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0answers
13 views

Directional/axes errors in structured grid?

Do you know any good article/review out there on the problematics of direction/axis preference coming from structured grid (cartesian ones for example) and depending on the interpolation scheme?
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0answers
25 views

Conceptual question about fitting of scattered data

What are the problems that arise when fitting (2D or 3D) a set of scattered data? (non uniformly distributed) I had some data I had to fit and I solved the problem using the triscatteredinterp() ...
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1answer
30 views

Jacobian matrices on unstructured grids: underlying map?

Suppose I have an unstructured polygonal mesh system like so: Each node $x$ has Cartesian coordinates $(x_1,x_2)$, so for a given node can form matrices like this: $$ J(x,y,z) = ...
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3answers
115 views

Parallel solver for sparse matrices on unstructured grids

I am trying to solve Euler equations on unstructured grids. Consequently, the problem reduces to solving Ax=b where A is a ...
2
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3answers
109 views

Computing the derivative on a mesh

I have a 2-D mesh of triangles and I have a scalar function $f(x,y)$ defined at all the vertices of this mesh. I want to accurately estimate $\frac{\partial f}{\partial x}$ and $\frac{\partial ...
1
vote
1answer
65 views

Number of faces in a 3D multi-type unstructured grid

Given a 3D unstructured grid consisting of mixed types of shapes (hex, tet, ...), is there a method to know how many faces (including boundary faces) are contained in the grid?
2
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1answer
65 views

Mesh with constraints

Is it possible to construct a constrained tetrahedral mesh of a domain using Tetgen or similar software? What I mean by constrained is that there are some nodes or edges that are not free but are ...
2
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2answers
114 views

Is there a bound on the number of edges, facets, and elements in a 3D simplicial mesh in terms of the number of mesh nodes?

I am currently working on a 2D finite element code with a mesh that contains duplicate nodes at certain interfaces where jumps occur. In order to set up the appropriate linear systems, I have to take ...
3
votes
1answer
75 views

How to enforce the boundary conditions

I want to solve a poisson problem on two domains,(interface problem: Let $\Omega $ be a square, $\Omega=\Omega1 \cup \Omega2$ and let $\Omega1$ be a circle inside the square. $\Gamma$ is the boundary ...
3
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1answer
245 views

Is there a mesh generator that will generate zero thickness elements for interfaces?

I have a geometry and a finite element method where there are a couple internal interfaces across which I want to enforce some fairly simple jump conditions. One recommendation I've gotten has been ...
3
votes
1answer
84 views

number of tetrahedra in unstructured mesh when edge length is halved

For a given 3D domain, two unstructured tetrahedral meshes M_1 and M_2 are generated. The average edge length in M_1 is double the average edge length of M_2. Are there estimates on the ratio of the ...
9
votes
3answers
276 views

N-dimensional Delaunay Tesselation Software Libraries

I have a set of known points/nodes irregularly spaced in N-Dimensional space (N>=2), and I would like a way to generate the Delaunay triangulation of these points, and return the corresponding ...
4
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2answers
368 views

First order finite volume spatial discretization of the heat equation on an unstructured triangle mesh

Consider a scalar field $u$ on an unstructured triangle mesh which is constant on each face. Let $A_i$ be the area of triangle $T_i$, $N(i)$ the set of triangles sharing an edge with $T_i$, and ...
2
votes
1answer
88 views

Location of Unknowns in Unstructured Mesh

I am currently learning a code which utilizes Scharfetter-Gummel discretization for unsteady drift-diffusion equations. For this scheme, a 2D unstructured triangular mesh is used, with the unknowns ...
4
votes
1answer
444 views

Grid mapping from an unstructured triangular mesh to a regular rectangular mesh

I am modeling fracture propagation using a 2-D dynamic unstructured grid. As the fracture propagates over time, the elements move accordingly. For a given time step, I would like to interpolate the ...
10
votes
3answers
1k views

Finding which triangles points are in

Suppose I have a 2D mesh consisting of nonoverlapping triangles $\{T_k\}_{k=1}^N$, and a set of points $\{p_i\}_{i=1}^M \subset \cup_{k=1}^N T_K$. What is the best way to determine which triangle each ...
5
votes
1answer
154 views

Largest unstructured mesh problem solved till date

What is the largest problem (in DOF) that has been solved till date using a fully unstructured mesh. I know about PFLOTRAN but I am not sure if it is the largest. If someone can point to relevant ...
8
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2answers
698 views

How to interpolate multipoint data to the cell centres of an unstructured mesh?

I have sets of multipoint field data, each point data set relates to a single cell of an unstructured mesh. The goal is to interpolate the data to the cell centre, directly or indirectly, in the most ...