Questions tagged [finite-element-method]
Tag for the usage of "FiniteElement" Method embedded in NDSolve and implementation of finite element method (fem) in mathematica.
943
questions
3
votes
1answer
56 views
FEM in 3D: assigning proper mesh for NDSolveValue
I am trying to compute electric potential in a simple 3D geometry containing (in a simplied version) 3 conductive rings (2 outer rings at 0 V, and the inner at 1 V) in different planes and I don't get ...
7
votes
1answer
150 views
Calculating the 3D Vector field of a permanent magnet with FEM
trying to calculate the magnetic field of a permanent magnet using the finite element method I struggle setting up the equation system properly. In the end I want to be able to calculate the magnetic ...
1
vote
1answer
84 views
The heat equation on the intervall [0,1] with Robin Boundary
I have the heat equation on the invervall $[0,1]$, therefore I define
heqn = D[u[x, t], t] == D[u[x, t], {x, 2}];
and I define my initial data which can be boring, ...
1
vote
2answers
59 views
Unable to plot a solution of NDSolve whilst being able to evaluate it
I want to define a function $f_c(x,y)$ as the solution of the PDE $\Delta f_c(x,y) = g_c(x,y)$, where $g_c$ is a given function depending on a constant $c$. I tried the following:
...
2
votes
2answers
262 views
How to solve this PDE
I had a try at numerically solving the heat equation with a source term:
$$
\frac{{\partial x}}{{\partial t}} = D\frac{{{\partial ^2}x}}{{\partial {z^2}}} + c
$$
...
4
votes
1answer
70 views
Using the result of NIntegrate as a potential in NDEigensysem
I am trying to find the eigenvalues and eigenstates of a Hamiltonian with a potential which cannot be analytically defined. In particular, it is the integral of the product between two functions:
<...
4
votes
1answer
121 views
How to solve Coupled a Parabolic and Elliptic PDE in NDSolve?
I want to solve a mixed PDE Parabolic-Elliptic system in 3-dimension (rectangular coordinate), as shown below:
The respective code version with parameters value, boundary and initial conditions is,
<...
4
votes
1answer
84 views
Problem with non-linear system of PDEs
I wish to solve the following system of hyperbolic PDEs: $\frac{\partial y}{\partial u}=\alpha \sqrt{2y-y^2}$, $\frac{\partial y}{\partial v}=-\frac{1}{\alpha}\frac{\partial\alpha}{\partial v}\:\left(...
0
votes
0answers
84 views
NDSolve a system of PDEs with Periodic Boundary Conditions
I would like to analyse the system of differential equations
$\begin{equation}
\begin{split}
\partial_tf_0&=\frac{C_{\mathbf{r}}}{(1+\lambda)^2}\bigg[\bigg(1+\frac{\lambda^2}{2}\bigg)\partial_{...
5
votes
1answer
114 views
Coupled pde for multiphysics joule heating with temperature dependent properties - error inconsistent dimensions
I want to simulate 3D joule heating and followed the wolfram multiphysics tutorial.
This multiphysics problem is comprised of the equation for the voltage field:
and the heat equation:
with the ...
3
votes
1answer
180 views
3D FEM Mesh - Accessing values of individual boundary elements
I have 3D mesh and calculate the heat equation using NDSolve. I want to access the temperature values on the individual boundary elements to solve another problem (...
7
votes
1answer
92 views
FEM Mesh - how to get elements belonging to ElementMarker
I want to get a list of all boundary elements belonging to a certain ElementMarker of a boundary mesh.
This code creates a simple mesh and allows to inspect the <...
1
vote
1answer
133 views
Can Mathematica do thermal/mechanical analysis of modeled solid systems?
I want to do thermal and mechanical analysis of various parts which may have complicated geometries.
I am contemplating buying SolidWorks because it does this: you model the part and then use their ...
1
vote
2answers
219 views
FEM 1D 3D region coupling - speed up coupling using boundary integration
I am working on a simulation of the heat equation involving a 3D solid simulation coupled to a 1D fluid simulation (convective term of heat equation). I am using the method of false transient as ...
1
vote
0answers
98 views
FEM 1D 3D region coupling - integration too slow for coupling with energy conservation
EDIT:
I reposted this question, removing everything that is not necessary for my coupling approach. Find the new post here.
I am working on a 3D simulation of the heat equation which is coupled to a ...
3
votes
1answer
77 views
FEM Meshrefinement for 1D Interval and Elements of order 2
I would like to create a 1D mesh of the intervall (-pi/2,pi/2) for solving a DE with FEM, with more elements close to +-1 - these elements should be of order 2, since order 1 elements yield too low ...
5
votes
1answer
74 views
3D FEM - How to use element markers for boundary integration
I am having trouble integrating over some curved boundaries and was thinking about using the element markers of the boundary mesh for integration rather than conditionals.
Is it possible to use ...
1
vote
0answers
59 views
Interaction between fluid flow and elastic obstacle (fluid-structure interaction) [closed]
I would like to model the velocity and pressure distribution of an elastic obstacle in a channel where the fluid flows. There are Navier-Stokes examples in Mathematica webpage with rigid obstacles but ...
2
votes
1answer
77 views
How to numerically solve Laplacian Equation in a system dependent boundary conditions?
I would like to solve the Laplacian equation in the following system in order to find out the potential and the Electric field everywhere. I have solved a couple of exercises by solving numerically ...
3
votes
1answer
84 views
FEM nonlinear anisotropic heat transfer with element markers
I'm trying to model a 2D nonlinear anisotropic heat transfer using FEM with element markers. I got stuck with errors and have no idea what to do to make it work...
I have simple toy-model: two ...
1
vote
0answers
74 views
Fail to inverse the Piecewise function embedded in a NDSolveValue
I am trying to estimate a function consisting of a Piecewise function that included in a FEM solver.
I firstly developed my mesh for the FEM model based on @Tim Laska's work. The code is shown as
<...
1
vote
1answer
60 views
2
votes
0answers
105 views
Solving Fokker Planck Equation for steady state solution using NDSolve
I am trying to solve the FPE (Equation (4) in paper) for the steady state solution to reproduce Fig 2(b)&(c) in mathematica using ND Solve. The functions and parameter values I used are as ...
3
votes
0answers
72 views
Custom mesh to help with a Fokker Planck eqn (refined rectangular mesh?)
Physicist here, new to SE and fairly new to MMA. I'm looking to solve a Brownian motion problem with inertia (m ≠ 0) and a velocity dependent diffusion coefficient, which in dimensionless units and ...
1
vote
0answers
92 views
How can I solve the 2D diffusion equation over a region that contains mobile sinks?
I am looking for guidance on how to simulate the following system in 2D.
I have a region, assumed to be rectangular for simplicity. A substance is diffusing into this region from its boundary. Again ...
3
votes
0answers
81 views
NDSolveValue for 2-D heat equation (PDE) coupled with ODE boundary and DiracDelta function [closed]
Recently, I am studying on the point source problem (PDE with DiracDelta) for heat equation.
The equations are as follow
The problems are arisen from not only the DiracDelta issues but the nonlinear ...
0
votes
0answers
65 views
Solving differential equation system with FEM when the equations depend on the mesh cell size
I am trying to implement Large eddy simulation with FEM for solving air flow simulation using Smagorinsky sub-grid stress model. In order to implement this there is a parameter (filter size) in the ...
2
votes
1answer
93 views
Define Implicit Region using Interpolating Function
Suppose I have a set of points $\{(x_1,x_2) : g(x_1,x_2) > f(x_1,x_2)\}$, how would I turn this into a mesh that acts as a region for PDE solvers, or even to use as a plotting region?
I have tried ...
1
vote
0answers
106 views
Boundary Value of Function Disagrees with Neumann Boundary Heat Equation
I'm trying to solve a time-dependent 2D heat equation with a source, initial specified heat distribution and heat flux loss at the boundary which goes with the temperature difference. Thus far, I've ...
0
votes
0answers
48 views
NDSolve with Piecewise function consideres some value inside Piecewise as Indeterninate
I'm solving a PDE, with one coefficient being piecewise. The issue appears to be that NDSolve somehow consideres piesewise boundary as ...
1
vote
0answers
52 views
Define the heat capacity Cp as constant values in the current version of Mathematica (Coupled PDEs)
I am trying to model a 2d heat transfer in fluid flow with nonlinear heat capacity Cp (e.g. Cp=1 + T[t,x,y]).
This benchmark problem is described as: the left side of the plate is heated, and the ...
4
votes
2answers
146 views
Modified Heat Transfer in Fluid Flow
I am trying to simulate Modified Heat Transfer in Fluid Flow (based on Buoyancy-Driven Flow in a Square Cavity ).
The modified heat transfer takes the form:
with the solid volume fraction:
The ...
4
votes
1answer
193 views
Different answer between HeatTransferPDEComponent and Matlab
I've been working on a 2-layer HeatTransferPDE Model.
The diagram of the model is
The two materials have an initial temperature of 37℃, and the outside is 75℃. The model is for heat insulation so it ...
2
votes
0answers
46 views
NDEigensystem potential with a singularity
Consider the following eigenvalue equation
$$-\frac{d^2}{dx^2}\Psi_n(x)+\left(gx^4+\frac{1}{x^2}\right)\Psi_n(x)=E_n\Psi_n(x),\qquad x\in(-10,10),\qquad\Psi(-10)=\Psi(10)=0$$
The boundary of $x$ is ...
5
votes
3answers
103 views
Plot the lines (nodes) for the given value from NDsolve output
I want to plot lines for a specific single value from the output in Nsolve (we need to find these nodes from the output ufun, then plot them).
...
7
votes
3answers
260 views
Smoother boundaries between components of segmented image
I'd like to use boundaries between components of a segmented image to create a mesh for finite elements, as described in Mesh for Images for three materials and meshes with multiple regions from 2D ...
2
votes
1answer
61 views
Custom Normalization for NDEigensystem
I am trying to solve the Laplace equation in polar coordinates
$$-\left(\frac{\partial^2\psi_n(r,\theta)}{\partial r^2}+\frac{1}{r}\frac{\partial\psi_n(r,\theta)}{\partial r}+\frac{1}{r^2}\frac{\...
0
votes
1answer
152 views
AceGen/ AceFem on new M1 Mac
Apple has updated its processors some time ago and I am curious if AceGen/ AceFem are compatible with this latest generation of the Apple M1 processors? And maybe someone can already report on the ...
0
votes
0answers
41 views
Deformation in Cylindrical coordinates in AceGen
How is it possible to obtain the deformation gradient in cylindrical coordinates in AceGen?
The usual procedure, which I understand, is given by the following:
...
2
votes
1answer
114 views
Neuman boundary conditions for system of PDE in 2D
The system of equations for three variables: n(x,y,t), b(x,y,t) and a(x,y,t)
The rest of letters are coefficients. System is defined over a square region with the lower left corner at the origin.
...
1
vote
1answer
106 views
AceFEM GlobalTask
I wonder whether there is any way to add data directly to the linear equation system in AceFEM.
I´m having external data that I want to superimpose to the linear system before solving it. The targeted ...
0
votes
0answers
44 views
Indexing of NDEigensystem Result on a Cluster
I am trying to run on a cluster (where the version 11 of Mathematica is available) a code involving the following calculation:
...
0
votes
1answer
59 views
Unable to set MaxStepSize when boundary conditions are specified using NeumannValue and DirichletCondition
Short story: I am trying to specify the maximum step size for NDSolve function, but it appears to be working only if I do not specify boundary conditions using NeumannValue and DirichletCondition ...
2
votes
1answer
72 views
AceFEM: MIEL example aborts for many load steps
I am currently using AceFEM version 7.303 and Mathematica 12.2 but had the same problem with other versions before.
My laptop as well as the server I use work with Linux.
When I run the example "...
3
votes
1answer
99 views
How to create a 2D mesh and obtain all the coordinates and connectivity
I know this is a really amateur question, but I´m kind of new in here. Though I´ve been trying for the last few days I simply cannot convert a set of points (well actually a region) to a mesh. But ...
6
votes
1answer
137 views
3D FEM Mesh problem - either bad mesh or inaccurate geometry
I am having trouble obtaining a good 3D mesh. I have tried lots of stuff, either resulting in a bad mesh or inaccurate geometry.
My geometry consists of a cuboid with a quarter cylinder cut out on a ...
3
votes
1answer
111 views
3D meshing of cyllindrical domain into hexahedral elements
I need a solution for generating a hexahedral mesh for a cyllindrical domain in Mathematica/AceFEM. Ideally, it should be close to cyllindrical symmetry not very far from the center. The best option ...
3
votes
1answer
119 views
What does "TetGenTetrahedralize: Tetrahedralize returned an error, 2. mean? Also error number 1,2,3...?
regioncalc5 = ToElementMesh[regioncalc4, MeshRefinementFunction -> ff]
TetGenTetrahedralize: Tetrahedralize returned an error, 2.
7
votes
2answers
158 views
NDSolve coupled PDE Grad function in source term error
I am working on a multiphysics problem involving heat transfer and electrostatics. I have been messing around with the Joule Heating Tutorial Case and got stuck with the heat source term not working. ...
4
votes
0answers
94 views
How to use NDEigenvalue to accurately estimate functional determinants?
Goal: Ultimately, I would like to find a trustworthy approximation for the ratio of the functional determinant of two differential operators using the formula
$$ \frac{\text{Det}[\hat{D}_0]}{\text{Det}...
