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Results tagged with finite-element-method
Search options questions only
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user 36260
Usage of the Finite Element Method embedded in NDSolve and details on the implementation of the fem in mathematica.
6
votes
1
answer
239
views
How can I create higher order triangle elements when using NDSolve`FEM?
I'm using the Finite Element Method to solve an elasticity problem and i need to use a more precise element such as a nine node triangle. For my surprise when I run the code :
Needs["NDSolve`FEM`"]
m …
- 2,964
5
votes
2
answers
1k
views
How to get the node id in a specific coordinate in a finite element mesh?
The following code generates a finite element mesh.
Needs["NDSolve`FEM`"]
order = 2;
mesh = ToElementMesh[ImplicitRegion[300 < Sqrt[x x + y y], {x, y}], {{0, 1000}, {0, 1000}}, MaxCellMeasure -> 2000 …
- 2,964
4
votes
1
answer
189
views
Refinement problems
I have a hole in an infinite plate and a code that generates a finite element mesh of it. I need more elements concentrated near the hole, because the solution varies more at this region. The issue he …
- 2,964
3
votes
5
answers
335
views
Adapt a 9-node element routine to a 8-node
The function GenerateGridMesh[a_, b_, nx_, ny_] creates a grid of 9-node finite elements mesh. I need some help to adapt this routine to create 8 node element mesh. This function has as input data the …
- 2,964
4
votes
1
answer
548
views
Finite Elements 3D
Does anyone knows how to solve the Laplace equation in a Sphere domain and with the following boundary conditions:
Consider alpha=0.
I have tryed the following code, but i don't belive the boundary …
- 2,964
8
votes
3
answers
603
views
How to find ids in a curved line in a finite element mesh?
Previous discussion about this problem has already occurred in this link:
How to get the node id in a specific coordinate in a finite element mesh?
I have the following code that generates a finite …
- 2,964
5
votes
1
answer
176
views
How to generate a GraphicsComplex using a quadratic approximation function?
The code below illustrates a finite element mesh composed by quadratic 9-node elemets. I'm using the GraphicsComplex and Polygon to plot the mesh, and I get a linear interpolation (see the figure). Ho …
- 2,964
4
votes
2
answers
289
views
Refine a quadrilateral mesh
I have created the following mesh for a slope stability problem:
<< NDSolve`FEM`
coordinates = {{0., 0.}, {75, 0}, {75, 30}, {45, 30}, {35, 40}, {0,
40}, {14, 14}, {60, 14}, {26, 26}, {47 …
- 2,964
33
votes
7
answers
5k
views
How to generate a mesh with quadrilateral elements?
I have the following code that generates a finite element mesh:
Needs["NDSolve`FEM`"]
order = 2;
mesh = ToElementMesh[
DiscretizeGraphics[
GraphicsComplex[{{0, 4}, {5, 4}, {5, 0}, {8, 0}, {8, 8 …
- 2,964
8
votes
1
answer
257
views
Performance improvement: Finite Element Mesh graphics
I have created a Finite Elements mesh on GID (quadrilateral 9 nodes elements). I exported the nodes and the elements topology and i'm reading it from the following two text files:
https://www.dropbox …
- 2,964
9
votes
1
answer
665
views
Help to create a 2D mesh generator (FEM)
I'm working in a finite element mesh generator. I built this function which generates an 8 node mesh (polynomials of order 2) without any interior node:
(*Generate Grid Mesh of dimensions axb with …
- 2,964
1
vote
1
answer
135
views
Transient darcy flow equation
I can solve the following stationary Darcy problem:
$div(\nabla u)=1$
with
$ u = 0 \in \Gamma_d$
<< NDSolve`FEM`
x0 = 40;
y0 = 30;
r = 30;
p = Polygon[{{0, 0}, {75, 0}, {75, 30}, {45, 30}, {35, 40}, …
- 2,964
2
votes
2
answers
144
views
How to interpolate and visualize a finite element integration point solution
I can intepolate the nodal solution using the function ufun = ElementMeshInterpolation[{mesh}, nodalsol] and visualize the nodal solution with the function SliceContourPlot3D[ufun[x, y, z], MeshRegion …
- 2,964
4
votes
2
answers
210
views
Solve Richards equation for unsaturated soils with FEM (`NDSolveValue`)
I am attempting to solve the nonlinear Richards equation for the dependent variable $\Psi(t,x,y)$. The equation is as follows:
$\frac{\partial\theta(\Psi)}{\partial t}=\nabla. (k(\Psi)\nabla(\Psi + y) …
- 2,964