Questions tagged [finite-element-method]
Tag for the usage of "FiniteElement" Method embedded in NDSolve and implementation of finite element method (fem) in mathematica.
746
questions
2
votes
1answer
50 views
NDEigensystem to solve differential equation
When trying to solve the differential equation
radialEqdouble[k_] = f''[u] + k*u^2*f[u] - u^4*f[u]
where k is a constant, I am able to produce a plot consistent ...
7
votes
3answers
253 views
Identify the Vertices and Lines around the edges of a free surface - Mesh/DiscreteGraphics
To write a mesher that closes a mesh surface using an implied surface from a boundary spline curve and mesh generated using DiscreteGraphics, I need to identify the Vertices and Lines around the edges ...
0
votes
0answers
51 views
InitializeBoundaryConditions::fembdnl: The dependent variable in the boundary condition needs to be linear [duplicate]
Checking the documentation on the error were of not that much help to me. Can someone please suggest how to deal with it?
...
0
votes
0answers
58 views
Closing Boundary Mesh with closed 3D Spline Curve
I am trying to make a 3D solid (with BoundaryMeshRegion) from surfaces created by spline curves.
In the follow simple example, I need to close the ends of this irregular tubular shape using boundaries ...
1
vote
2answers
110 views
Create a “loft” surface from two BSplineCurves?
Is there a way to take two arbitrary BSplineCurves and create a loft surface? I would like to then create a mesh to send to NDSolveValue.
2
votes
1answer
81 views
Create graded mesh
I want to create graded mesh inside a cube, with finer mesh in the left half and a coarser mesh in the right half. My plan was to partition the cube with a 2D plane and then generate boundary mesh ...
2
votes
0answers
134 views
Solving a Modified Biharmonic Equation on a Square
I am seeking to solve the differential equation
\begin{equation}
\left[\partial_{\overline{x}}^{4}+2\left(1+\delta\right)\partial_{\overline{x}}^{2}\partial_{\overline{y}}^{2}+\partial_{\overline{y}}^{...
7
votes
3answers
547 views
Solving heat equation on a cylinder with insulated ends and convective boundary conditions
I am trying to solve heat equation on a cylinder whose ends are thermally insulated and its circular face is exposed to convection. Therefore I have Neumann boundary condition on all faces of the ...
0
votes
1answer
99 views
FEM analyis of flow in a hydrocyclone [closed]
I am interested in solving the flow in a hydrocyclone (steady Navier Stokes equation). I have an STL file of the 3D geometry. My question is how to extract the internal geometry of the hydrocyclone ...
4
votes
2answers
136 views
eigenvalue and eigenfunction of complex euler-bernoulli beam
So I am new to Mathematica and am trying to solve the euler-bernoulli modal equation for a U-shaped Cantilever beam given by equations :-
where i is the index of the region. In total there are 2 ...
6
votes
3answers
327 views
Time dependent Schrödinger equation in 2D
I have the following Schrƶdinger equation in $2D$:
\begin{cases}
\partial_t \Psi(x,t) = V(x,t) \Psi(x,t) \quad x \in [-10,10]^2\\
\Psi(x,0)=\exp( \frac{1}{2} (-x^2+y^2))
\end{cases}
where the ...
5
votes
2answers
178 views
NonLinear system for chemotaxis
I want to solve the chemotaxis mode, given by the next non-linear system:
It is taken from Murray's book: equation (11.30) at pag. 408
$$\frac{\partial n}{\partial t} = D \frac{\partial^2 n}{\partial ...
3
votes
1answer
68 views
Inactive[Grad] is lost when NDSolve parses PDE
I encountered this when trying to solve the PDE mentioned here. I've transformed the equation to the following:
...
0
votes
2answers
77 views
Error when using NDSolveValue. Lists are not the same shape
Please, help me with the following issue.
I am solving the following system of the coupled PDEs
with the following boundary conditions
and initial conditions.
After performing the following ...
1
vote
1answer
89 views
How to solve a 3D permanent conjugate heat transfer problem?
I want to solve this conjugate heat transfer problem on NDSolve but Mathematica always quits the Kernel. Can you help me? I do not know exactly how to use the numerical methods that are NDSolve method ...
4
votes
1answer
121 views
Steady state solution (1D) of nonlinear dispersal equation
Now I'm interested in the equation $$\frac{\partial }{\partial x}\Bigl(\text{sgn}(x) u \Big) +\frac{\partial}{\partial x} \Bigl[ u^2 \frac{\partial u}{\partial x} \Bigr] =0$$ with boundary conditions $...
11
votes
2answers
399 views
Nonlinear dispersal equation modeling insect aggregation
I'm a newbie with Mathematica, I know it's a basic answer, but I can't solve the problem on my own.
I have the following equation reflecting insect aggregation at low population densities (taken from ...
3
votes
1answer
77 views
Shooting Method with extra Unknown Condition
I've been trying to solve a system of 3 coupled 2nd order ODEs, for a real variable $x$, $0\geq x\leq \infty$. The equations are the following:
\begin{align}
&x^{2}\,h''(x) - x\,h'(x) + x^{2}\,g^{...
2
votes
1answer
71 views
Solving the PDE $\partial_t u = \partial_x (u^2 \partial_xu)$
I'm trying to use Mathematica to solve the following equation $$\partial_t u = \partial_x (u^2 \partial_xu)$$ with $$u(0,t)=u(1,t)=0$$ and $$u_0(x)=\sin(\pi x)$$ in order to check a numerical method I ...
0
votes
0answers
79 views
Nonlinear Differential Equation (Nonlinear Helmholtz) - How to solve?
I am relatively new to Mathematica, but I know that it is a powerful tool. I am looking to solve a nonlinear equation that could be seen in nonlinear optics. I have tried in MATLAB, but was struggling ...
2
votes
1answer
92 views
Nonlinear diffusion equation: Periodic boundary conditions not satisfied (BUG?)
it's me again.
Strange stuff to report today. I suspect I've found a bug! Here is the nonlinear diffusion equation direct from the Mathematica documentation for FEM.
...
0
votes
0answers
33 views
NDSOLVE-Error (“For the method \!\(\”IDA\“\), only machine real code is available. ”
I am trying to solve mass transfer equations in an adsorption column to obtain the breakthrough curves. Previously, I asked a question on this and received great help:NDSolve for system of PDEs -Error:...
11
votes
4answers
482 views
3D FEM Vector Potential
I am trying to reproduce an FEM result in a paper. Due to possible copyright I cannot show the result directly but fortunately there is a free link
An Incomplete Gauge for 3D Nodal Finite Element ...
4
votes
1answer
147 views
Solving Helmholtz equation in 3D for torus
How I can solve the Helmholtz equation in 3D domain?
According to the following post, I encounter an error when I run the program.
Any help would be graet!
TOTAL PROGRAM :
This section should be ...
4
votes
1answer
107 views
PeriodicBoundaryConditions: missing points (a simpler example)
EDIT: I reported this to Mathematica support. Will update later.
I just posted on this issue, but I found a more elementary example which I think will make the issue more transparent.
Apparently, ...
0
votes
0answers
47 views
PeriodicBoundaryConditions misses points with coarse mesh?
EDIT: I posted a question that gives a simpler demonstration of this problem.
I'm noticing that some boundary points are "missed" by ...
0
votes
0answers
67 views
solving a 2D eigenvalue problem for a partial differential equation
I'm fairly new to Mathematica and I'm looking for a way to solve a partial differential equation subject to periodic boundary conditions. The form of the equation looks like this:
$\frac{\partial^2}{\...
2
votes
1answer
64 views
Implementation of Dirichlet-Neumann method
I am new in Mathematica and I was trying to find documentation on the Dirichlet-Neumann and Neumann-Neumann methods (which are part of Domain Decomposition Method), but I couldn't find any. Can ...
2
votes
1answer
156 views
How do I apply the biharmonic operator based on the Laplacian?
I want to solve the following equation
Any help would be great.
Definition surface
...
0
votes
0answers
45 views
Magnetostatics analysis of Switched Reluctance Motor in Mathematica
Accidentally stumbled upon magnetostatic calculation in Mathematica.
https://www.wolfram.com/language/12/nonlinear-finite-elements/magnetostatics.html?product=mathematica
I would like to ask a ...
3
votes
2answers
99 views
OpenCascadeLink Viewing and Assigning Element Markers
I recently upgraded to MM 12.1 so I could use OpenCascadeLink for 3D meshing following the excellent answer to a question regarding 3D meshing:
3D Meshing Internal regions
Assigning boundary element ...
6
votes
1answer
158 views
3D FEM Meshing Internal Regions
I am trying to set up a 3D element mesh with intersecting regions having different mesh densities. I am having difficulty setting up the defining boundary meshes from which I will then apply ...
4
votes
1answer
85 views
Different results in DEigensystem compared to NDEigensystem for Laplacian eigenvalue problem (-Īu=Ī»u) on unit square
I want to calculate the solution to the Laplacian eigenvalue problem on the unit square with trivial Dirichlet boundary conditions:
$$- \Delta u(x,y) = \lambda u(x,y) \text{ on } {[0,1]}^2$$
with $u(0,...
7
votes
0answers
99 views
Parsing error [bug?] with systems of nonlinear PDEs, Mathematica 12.0.0
I find the following behavior using 12.0.0. (EDIT: I asked a friend to try it in 12.1.1 and he finds the same result.)
Here is a system of coupled nonlinear PDEs that ...
1
vote
0answers
71 views
NDSolveValue not working correctly
So I am trying to get a good representation of the 2d heat equation with mathematica but it does not seem to work correctly:
...
4
votes
1answer
129 views
Animating the solution to the Insulated 2D Heat equation with inital condition in a rectangular region
I am very new to mathematica and I tried to give my best shot at animating the 2d heat equation with a given initial condition:
...
3
votes
2answers
122 views
Error in definition of PeriodicBoundaryCondition?
The documentation for PeriodicBoundaryCondition (https://reference.wolfram.com/language/ref/PeriodicBoundaryCondition.html) has: Where it says $u ( x_{target} ) = a + b\ u ( f ( x_{target} ) )$, I ...
5
votes
1answer
171 views
Mass Transport FEM Using Quad Mesh
This question is a follow-up to my previous question and an attempt to implement @Tim Laska's excellent approach of setting up an anisotropic quad mesh. I'm solving a similar problem to @Tim Laska's ...
1
vote
0answers
89 views
Why is there no heat being transfered in my program?
I have been working on this code and am new to this coding language. I have been trying to model the transfer of heat through a hot plastic being cooled in a water bath. For some reason I have not ...
4
votes
2answers
277 views
NDSolve with equation system with unknown functions defined on different domains
Based on @xzczd's excellent answer on solving an equation system with unknown functions defined on different domains, I've tried to apply the same technique to a similar system shown below:
Equations:
...
14
votes
4answers
693 views
FEM: Why are the numerical solutions of field equations with D and Inactive[Div] and Inactive[Grad] different?
Suppose you have the DE
$$
\frac{d}{dx} \left(
c(x) \left[\frac{d}{dx}u(x)\right]
\right) + n(x) = 0
$$
and you want to solve for $u(x)$ with some BCs with given $c(x)$ and $n(x)$. I thought that ...
0
votes
1answer
145 views
NDSolve for system of PDEs -Error: fewer dependent variables!
I am trying to solve the equations below to find the breakthrough curve in an adsorption process:
...
2
votes
1answer
91 views
ToElementMesh Error/General meshing strategies
I am trying to create a mesh using ToBoundaryMesh as opposed to DiscretizeRegion. I was hoping this would be a better strategy ...
4
votes
1answer
78 views
Periodic extrapolation out of the domain of the solution of a PDE in two directions
As a prototypic problem
...
asked Jul 25 at 7:07
ĪĪ»ĪĪ¾Ī±Ī½Ī“ĻĪæĻ ĪĪµĪ³Ī³
8,1512 gold badges15 silver badges36 bronze badges
6
votes
1answer
175 views
Improving mesh and NDSolve solution convergence
I have developed the code below to solve two PDEs; first mu[x,y] is solved for, then the results of mu are used to solve for phi[x,y]. The code works and converges on a solution as is, however, I ...
4
votes
1answer
150 views
How to solve the wave velocity in steel
In the simulation of stress wave propagation, I have the following two problems.
First question:
This question comes from page 69 of this book.
The Lame equation for a linear elastic body without ...
5
votes
2answers
243 views
Mesh Generation help
I am having trouble generating a mesh of a rectangle inside another rectangle. I have been following the steps on this article: https://reference.wolfram.com/language/PDEModels/tutorial/HeatTransfer/...
2
votes
3answers
88 views
Using NIntegrate with interpolating function
I am relatively new to Mathematica and have been trying to use the NDEigensystem command to work with some quantum systems. This is actually inline with a previous question I had asked about a week ...
4
votes
1answer
80 views
9
votes
1answer
328 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:
...
