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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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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500
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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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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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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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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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How can we improve transonic flow visualization?
With this code we can make 2D FEM simulation of transonic flow around airfoil NACA 0012 at Mach number of 0.925. It takes about 5 minutes on the XENIA-15 laptop of 32 GB memory with processor Intel ...
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8
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Numeric Solution Hydrogen Atom
I'm trying to solve the Schrödinger equation for the hydrogen atom without made the variable separation of the polar and radial coordinate. It is my test code to extrapolate to another system with its ...
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Does current Mathematica capability allow solving PDEs (e.g. reaction diffusion equation) over surface of a mesh or surfaces
I came across this nice paper (https://arxiv.org/pdf/1605.01583.pdf) where the authors simulated a reaction diffusion system over the surface of a gecko, primarily to understand how various patterns ...
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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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ParametricNDSolveValue causes kernel to crash
Bug introduced in 12.1.1 and persisting through 13.2.0.
In the course of answering question 228693, I found that
...
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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 ...
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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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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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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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Inactive PDE terms in FEM without Neumann boundary conditions
I am solving a Poisson-like set of PDEs for u[x,y] and v[x,y] in the square region ...
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Solve 3D convection-dominated PDE with discontinuous coefficient, without tiny mesh
I'm trying to simulate a self-propelled particle diffusing on a disk. The direction of the self-propelled velocity $\vec{v_A}$ doesn't change, while it speeds up at the boundary and slows down at the ...
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FEM: modelling 2D flow under periodic forcing
Despite many examples of periodic boundary conditions being presented, it remains difficult to obtain a periodic solution. Let us consider a simple example of a flow in a two-dimensional channel under ...
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NeumannValue nonlinear pde?
Inspired by the highly interesting question Solving Burger's equation with NDSolve at large time I'll try to understand Finite-Element-solution for nonlinear pde in more detail:
Burger pde
$u_t(x,t)+u(...
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Finite-Slip Boundary Conditions
Equations
I am trying to solve the linearized Navier-Stokes equations for a 2D electron fluid given by:
$$
\begin{aligned}
\sigma \nabla \Phi + D^2 \nabla^2 \boldsymbol{J}&=\boldsymbol{J} \\
\...
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How to use NDEigenvalue to accurately estimate functional determinants?
Goal: Ultimately, I would like to find a trustworthy approximation for the ratio of the functional determinant of two differential operators using the formula
$$ \frac{\text{Det}[\hat{D}_0]}{\text{Det}...
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Heat balance multilayer with heat flux continuity
I am solving the heat equation (diffusion only) over a 3-layer system (physical properties varying from layer to layer).
...
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Speed improvements and confusion for MapThread and Dot
I have a question / confusion over improving the speed of MapThread[Dot,...] for lists of tensors. My problem involves taking two lists of tensors and then ...
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When solving a heavy PDE Mathematica falls out: what can be done
I am solving a heavy PDE. The mesh is huge, and Mma falls out after few tens of minutes solving: the cell becomes inactive, kernel (pressumably) quits, all variables turn blue.
My question is, what ...
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FEM code working well in v.12.1, has warning in v.13, and not working in v.13.2.1
Let us consider sound in a glass. Numerical model has been described here. FEM code is given by
...
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How to make gaussian pulse move using Boundary Conditions (one spatial dimension)?
I'm trying to solve a system of normalized coupled PDE's to model Raman scattering. Essentially, a gaussian light pulse of 300ps duration enters the raman active medium at ζ = 0 which then drives the ...
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answers
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Decomposing an eigenfunction of helmholtz equation into plane waves
I have defined a region and found the eigenmodes of the 2D Helmholtz equation in it:
...
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What is the correct way to create an animation in parallel using the result of NDSolve?
For example, in the following code ParallelTable takes 23 minutes:
...
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103
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Understanding `NeumannValue`
From this interesting question Reveal the formal PDE of FiniteElement
...
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Fem solution of Helmoltz equation
I'm trying to solve the Helmoltz equation :
https://en.wikipedia.org/wiki/Helmholtz_equation in a 3d space, in vacuum, using FEM.
I expect the solution to be an function oscillating in the x direction,...
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3
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answers
90
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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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108
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Coupling AceGen with Abaqus
I am using Abaqus for nonlinear FEA and, I have generated a UEL (User defined Element Subroutine)using AceGen. But the .log file generated by Abaqus shows a syntax error when I try to run a job using ...
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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 :
...
3
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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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100
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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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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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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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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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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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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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3
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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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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 ...
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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)...
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answer
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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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Numerical instability when using NDSolve to simulate phase separation
I'm using NDSolve to simulate the following model of phase separation:
where rho_T=rho_1+rho_2. The term with chi causes rho_1 and rho_2 to repel each other. However, there is a numerical instability ...
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Implementation of Neumann-like boundary condition
If we wish to solve an elliptic PDE, say $\nabla^2\phi=\text{given}$, on a domain $\Omega$ with Neumann boundary conditions, $\hat{\mathbf{n}}\cdot \nabla \phi\Big|_{\partial \Omega}=\text{given}$, ...
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3D BoundaryMeshRegion Minkowski difference via RegionErosion Failure
I need to be able to produce Minkowski difference of an arbitrary BoundaryMeshRegion and a cylinder.
...
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Make NDSolve return solution over only part of domain
Consider the following pair of PDEs, for which I will solve in the mesh built below. The mesh needs to be much larger than the region of interest to mimic boundary conditions "at infinity".
...
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Coupled PDEs with different dimensions and boundary conditions
The geometry of the problem is described by a cylinder inside a rectangular domain. The equations describes the region in between them.
I have 2 PDEs for U(x,y,z) in the bulk region and V(z) for -0.5&...
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Problems with using NDSolveValue to solve two-dimensional Fokker-Planck equation
When I use NDSolveValue to solve the following two-dimensional Fokker-Planck equation, it works well:
...
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