Questions tagged [finite-element-method]
Tag for the usage of "FiniteElement" Method embedded in NDSolve and implementation of finite element method (fem) in mathematica.
870
questions
0
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0answers
42 views
Solve Partial Differential Equation with Neumann Boundary Condition [closed]
I am trying to solve the heat equation with certain boundary conditions (one-dimensional in space).
I tried it this way:
...
0
votes
0answers
53 views
FindRoot::dfmin: The minimal damping factor of 1/10000 has been reached
I have to solve a highly nonlinear parametric system of three PDEs.
I don't know to which extent the results are trustable. Indeed, the graph shown
by ParametricNDSolve also presents the error message ...
4
votes
1answer
86 views
Export solutions of partial differential equation in mathematica
I have a system of coupled first order partial differential equations. Minimal code is shown below:
...
5
votes
2answers
108 views
Unable to solve nonlinear PDE with NDSolve
Lately, I've been trying to solve the following PDE:
\begin{equation} -v_0 |\nabla F| + {\bf f}\cdot \nabla F +D\nabla^2F = -1
\end{equation}
inside a 2D region between two disks both centered in the ...
4
votes
1answer
63 views
Is it possible to specify a node in ToElementMesh?
I want to make the mesh created by ToElementMesh has a node at my specified position. For example, in the following code, I discretize a disk to element meshes with ...
5
votes
0answers
104 views
AceFEM: Divergence in iterative procedure (Newton-Raphson) for fine meshes
I am trying to model a problem of a nearly incompressible $10~\rm{m} \times 2~\rm{m}$ beam with a uniformly distributed end load. The beam has a Young's modulus of $200~\rm{Pa}$ and a Poisson's ratio ...
6
votes
3answers
399 views
1
vote
1answer
73 views
ParametricRegion
I need to solve a PDE inside a region confined between two waves (as in the figure below). The waves amplitude and period do not matter at the present point (they can be arbitrary) I just need an ...
11
votes
2answers
276 views
Total flux of the gradient of the numerical solution of a PDE through a surface
Trying to solve the following PDE with BC T==1 on a spherical cap of a unit sphere and T==0 at infinity (approximated as ...
0
votes
1answer
58 views
Is it possible that the following pde be NDSolve-d?
I am working on an HJB recently and wish to get a numerical result. Can NDSolve on Mathematica 12.2 handle this?
$$
V_t+(e^{-\sqrt{t}}+0.4e^{-2.5t}+0.01x)V_{x}+1.12e^{-2t}V_{xx}=\frac{1}{2}e^{-3t}\...
4
votes
1answer
179 views
Gradient of the numerical solution of a PDE
Solving the following PDE, defined in the same domain of a previous question:
...
9
votes
1answer
199 views
DirichletCondition doesn't always work with RegionBoundary
I am trying to solve the heat equation on a circle with a square shaped hole in it. It works:
...
2
votes
1answer
96 views
AceFem Error in SMTShowMesh
I consider for a calculation a sphere embedded within a matrix. To plot the results and especially the behavior around the spherical inclusion I want to "cut" through the matrix. That seems ...
5
votes
1answer
124 views
Heat transfer with functions defined on different domains
I'm attempting to model a situation in which a polymer initially at a higher temperature is sandwiched between two cooler metallic mold pieces with conductive boundary conditions in between the ...
3
votes
1answer
127 views
Create a spherical Hex mesh from given surface points
For my calculations I got two spherical meshes. One is a surface mesh of quadrilateral elements and the other is the corresponding "inner" hex mesh. The problem with the meshes is, that the ...
1
vote
3answers
125 views
Interpolating and plotting 3D data
I am having trouble interpolating and plotting a set of 3D data. As it appears I have an unstructured grid, tried Interpolation[data, InterpolationOrder->1] but ...
9
votes
2answers
124 views
Error when using NDSolve for $\epsilon y'' - y' + y^2 = 1$
Error when using NDSolve for $\epsilon y'' - y' + y^2 = 1$ with $0<x<1$ and $y(0) = \frac{1}{3}$, $y(1)=1$
My attempt:
...
1
vote
0answers
33 views
NDEigensystem solutions depend on how many solutions I ask for?
Background
I am using NDEigensystem to solve the following eigenvalue problem:
$$ \left( \begin{matrix} m&-i\partial_x \\ -i\partial_x & -m\end{matrix}\right) \left( \begin{matrix} u_u(x) \\ ...
3
votes
1answer
140 views
Solving sine-Gordon equation with boundary condition
I need to numerically solve the sine-Gordon equation
$$ \partial_{x,x} u(x,t) - \partial_{t,t} u(x,t) - \sin(u(x,t)) -\alpha \partial_t u(x,t) + \gamma =0 $$
for $x\in [0,15]$ and $t\in [0,2]$ with ...
9
votes
3answers
412 views
Laplace's equation in spherical coordinates with Neumann b.c
I am trying to find the temperature field in a semi-infinite solid on whose surface there is an isotherm spherical cap sunken by a length p. For example:
...
5
votes
1answer
162 views
FEM: how to redo a composed boundary mesh for better quality?
Suppose you have region with 2 materials: one embedding material (matrix) containing some particles (...
8
votes
1answer
296 views
FEM: elastic cylinder under circumferential pressure
Suppose you have an elastic cylinder of radius $R$ and height $H$ and you want to solve the mechanical 3D equilibrium with Mathematica's FEM.
How do you impose a pressure $p$ only on the cylinder ...
0
votes
0answers
94 views
How to pose Dirichlet and Neumann BCs on same boundary?
Let' s look on the Laplace equation in a rectangle area:
Eq0 = Inactive[Laplacian][u[x, y], {x, y}]
\[CapitalOmega] = Rectangle[{0, 0}, {2, 1}]
and try to solve it ...
3
votes
1answer
75 views
Mesh with Prescribed Vertices
Mathematica has documentation for triangulating regions bounded by curves using e.g. TriangulateMesh. This is very useful for the work that I (aspire to) do drawing pictures of complicated surfaces ...
9
votes
1answer
386 views
Stokes equations in 2D with traction boundary conditions
This is a follow-up to a previous question (see here). We would like to solve the two-dimensional Stokes equations using the FEM package in Mathematica, when we prescribe traction boundary conditions. ...
2
votes
1answer
208 views
Numerically solving 2 nonlinear PDEs of 2nd and 1st order
I want to compute flux coordinates $\{\psi,\theta,\chi\}$ as functions of cylindrical coordinates $\{r,\theta,z\}$ in the problem of ballooning mode instability in mirror traps (also called open traps)...
1
vote
0answers
48 views
find a weak form to Navier equations [closed]
I want to find a weak form to Navier equations and obtain a solution formulation .
I am interested in solving this problem using a finite element solver for which we need to introduce these equations ...
0
votes
1answer
73 views
Diffusion equation with non uniform diffusion constant
I am trying to numerically solve a 3D diffusion type equation with a spatially varying diffusion $\nabla\cdot(K \nabla T)=\partial T/\partial t$ with K a given function of space with different ...
-2
votes
4answers
269 views
Extrude 3D list with thickness n
I have a 3 dimensional list of points which i would like to extrude in z coordinate with thickness n, i.e. z_{i} -> z_{i}+n for all points in z. There is a similar question concerning 2d list where ...
5
votes
1answer
111 views
Parallel/Multi-thread element code generation using AceGen
I am using AceGen to generate source code for finite element simulations in AceFEM. I have elements with a very large number of vertices/degrees of freedom which can take a very long time to compile.
...
1
vote
2answers
122 views
Print global stiffness matrix in AceFEM
I have a 2D linear elastic simulation in AceFEM and for post-processing purposes I would like to print the global stiffness matrix and global displacement vector.
I am able to get the global x and y ...
1
vote
0answers
76 views
Laplacian and NDSolve and DSolve
I am trying to solve a simple test example using Laplacian. But I step from one problem to the next.
First I did not realized, that MMA uses spherical coordinates ...
2
votes
1answer
52 views
Solution from NDSolveValue contradicts the boundary condition
I have a PDE problem, and here is my code:
...
9
votes
3answers
391 views
Mass Transport Model
I've asked similar questions before about Mathematica's Mass Transport model. My aim is to model these systems and show how they change by manipulating various parameters.
This time it's the following ...
4
votes
2answers
131 views
ImportMesh complains the element mesh has insufficient quality of 0
I'm using ImportMesh in FEMAddOns package. When I imported the following mesh created in Abaqus
the following warning occurred:
ToElementMesh::femimq: The element ...
6
votes
2answers
167 views
2D Chladni patterns realistic animation
My wish is to create a (realistic) animation of the patterns appearing during the Chladni experiment.
I tried something, but it is not continuous because it is based on the eigenmodes, so the ...
3
votes
1answer
86 views
How to display all nodes in the mesh,not just on the border
How to display all nodes in the mesh,not just on the border
...
4
votes
1answer
304 views
Stokes equations in 2D with Neumann conditions
I would like to solve the 2D Stokes equations within a unit disk, say $\Omega$, by using the finite element method (FEM) as it is implemented in NDSolve (by loading ...
0
votes
1answer
83 views
initial condition in finite element method
I want to apply the initial condition below to the linear element
c(x; 0) = sin(10πx); if x in [0; 0:1] and
c(x; 0) = 0; if x in [0:1; 1].
I tried like
...
1
vote
1answer
79 views
This is a shap function generation code and result of quarter singular element mesh. Is it correct？
This is a form function generation code and result of quarter singular element mesh. Is it correct？
...
2
votes
1answer
128 views
How to prevent NDSolve to store result for each time step?
It's very painrful especially using FEM that Mathematica gives a solution for transient Navier-Stokes equation at each time step. Is it possicle to control output? This is my code:
...
4
votes
1answer
122 views
Mass Transfer Value
I'm trying to model the following boundary condition using MassTransferValue.
$$
D_A \frac{\partial[A]} {\partial x} + D_B \frac{\partial[B]} {\partial x}+ D_C \...
2
votes
1answer
75 views
Solving PDE with prescribed rectangular mesh
Question: I want to solve a PDE using NDEigensystem. The region is a rectangle Rectangle[{0,-70}, {20, 70}]. How can I make a ...
11
votes
2answers
462 views
Numerically solving Helmholtz equation in 2D for a Guitar
Hi I am new to using Mathematica, so am not too confident. I am essentially trying to model vibrations of a guitar sound board for a project. It would be great to get some visualisations of the ...
2
votes
1answer
114 views
How to construct quarter point element in finite element [closed]
When calculating the stress intensity factor of a cracked body, singular elements are usually used to divide the region near the crack tip in order to meet the requirement of singularity at the crack ...
3
votes
1answer
82 views
6
votes
1answer
158 views
What does it mean by order -1 of InterpolatingFunction?
Bug introduced in 12.1 or earlier, fixed in 12.2.
In the above code, the InterpolatingFunction object has order -1. In the documentation
https://reference.wolfram.com/language/ref/InterpolationOrder....
0
votes
1answer
58 views
NDEigensystem does not evaluate
I am trying to obtain the eigenvalue of a certain $4\times 4$ matrix differential operator. The region I consider is a rectangle of size $5\times 200$. At left and right side, I applied the periodic ...
4
votes
1answer
76 views
Conceptual question - What FEM does on top of NDSolve, how to use it?
I have few conceptual questions concerning FEM -all are conceptual and their answers might be intertwined hence I ask all in 1 post-:
What FEM does on top of NDSolve?
Because NDSolve already divide ...
1
vote
0answers
47 views
NDSolve with boundary conditions [closed]
I am trying to solve Laplace's equation with a boundary condition. The condition is that there is a box with zero potential on its walls, a 1D plate with potential V at the top of a two dimensional ...
