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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
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Contact with rigid obstacle in AceFEM

Does anyone of you know how to specify the simulation when a deformable body is affected by contact with some rigid body? I think it should be possible, but I am unable to find it in the manual.
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2answers
191 views
+500

How to apply different equations to different parts of a geometry in PDE?

I want to solve two coupled partial differential equations on two dimension. There are two variables v and m. The geometry is a ...
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0answers
77 views

Neumann boundary condition is not satisfied

I want to solve the diffusion equation on a disk centered at (0,0) with a radius of 1. I also want the flux at a radius of 0.8 to be zero. I have this initial condition at time zero: ...
6
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2answers
195 views

How to diminish computation time when nonlinearity appears in 2D heat conduction equation?

I am trying to simulate heating and melting of the steel plate by means of FEM.The model is based on nonlinear heat conduction equation in axial symmetry case. The problem statement is the next: $$ \...
2
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1answer
77 views

NDSolve with Finite Element ignoring terms in partial differential equations?

Solving a 1D dispersive wave equation with NDSolve and the finite element method seems to give completely wrong results. Consider the 1D PDE below ...
3
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1answer
115 views

How to specify non-reflective boundary conditions when NDSolving two coupled first order PDEs?

Due to a lack of fruitful answers after 3 days, this question has been reformulated in a more direct way compared to its first version. Consider the telegraph equation problem expressed as a system ...
6
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0answers
59 views

Direction of NeumannValue on boundary

When solving partial differential equations NeumannValue is used to specify the flux across the boundary. For normal fluxes the detailed notes state They appear on the boundary ∂Ω of the region Ω ...
10
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2answers
111 views

ToElementMesh of Region with Hole

When I try to mesh the following region it fails. Why? Is there a workaround? ...
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0answers
53 views

Absorbing/Derivative Boundary Conditions

I am attempting to solve a differential equation, however I am having issues implementing boundary conditions that reduce the impact of reflections/instabilities. I've had a look at similar ...
13
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2answers
529 views

Meshing the cow

As a simple example for applying stl-files I took "cow" out of MMA example data. I'm able to discretize the Graphic without problems ...
2
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1answer
82 views

Access to the temporary solution in NDSolve with StepMonitor

I want to step-monitor at each time step of a spatio-temporal NDSolve (using the finite element method) the maximum bending of the function sampled over the curent mesh. For this I first need access ...
5
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3answers
240 views

How to create “Volumemesh” from closed “surfacemesh”?

Given a surface region (MesgRegion netz2D), for example ...
3
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2answers
78 views

Making NDSolve choosing by itself a spatial meshing leading to correct integrated results

In a previous post, I was asking how to force a fine spatial meshing in NDSolve using the FiniteElement method. The solution was ...
4
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3answers
78 views

Forcing at least $n$ spatial steps in solving a 1D spatio-temporal PDE problem with NDSolve

I want to solve the telegraph equation with a spatial discretization forced at 200 points. I tried: ...
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4answers
322 views

Poisson equation with pure Neumann boundary conditions

Dear Mathematica users, I would like to numerically solve a, as the title says, Poisson equation with pure Neumann boundary conditions $-\nabla^2(\psi)=f$ $\nabla(\psi)\cdot \text{n}=g$ Is it ...
2
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1answer
107 views

Numerically solving the Laplace equation in a 2d cylinder

Consider the following Laplace equation and boundary condition $$\begin{equation}\begin{cases} \Delta \theta(r,\phi)=0 \\ \int d \vec{\ell}\cdot\nabla \theta(r,\phi)=2\pi \end{cases} \end{equation}$$...
7
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1answer
130 views

Absorbing Boundary Condition for Complex/Coupled PDE

Context: This question is relevant to the physical problem of an excited leaky cavity. The boundary condition on the inside of the cavity is Dirichlet. The other end of the cavity is partially blocked ...
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3answers
384 views
3
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1answer
48 views

PostProcessing the SMTNodeData values in the deformed configuration

I have been struggling with this problem for a long time. I know that this question is not specifically related to AceGen or AceFEM, but I would like to know if anyone had a similar experience in ...
1
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1answer
77 views

Euler-Bernoulli beam equation

I'm trying to solve Euler-Bernoulli beam equation with simply supported edges.$\frac{\partial^2} {\partial x^2} [ E I \frac{\partial^2 w} {\partial x^2}] + \rho S \frac{\partial^2 w} {\partial t^2} = ...
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1answer
59 views

Finite element mesh generation with specified coordinates [closed]

I am trying to use Mathematica's FEM capabilities, but I want to generate my own QuadElement mesh. (The key word in here is trying.) ...
3
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1answer
273 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{...
7
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1answer
660 views

How do I use low level FEM?

How do I simulate the following partial differential equation using Low level FEM in Mathematica? D[u[x,y], x] - D[u[x,y], y] = x Sin[x y] - y Sin[x y] The ...
3
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1answer
91 views

NDSolveValue for Laplace equation not converging to analytic solution

I'm solving Laplace equation $\nabla^2 \phi = 0$ with BC's $\phi_x(x=\pm 1) = 0,\, \phi_y(y=-h) = 0$ with a specified BC along the circular arc $x^2 + (-1 + y)^2 = 4$, which I call $\Gamma$ (so the ...
5
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1answer
119 views

Recycling solutions of multidimensional NDSolve

Dear wolfram community, I hope my problem is clear and easy to solve. I have already solved the following heat equation over a domain: ...
2
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1answer
78 views

Heat Equation with Mathematica Neumann / Dirichlet Conditions

This is the question I am trying to solve After fours hours of research and 61 attempts (just today) on how to do this, I'm asking for help. I've been in hospital and am now trying to catch up on ...
4
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1answer
76 views

Multiple Boundary Conditions for NDSolve in mesh with multiple interfaces

Here is my problem: I want to solve a Laplacian equation in a 2D geometry with multiple interfaces, each interface presenting a different boundary condition. As for an example, I am working on a ring ...
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2answers
117 views

Distinguish between inner and outer boundary in MeshRegion

For example, this is a 2D MeshRegion with one (or more) holes in it: ...
2
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1answer
56 views

How to set the NeumannValue conditions when the conditions are Discrete points?

For example i can use Piecewise when the condition is a Continuous function ...
0
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2answers
204 views

Solving the 3D Poisson equation on the surface of a cube using a relaxation method

The code below is from another question asked by someone else about solving the 3D Laplace equation for truncated octahedron in a cube matrix, How to solve Laplace equation in 3D?. I wanna know, how ...
9
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1answer
261 views

How to solve this 2nd-order ODE with singularity?

I tried solving the eigenvalue problem of a 2nd-order ODE $$[b^2(k-2)^2y^2-2b(k-2)(1+2ky)+4k^2+b^2(k-2)3y]f(y) \\- 3b(3by-2)f'(y)\\-(3by-2)^2f''(y)=\lambda f(y)$$ with ...
10
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1answer
177 views

FiniteElement v.s. TensorProductGrid: which is reliable for Schrödinger equation with periodic b.c.?

This is a problem comes up in the discussion under this post and I think it's worth starting a new question for it. I suspect the underlying issue is the same as in this post, but not sure. Consider ...
4
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4answers
408 views

Inhomogeneous Neumann boundary conditions for diffusion equation

I am new to Mathematica and I have a problem specifying Neumann boundary conditions in diffusion equation. The best result I managed to get is this. ...
3
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1answer
152 views

Eigenvalues of a non-Hermitian complex periodic potential

I have an eigenvalue problem: $$-\frac{d^2}{dx^2} \psi(x) +V(x)\psi(x) = E \psi(x)$$ where $V(x)$ is a complex periodic potential: $$V(x) = 4[\cos^2(x) + i 0.3 \sin(2x)]$$ It has been claimed that ...
5
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1answer
75 views

How to set a NeumannValue on a given ElementMarker on the boundary of a mesh?

How can one apply a NeumannValue on an ElementMarker on the boundary of an ElementMesh for a ...
5
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1answer
145 views

Help with 3D FEM calculation of a heat equation

I want to solve a heat transport problem in a long tube where 4 coolings rods are inserted. Fluid flows down axially, and there's radial heat conduction. First, the shape is defined: ...
9
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0answers
312 views

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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0answers
120 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 ...
3
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2answers
58 views

Problems using DensityPlot when solving Laplace's equation

I am trying to solve Laplace's equation in 2 dimensions with potencial boundary conditions at the edges of an external square and an internal circle. Everything seems to work fine until the point ...
3
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1answer
101 views

How to control boundary markers for overlapping FEM meshes?

I am trying to create FE meshes from vector or bitmap images and have come across the following issue. This is best shown using the following simplified code. ...
4
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1answer
151 views

How to create meshes with multiple regions from 2D images?

I would like to import 2D images to Mathematica and to use them to create meshed regions which can then be used for FEM. I create the images in Adobe illustrator so can either import a vector based ...
3
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2answers
103 views

Convergence of PDE solution using method of lines

I'm afraid that this will turn more into a math question rather than a Mathematica one. I'm trying to solve the equation $$\frac {\partial n}{\partial t}=D\frac {\partial^2n}{\partial x^2}$$ $$\...
4
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2answers
120 views

How to make a frustum of a cone

For finite element purposes I need a frustum of a cone with a finite wall thickness, i.e. a tapered pipe. To make a cone is easy ...
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0answers
47 views

How to create surface mesh from a given 2D mesh toplogy?

I would like to convert a very easy(examplary) mesh(2D) ...
6
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1answer
111 views

ElementMesh from ImplicitRegion cuts corners of region

I'm trying to define a region within a cell and below a level set of a function using ImplicitRegion and ToElementMesh. Here I ...
3
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2answers
139 views

Schrödinger equation for a hydrogen atom and lack of memory

I'm trying to solve the Schrödinger equation for a hydrogen atom in the Cartesian coordinate system. This is my code ...
4
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1answer
119 views

MeshRefinementFunction for region gives error

I would like to refine a mesh within a given path/volume, that is specified by the MeshRefinementFunction option given in ToElementMesh[]. For starting i took a simple 3D MeshRegion of a Tetrahedron <...
4
votes
1answer
221 views

How does this Mathematica code work?

I am trying to work with a simulation of Brain Tumor growth and I was fortunate to get a very great example at http://community.wolfram.com/. However, I need clarifications on some of the code. I ...
4
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0answers
226 views

Solver for unsteady flow with the use of the Navier-Stokes and Mathematica FEM

There are many commercial and open code for solving the problems of unsteady flows. We are interested in the possibility of solving these problems using Mathematica FEM. Previously proposed solvers ...
6
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1answer
131 views

2D interpolation of function with dependent interpolation border

My problem is to compute $$\int\limits_{x_{min}}^{x_{max}}\int\limits_{y_{min}}^{\sqrt{x^{2}-a^{2}}}W(x,y)g(x)\ dx\ dy$$ Because $W$ have highly oscillatory 2d complex numeric integral inside, dumb ...