Questions tagged [finite-element-method]
Usage of the Finite Element Method embedded in NDSolve and details on the implementation of the fem in mathematica.
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Why does NDSolve solution not match physical intuition?
Related to a previous question I posted, I am trying to solve for the electric potential on a box which obeys Ohm's law:
\begin{equation}\nabla\cdot(\overset{\scriptscriptstyle\leftrightarrow}{\sigma}...
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How to calculate a numerical Fourier transform obtained from NDSolve?
We numerically solve for the electric potential on a box which obeys Ohm's law:
\begin{equation}\nabla\cdot(\overset{\scriptscriptstyle\leftrightarrow}{\sigma} \nabla \Phi) = 0, \label{Eqn:OhmsLaw}\...
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Normalization of solution of a PDE
I am trying to solve the following PDE:
pde = D[P[x, t], t] + D[J[x, t], x] == 0;
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Area, perimeter and other geometric parameters of a "cucumber"
From the simulation, I have got a region with a shape of a cucumber. Here are the boundary points of this region:
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How to solve system of PDEs (e.g. Navier-Stokes)
I need to solve system of PDEs.
The system of PDEs:
Boundary and initial conditions:
.
I used NDSolve but have some troubles (code below):
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Why does NDEigensystem not show the minimum eigenvalue for a certain parameter range in the cylindrical coordinate system?
In my previous question Why NDEigensystem does not show the minimum eigenvalue?, I asked why the NDEigensystem does not show the minimum eigenvalue for the ...
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FEM stress analysis by considering bending moment
I found an example of using FEM for stress analysis in the forum, the code provided by @user21, which is very friendly for beginners.
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Why NDEigensystem does not show the minimum eigenvalue?
I would like to find eigenvalues and eigenfunctions using NDEigensystem. The following system is considered: $$H[u(\rho,z)]=-\frac{1}{2}\Delta u(\rho,z)+Vu(\rho,z)$$...
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How to install AceFEM in MacOS?
I downloaded the Evaluation/student version and ran Install.nb according to the official installation instructions^1, it returned some errors as follows.
Cannot load installation package. Problematic ...
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Plotting InterpolatingFunction of a solution of Fokker-Planck equation
I want the 3D surface plot of -Log[sol[x,y,8]] but I can't handle the InterpolatingFunction error. Please help me in extracting the function.
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Meshing problem using OpenCascadeLink
I have encountered a meshing problem and I am a bit stuck with it. I tried to replicate the problem while removing most of the original code to be more concise.
I am using OpenCascadeLink to perform ...
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Solving 3D heat equation with an off-center boundary condition
So i have this code (albeit a simplified version but it'll do for this question)which solves a time dependant 3D heat equation on a cylinder.
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SMSDo Error when try to use counter variable i as vector index in loop
I try to evaluate the following code, but I get
"Error during numerical evaluation of expression with random numbers."
Expression contains parts that canot be evaluated.
Messages: ...
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Solid Mechanics FEM Simulation with Different Material Properties
How would I assign different material properties to the "bar" and "support"? Meaning, for example, the bar would be assigned the properties of single-crystal Copper and the support ...
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Displaying NDEigensystem Results
I want to display a collection of deformed meshes in a GraphicsGrid where the surface colors are proportional to the displacement.
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2D transient heat equation solution
I want to calculate the time- and space- dependent temperature of a 2D system where there are 3 materials, with different thermal properties.
The system can be described by the schematics:
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How to extract particle velocity from acoustic pressure in an adjustable region?
I have set up an adjustable region in which to compute acoustic pressure, and would like to also know the particle velocity components, which are related to the gradient of the pressure. But I cannot ...
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Why are my AceGen results not matching with the commercial FE software?
I conducted a linear FE analysis of a 3D cantilever beam using AceGen/Acefem and Ansys. I find that results are a little bit off from the ansys results. For e.g., the deflection reported at the ...
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Setting up a strategy delivering a smooth heat transfer solution
I have a polymeric film that undergoes a two-step cooling process. First, it spends time1 in air. Then it comes in contact with a piece of steel at a temperature <...
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How to model partial wavefunction collapse when part of a wavefunction hits a barrier?
This code models a complex Gaussian wavefunction expanding from the origin, part of which hits a barrier at x=10, Abs[y]<15. The code shows the wavefunction reflecting off the barrier, which is ...
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Mathematica can't communicate with subkernels
i was working some huge matrices in the context of FEM, so sometimes it seems they were too big and the kernel crashed. Normally that isn't a problem, but after one time i couldn't connect to the ...
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A Problem from Helmholtz Resonator Tutorial
To learn the methods used in the Helmholtz Resonator tutorial, I cut and pasted all the tutorial lines into a version 13.0 notebook, with a few comment lines to track with the tutorial discussion.
The ...
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Where to find SolidMechanicsExtendedStrain and SolidMechanicsExtendedStress?
The introduction to solid mechanics from Wolfram:
https://reference.wolfram.com/language/PDEModels/tutorial/StructuralMechanics/SolidMechanics.html#775646651
mentions two functions:
PDEModels`...
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StreamPlot - streamlines are outside the plotting domain
I am trying to plot some streamlines, where the domain is given by a mesh. The results are good, but sometimes there are streamlines, that do not end at the boundary of the domain and are plotted a ...
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Solving Helmholtz Equation in 2D for Circular Disk with DEigensystem, NDEigensystem
I would like to solve the Helmholtz equation with Dirichlet boundary conditions in two dimensions for a circular disk with a radius of 1.
$\Omega =$ some boundary e.g. a circle
$
\nabla^2 u(x,y) + k^...
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Flipping triangles in a triangulated MeshRegion surface
Given a triangulated MeshRegion surface consisting of over 3000 triangles, with flipped faces, can I easily and automatically flip those triangles using Mathematica?
For some unknown reason the ...
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Question regarding initial guesses for Newton's method in AceGen/ AceFEM
I am trying to solve a system of equations with the command SMTNewtonIteration[]. This method needs initial guesses for the degrees of freedom I am looking for. Is ...
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FEM Capacitor Not Converging with Parallel Plate Model
I am trying to model a 3D electrostatics finite element model of a capacitor to see if I can accurately model the behavior of a parallel plate capacitor before I alter the geometry of the electrodes ...
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NDSolve and Non Linear Schrödinger Equation
I tried to solve the problem
$$iu_t+vu_{xx}+|u|^2u=0$$
Initial condition : $$u(x,0)=\sqrt{2} sech{(x+10)}e^{ix}+\sqrt{2}sech(x-10)e^{-ix}$$
BC: $$u(-50,t)=u(50,t),\quad \partial_xu(-50,t)=\partial_xu(...
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Meaning of divergence message?
I am using the command SMTNewtonIteration[] to solve a boundary value problem in AceFEM and get the following error message:
What does this message mean exactly? ...
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Infinite expresssion 1/0 encountered when use NDSolve for 3D axisymmetric Navier-Stokes (Euler) equations
The PDEs we are interested in solving using NDSolve is the vorticity-stream formulation of the 3D axisymmetric Navier-Stokes (Euler) equations (Ref.1 :T. Y. Hou, Potential singularity of the 3D Euler ...
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Integrating over an ElementMarker area in FEM
I'd like to know if there is a way to integrate an interpolating function obtained by solving a PDE in the FEM framework over a region with an ElementMarker assigned to it? I'm not sure if I'm clear ...
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PDE Problem: NDsolve give the results inconsistent with the initial state [duplicate]
We are solving the non-linear PDE, like this
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AceGen/AceFEM: Divergence in a term, that should be equal to zero
I have a problem concerning the order of the evaluation of the AceFEM parameters.
My AceGen Element contains, among many others, an expression of the form
B (aa - bb/(cc Exp[dd w^2] + ff))
with B, aa, ...
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How to plot the region with LineElement when the element number increases?
I want to plot the square wave region for FEM solver, and when the tooth number of the square region is 3, then the total coordinates is 12, when the tooth number of the square region is ...
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Alternative Material Models for Finite Element
The Solid Mechanics capabilities of Mathematica make it an interesting alternative to using other software especially when considering multi-physics problems. I would like to collect here (for the ...
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Is there any documentation for vibration and solid mechanics research via Mathematica? [closed]
I am interested in the solid mechanics (elastic mechanics and structural mechanics, etc.), and vibration, is there any material or documentation in this aspect via FEM in Mathematica?
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Nonphysical results with NDSolve for two coupled nonlinear ODEs
I have a thermal problem, where I have two long strips of metal connected to each other by a dielectric along their length(sketch attached). The lower strip has its temperature defined at each end. ...
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How to plot the derivative after indicating the value?
I have used the FEM tool to solve this PDE system with control equation and boundary conditions, after calculation the ufun1[x, y] are calculated, and I want the ...
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Invalid PeriodicBoundaryCondition for Navier Stokes problem using NDSolveValue
Background: I'm looking to have a 2D re-entrant channel of a geophysical flow that is forced by a wind stress at the surface ("taux"; below) and experiences planetary rotation ("cor&...
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Integrate doesn't give a result for non-linear functions
I use Acegen for Finitie Element formulation that gives out residuals and tangents by taking in the field values as inputs. For this in my residual formulation I need to integrate a nonlinear term ...
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Solving partial differential equation: boundary problem
Here we are solving a set of non-linear equations. And the parameters are
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Setting up a PDE for a time-independent Schrödinger equation
I am trying to solve a 2d Schrödinger equation with a non-separable potential because I want to calculate the probability of reflection for different angles of incidence of a plane wave.
Here I ...
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How to unite the region of ParametricPlot and set up the mesh for FEM?
I have used the ParametricPlot to plot the sector of the disk and use Show to combine them in one picture, however it cannot be ...
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How to extract gauss coordinates in AceGen/ AceFEM?
I am trying to implement a 2D turbulence problem with the model of Spalart-Allmaras. Therefore, I need to extract the global gauss coordinates to define parameter 'd' which stands for the distance to ...
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How to transform the default coordinate when set up the mesh with FEM method?
I want to establish the electromagnetic field of the motor based on the finite element method, because the governing equations are different in different regions, so we need to first build the shape ...
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Inaccuracy for FEM for 3D Heat Equation
I'm simulating the heat transfer within a cylindrical rod, with external heating from its sides.
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Mesh `Cylinder[{{0,0,0},{0,0,1}},1]` with inner boundary `x=y=0`
In a meshed cylinder Cylinder[{{0,0,0},{0,0,1}},1] I need to specify DirichletConditions along ...
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NDSolve stops solving past a certain time
This is a continuation of the post I've made Unable to solve Delay PDEs Error in Boussinesq Approximation. I apologise if I shouldn't have posted a seperate question for this but I think that the ...
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Steady state fluid flow for downward flow past an obstacle
I was attempting to simulate fluid flow past a circular obstacle. The following is the code which I used
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