FVM, ...
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### Can the mesh generation methods in FVM and FEM be totally based on the knowledge of the mesh generation theory in computer graphics?

The main references of mesh generation methods in computer graphics (CG) I found are discrete Differential Geometry [1] and a famous book "Polygon Mesh Processing" [2], while the "...
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### Flux sign and face normal confusion in finite volume method

I implemented a solver for the 2D steady-state heat equation (without heat generation and homogeneous material) $\nabla. (k\nabla T) = 0$, using finite volume method, however, I am having some ...
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247 views

### Surface mesh from labeled 3D points

I'm trying to figure out how to create a surface mesh from a set of labeled 3D points. The 3D object could be something like part of a cave system or asteroid where there would be parts of the surface ...
1 vote
109 views

### Partial differential equation FEM application

I have a PDE which looks like Helmholtz wave equation on one dimensional domain. $$\dfrac{d^2u(x)}{dx^2}+\pi^2u(x)=f(x)$$ where $-\infty <x<\infty$ Also, $f(x)= 1$ for $-0.25<x<0.25$, I ...
249 views

### Determining the voxels between two boundary surfaces

Issue description I am working on human brain tACS simulations where I have the models of the skin, skull, csf, brain and ventricles in STL format. The shape does not matter and there are no ...
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112 views

### Mesh partition quality

I am working on static FE mesh partitioning and in order to achieve a good quality partitioning I want to know how to drecrease interprocessor communication by increasing the connectivity of elements ...
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105 views

### Why addCylinder function not respecting the given coordinates?

I tried to generate 3 very simple cylinders, each other connected to it end, however the cylinder get connected to an unexistent point in space as the image shows: It was supposed to each segment be ...
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### Gmsh for .inp file

How do I get an .inp file from Gmsh? I need to create a simple geometry and mesh it and define the boundary conditions in Gmsh and export it as an ...
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### Creating a mesh around an 1-D line to form a 2-D object

Given the following code, how can I perform a mesh generation around the line, to make a 2D form in GMSH API? Extrude or Mirror ...
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1k views

### Minimum number of elements (mesh size) for electromagnetic simulation

Does someone have a reference for the minimum number of elements (or maximum mesh size) for electromagnetic simulations where a mathematical or numerical explanation is given? I have found several ...
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887 views

### What are the alternatives for ABAQUS in generating an *.inp file from a CAD model

ABAQUS gives a .inp file (in pre-processing stage) where the information with regard to the preprocessed model is defined, information such as geometry, mesh type, number of elements, boundary ...
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### Why FVM can handle unstructured meshes while FDM cannot?

How come Finite Volume Method(FVM) handle the unstructured meshes and Finite difference Method cannot, whereas in FVM to approximate the fluxes at the boundary we use the central differencing? My ...
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