Questions tagged [finite-element-method]

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

73 questions with no upvoted or accepted answers
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From where to learn finite element method?

Can anyone reccomend me a book or site for learning finite element method with mathematica, besides wolfram language official site, https://reference.wolfram.com/language/FEMDocumentation/tutorial/...
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353 views

Create vtk file of ParaView from Mathematica [FEM post-processing]

I'm doing FEM in Mathematica and want to visualize the results in Paraview (e.g., create a video of the displacement field). Now I have the element mesh, the displacement and stress fields. How can I ...
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508 views

Stress Operators for Finite Element Analysis

For stress analysis in the finite element method you need a stress operator. For two dimensional plane stress it can be found here. For two dimensional plain strain it can be found here. I need the ...
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564 views

benchmark of Mathematica's FEM?

Does anyone have any numbers on how mathematica compares to other commercial (eg ANSYS) or free FEM softwares (eg. FreeFEM++, FEniCS, elmer)? If this is too vague say solving the diffusion equation in ...
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468 views

FEM Mesh for pipes and tubes

I work with pipe systems and would like to use finite elements within NDSolve for regions inside or exterior to a pipe. How to do I make a mesh of the region ...
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516 views

Symbolic Weak Form

Usually I write the weak form by hand for my FEM code, but it's a little annoying and mechanic sometimes. So, I wonder, is there any way to generate the symbolic weak form in Mathematica? For ...
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355 views

How to increase boundary mesh quality?

Update: I tracked down the current issue to errors generated by numerically integrating over the boundary mesh. What's the proper way to integrate a function over the boundary of an implicit region? ...
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153 views

Transition to turbulence

I found that a 3D model of viscous flow in a rectangular channel with jump section implemented on the basis of FEM demonstrates a transition to turbulence. We use an algorithm for unsteady flows ...
5
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172 views

NDSolve post-processing: Calculate the flow over a FEM-boundary

I'm trying to calculate the heat loss from buried pipes with NDSolve`FEM. For this I set Dirichlet conditions at the model top and bottom and temperature dependant Neumann conditions at the contact ...
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72 views

system of coupled nonlinear pdes with FEM (magneto-hydrodynamic mass transfer)

EDIT 01 See end of post for an update. Original Question I'm trying to reproduce the magneto-hydrodynamic flow studied here using the nonlinear FEM functionality, and have been having trouble ...
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205 views

Problem computing a cylindrical Heat equation with a parameter alpha

i have been struggling to compute a particular instance of cylindrical 3D heat equation. Here is my code : ...
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55 views

how to download Finite ELements tutorial as PDF

For long tutorials, I prefer hard copy. Is it possible to download from somewhere this document https://reference.wolfram.com/language/FEMDocumentation/tutorial/FiniteElementOverview.html as PDF ...
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85 views

1-D stress (displacement) analysis in annulus by considering viscoelasticity

I am a new Mathematica user, and I was trying to solve a stress (or displacement) field problem in an annulus. Here is the problem in the polar coordinate: The inner radius of the annulus is $b$, ...
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62 views

Interface points of NDEigensystem

When solving an eigenvalue problem with "NDEigensystem", e.g. a 1D Eigenvalue problem with the interval composed of different materials, which should be solved by the pure numerical method such as FEM,...
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170 views

Postprocessing of FEM: extremely slow speed of NIntegrate

I've gone through the documentation for NDSolve FEM. There are quite a lot tips and techniques for accelerating NDSolve, and only quite few tips for post processing. Somehow I found out that the ...
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168 views

Using of FindMinimum in constrained problem

There is a constrained optimization problem based on finite element method. We should find the optimal distribution of density inside the our region for minimazing the energy of deformation. The ...
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242 views

Reducing a FEM 3D Interpolation Function to a 2D Interpolation Function

I'm trying to solve the heat equation in 3D using FEM and back out a slice in the xz plane. My problem is when I define a function that is a slice in the xz plane it uses the full 3D interpolation ...
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133 views

Stress analysis in a disk with circular holes

Writing the following code: ...
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162 views

Coupled parabolic differential equations with time delay

Is it possible for NDSolve to solve delay partial differential equations with simple Neumann boundary conditions? An example I have is as below: ...
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1k views

FDTD Electromagnetic Simulations with Mathematica

Mathematica has some Finite Element capabilities (as explained here). Do you think mathematica is a realistic/sensible option for electromagnetic simulations? (aka making a movie of electric fields ...
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276 views

How can I improve the solution of my PDE?

I want to improve the last code to find a better solution for umi. For now I'm using only MaxStepFraction. Also, when I put no ...
3
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527 views

Nonlinear FEM and FindRoot

I'm trying to develop a kind of nonlinear FEM application using mathematica to solve a bvp like the following: $$ \gamma(u') ~u^{iv} + 2 \gamma'(u') u''' u''+ u''^3 = f(x) $$ where $u = \tilde{u}(x)...
3
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1answer
329 views

1st-order linear ODE system gives inaccurate/biased solutions

Consider an ODE eigensystem $$ t(y+\frac{1}{s})a(y)+[(q+\frac{1}{2}+\frac{s}{2}y)+s(y\partial_y+\frac{1}{2})]b(y)=\lambda a(y)\\ t(y+\frac{1}{s})b(y)+[(q+\frac{1}{2}+\frac{s}{2}y)-s(y\partial_y+\frac{...
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138 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}}^{...
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64 views

Matrix integration just spits out the inputs

I just started to use Mathematica two days ago. I am trying to solve a stiffness (K) matrix of a 4-node is-parametric truss element for my exam on next Monday. The integrand is a 4 by 4 matrix with ...
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105 views

Solving Ultrahyperbolic Equation (4D) With NDSolveValue

So we were trying to solve the Ultrahyperbolic Equation with two spatial dimensions and two time dimensions in Mathematica using NDSolveValue. We understand that the problem, in general, is not ...
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61 views

Modelling transparent boundary conditions on a quantum graph with Mathematica NDSolve and finite-element method

Continue to this issue I am now trying to apply a solution from the question above to three-bonded star graph. My idea is to take the third bond at [10,20] because I am using only one function u[t,x]....
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42 views

Application of spatially varying boundary conditions and source term in AceFEM

I am trying to model a simple 2D steady state heat conduction problem using automatically generated Q2 elements. The problem consists of a square domain with prescribed temperatures along the bottom ...
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85 views

Quasi-periodic boundary conditions

I am trying to solve the following problem using Mathematica's NDSolve $$ \partial^2_{y}\psi+\partial^2_{x}\psi-2\,i\,q\,B\,y\,\partial_{y}\psi-q^2B^2y^2\psi+q\,B\,\psi=0 $$ subject to the boundary ...
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64 views
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48 views

Computing the first eigenfunction of the p-Laplacian in a real interval

How can I numerically compute the first (non-negative) eigenfunction $u$ of the $p$-Laplacian ($p>1$) in a bounded interval $(-a,a) \subset \mathbb R$ (up to positive multiplicative constant)? $$-\...
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99 views

Modelling a Crankshaft

In the linked documentation, a crankshaft is imported as a GraphicsComplex, which can then be turned into a Finite Element Mesh for the purposes of Finite Element Analysis. I wondered if anyone knew ...
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58 views

Is Inactive Form avoidable when using NDSolve for non-linear ODEs

So this is basically the same question as here referring to information provided here. However, I am wondering if this inactive form is always necessary or more of a convenience. For example, ...
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170 views

Non constant coefficient in heat equation

I have to solve the following heat equation over a cylindrical domain. In cylindrical coordinates the PDE Equation reads: ...
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87 views

Formulating equations for 3D stress in the finite element method

I would like to know how you formulate equations for the finite element method for stress calculations. We know the answer because user21 has put it here. It involves usage of ...
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0answers
74 views

AceFEM: Matrix condensation and elimination of local unknowns

Lately I have been working with non-linear mixed hybrid elements. The basic article that I took for my research is one by T.H.H. Pian dn K. Sumihara: Rational approach for assumed stress finite ...
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265 views

Use Mathematica FEM-functionality for further calculations

I would like to use MMA FEM abilities for example to apply galerkin's method to solve intergal equations or nonstandard numerical applications in a given mesh m. Is it possible to extract the "node-...
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264 views

Solving a coupled PDEs using FEM with Robin conditions

The same type of question has been answered here but for single PDE. The main issue I am facing is how to write the weak form for two PDEs. $$\epsilon^2\frac{\partial ^2u}{\partial x^2}+\frac{\...
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0answers
85 views

AceFEM: Tie - Option Issue

I try to use the "Tie" Option of the SMTAnalysis[] function. In general, I want to have some additional Nodes (two kinds of them) at certain (not all) coordinates tied and at some not. What I have is ...
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0answers
137 views

AceGen: Solving the dynamic equation in the middle of the time step

Note: This question is about AceFEM and AceGen package for automatic code generation for finite element analysis. If the question is not specific enough, I will try to refrase it, but I am a fairly ...
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0answers
179 views

ElementMesh (rendering?) issue

The appearance of the following ElementMesh is bad as you can see for example on the inside surface of the shell. The same problem happens converting to a ...
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0answers
115 views

Eliminating instabilities in a transient finite element solution at a discontinuity near t = 0

I have found a transient solution to the 1D heat equation where the initial condition is discontinuous. The results are accurate except for when time is small. The initial condition looks like this: $...
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0answers
314 views

How to Implement a “Function Object” suitable for NDSolve and Finite Element Method?

I have a bunch of methods that shoud return an expression that behave like a function, i.e. an expression that, when supplied with suitable arguments, evaluate to something. A simple ...
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233 views

Puzzling NDSolve[] behavior for PDE (smooth solution, inconsistent with boundary conditions)

Consider the following: NDSolve[{D[z[x, y], x, x] + D[z[x, y], y, y] == 0, z[x, 0] == Sin[x], z[0, y] == Cos[y]}, z[x, y], x, y] {{z[x, y] -> ...
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1answer
58 views

How to numerically integrate the time of two oscillatory functions from NDEigensystem

I am trying to numerically integrate phi*psi. And no matter which method I chose, the NIntegrate failed. ...
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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: ...
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0answers
90 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 ...
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0answers
88 views

Heat transfer FEM with nonlinear Cp

I would like to solve a 3D heat transfer problem with nonlinear heat capacity Cp (Cp=1*T[t,x,y,z]). My problem is very simple: a slab with the bottom surface insulated and the other five surfaces ...
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1answer
82 views

Writing a solution dependent coefficient in a PDE using Do & Table command

The goal is to find the displacement response of the following equation with the updating coefficient on the time and disp domain called difusion coeficient or Epsilon. For this purpose, Epsilon is ...
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64 views

Longitudinal Bar Vibration & Boundary Condition Problems

I am trying to solve the PDE for longitudinal vibrations in a bar (as shown for example at Youtube Longitudinal Bar Vibration). My challenge is the application I am trying to solve has these boundary ...