Questions tagged [finite-element-method]

Tag for the usage of "FiniteElement" Method embedded in NDSolve and implementation of finite element method (fem) in mathematica.

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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
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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
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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, ...
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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
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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
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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
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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
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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(...
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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
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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
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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
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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
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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
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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 ...
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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
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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
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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
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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
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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
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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 ...
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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 <...
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1answer
60 views

Obtaining more values from `NDEigenvalues`

When I run this code ...
2
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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
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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 ...
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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
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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 ...
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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
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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 ...
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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 ...
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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 ...
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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 ...
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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
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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
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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
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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
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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}...

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