Questions tagged [finite-element-method]
Tag for the usage of "FiniteElement" Method embedded in NDSolve and implementation of finite element method (fem) in mathematica.
1,360
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4
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Nonlinear PDE with a trivial and nontrivial solutions: how to?
I am solving the following PDE:
eqMain = D[z[x, y], {x, 2}] + D[ z[x, y], {y, 2}] -
(a - x/(x^2 + y^2 + 0.0001))*z[x, y] - z[x, y]^3==0;
with the zero ...
- 37k
4
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1
answer
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Problem with NDSolve for 1st order non-linear system of PDEs
I wish to solve the PDE system
\begin{align}
x_u^2+y_u^2+\left(xx_u+yy_u \right)^2&=1\\
x_v^2+y_v^2+\left(xx_v+yy_v \right)^2&=1
\end{align}
subjected to $x(0,v)=0$ and $y(u,0)=0$. However, ...
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6
votes
2
answers
252
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SolidMechanicsStress returns, that the stress is equal to zero
Bug introduced in 13.1 and fixed in 13.2.0
I am trying to compute a deformation and a stress of a material with a custom material law. I have successfully computed the deformation using ...
- 330
3
votes
1
answer
220
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Solving 3D Nonlinear Integral Partial Differential Equation
I am trying to solve Equation number (1.2) numerically in MATHEMATICA. This equation is solved in the papers https://arxiv.org/pdf/2205.05193.pdf, https://arxiv.org/pdf/2202.13264.pdf, and https://...
- 279
7
votes
2
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153
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Create a domain for an Hexahedron with the floor replaced with an Indian Burial Mound
I am trying to create an acoustic model domain for a small park that contains an Indian burial mound.
The park is laid out using a 3D cartesian coordinate system in units of meters.
A Hexahedron ...
- 2,207
10
votes
3
answers
327
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Can NDSolve be initialized with a close solution?
I have a set of 4 first order ODE with 4 initial conditions to be met. It models a simple damped pendulum like the one described here. What changes is the damping term and I switched to first order ...
- 933
4
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1
answer
115
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Is it possible to remove an element during computation in AceFEM?
The title says it all. I know there have been a lot of enhancements in the recent versions of AceGen/AceFEM. I would like to know if there is a possibility of removing an element during computation (...
- 1,243
10
votes
1
answer
185
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1D diffusion problem: Troublesome NeumannValue
Bug introduced in 13.1 or earlier and fixed in 13.2.0
Mathematica solves the diffusion problem (two Neumann-conditions)
...
- 42.9k
0
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0
answers
28
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Flux boundary condition on a line using derivatives [duplicate]
I am solving a partial differential equation for heat-transport on a rectangular domain of width W and length L with fluid flow.
$$ v_{max}\bigg(1-\bigg(\frac{x-W/2}{W/2}\bigg)^2\bigg) \frac{\partial ...
4
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1
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239
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How to get the cross sectional area of a wine bottle picture/photo by doing an appropiate image processing on it?
We are working on a PDE Acoustic model in which the geometry of analysis
is the cross-sectional area of a wine bottle. We want to get the
geometry from a wine bottle image by doing an appropriate ...
- 101
2
votes
0
answers
49
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System of PDEs with coupled Neumann BC--how to use NeumannValue?
I have the following system of PDEs for functions $u_1,u_2$ in a region $\Omega\subset\mathbb R^2$:
$$
\begin{cases}
2\partial_{xx}u_1+\partial_{yy}u_1+\partial_{xy}u_2-u_1=f_1 & (x,y)\in\Omega\\
\...
- 226
5
votes
2
answers
139
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1
vote
2
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122
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NDSolve with piece-wise function and BVP
How to numerically solve a system of differential equation with boundary conditions and piece wise affine functions ?
Consider the following system of differential equations from some optimal control ...
- 11
1
vote
0
answers
73
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Building a structure out of cubes one block at a time
I have simplified code in which the motion of a point charge is simulated N times (one particle at a time) in a static electric field. When the point charge comes to rest (using WhenEvent boundary ...
- 363
4
votes
0
answers
158
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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 ...
- 85
3
votes
2
answers
179
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BoundaryMeshRegion Error: Boundary surface is not closed
I am trying to create a BoundaryMeshRegion comprised of many cubes with random locations, in a relatively small region.
I have had success implementing my technique for a smaller number of cubes (say,...
- 363
9
votes
2
answers
434
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Calculating the 3D magnetic vector field of a permanent magnet, with shape given by STL File
following my earlier question Link, I am trying to calculate the magnetic field of a permanent magnet. The shape of the magnet was generated with FreeCAD and is provided to Mathematica by an .STL file....
- 797
5
votes
1
answer
234
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Monte Carlo Simulation of Charged Particles in Non-Uniform Electric Field
I have a code (provided below) which simulates the motion of an ensemble of charged particles which are subjected to a complex static electric field which passes through some aperture in a metallic ...
- 363
1
vote
1
answer
83
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Different boundary conditions
I have a problem regarding the definition of multiple boundary conditions in AceFEM.
I am dealing with coupled problem simulations (displacement and magnetic potential) and therefore I have to apply ...
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2
votes
1
answer
142
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How to solve Neumann boundary ODE with shooting method?
$\rho(x)$ is the distribution function.
I'm trying to solve the following equation:
$D_t\frac{\partial^2\rho}{\partial x^2}-\frac{\partial (v_0\rho)}{\partial x}=0$
$D_t\frac{\partial\rho}{\partial x}-...
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3
votes
1
answer
105
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How to solve PDEs for function $\Psi(z,\bar{z})$ dependent on independent variables $z,\bar{z}$? (Wirtinger derivatives)
For the past few days, I have been struggling to convey to mathematica to solve a PDE that is in terms of the independent variables $(z,\bar{z})$. I know mathematica supports solving PDEs with respect ...
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1
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1
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133
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How to set a adiabatic boundary conditions for a convection function?
$\rho(x,t)$ is the probability function, $x\in[-1,1]$.
I'm trying to solve the convection function with adiabatic boundary condition as follows:
$$
\partial \rho/\partial t=D_t\frac{\partial^2\rho}{\...
- 85
4
votes
1
answer
187
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Set Neumann Boundary Condition in NDEigensystem function
I want to get the eigenvalue and the eigenfunction of the following partial differential equation:
$$ -(\frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2})\psi_n (x,y) + [\frac{1}{4}(x^...
- 41
3
votes
1
answer
257
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Semi-classical approximation of modified Schrodinger's equation on a sphere leads to ndsz warning
I know this error is very common. I checked out a good number of proposed solutions to this problem, but unfortunately, none of them helped in my case.
I would appreciate any help or hints on how to ...
- 33
3
votes
2
answers
133
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What bump function to use in a system of partial differential equations?
I am solving a system of three time-dependent partial differential equations on a circular domain, using the finite element method. However, in the outer part of the domain ($r>R$) the equations ...
- 31
6
votes
2
answers
264
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Extract 2D quad mesh from 3D hexahedral mesh
I would like to extract 2D mesh of outer surface of 3D meshed object.
Let's say I have 3D mesh data from here and I import the data into Mathematica.
...
- 611
1
vote
1
answer
97
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It is possible to use a different stress tensor than Cauchy stress tensor when creating a custom material law?
I would like to use Mathematica to solve some solid mechanics problems, which will include an implementation of a different model than the ones that Mathematica offers. The way how to write custom ...
- 330
4
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1
answer
120
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NDSolve for Fluid Flow - Monitor Residuals
I'm using NDSolve for fluid flow and would like to monitor the convergence of the solution more closely. I have a simple stationary case set up. NDSolve should return the solutions for u,v and p. ...
- 401
3
votes
2
answers
169
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Inactive nonlinear ODE system results in NDSolveValue::femcnmd warning
I am currently trying to solve a set of 1D steady state ODEs using NDSolveValue in the form of Inactive[Grad] and ...
- 181
3
votes
3
answers
158
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Iterative pde solution NDSolve && NIntegrate
I try to solve a diffusion pde depending on a timedependent argument.
Step by step I have no problem to evaluate several solutions:
first step (timefunction 0):
...
- 42.9k
3
votes
2
answers
140
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How to refine FEM mesh for steady state 1D problem?
I am solving a system of 3 steady state 1D ODEs, however the system consists of component that has sharp changes at x = 1, which is very hard to capture. Is there a way to specifically increase the ...
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4
votes
1
answer
101
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3D Mesh refinement near sphere boundary and on surface revolutions
I am trying to solve an advection-diffusion problem inside surface of revolutions. I have high velocity gradients near the boundary of the bounding surface. Is there a way to refine the mesh near the ...
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3
votes
1
answer
100
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Error Meshing with ToElementMesh (ToElementMesh: Cannot set region holes.) for certain objects
I have had a problem properly meshing certain .obj files, where others are meshed successfully.
Here is an example of a successfully meshed .obj:
Whereas, using the code at the bottom which includes ...
- 363
3
votes
1
answer
77
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Keeping mesh coordinates unchanged for Implict Region [duplicate]
I am trying to generate a 3D mesh for Finite Element simulations. I need to provide some precomputed inputs to the mesh points and will like my mesh to be the same for a given shape. However, ...
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1
vote
1
answer
151
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Getting error message "The minimal damping factor of 1/10000 has been reached"
As a very beginner into Mathematica, I encounter error message as shown below when I am solving the system of three second order ODEs numerically using ...
- 181
4
votes
1
answer
153
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Finding sub-regions in an STL file for Finite Element
I use an external software (Amira) to segment X-ray tomography images and then create a surface mesh which I can then import into Mathematica as an STL file. This file has two enclosed regions, ...
- 3,683
0
votes
0
answers
70
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Using NeumannValue in finite element method to replace a derivative boundary condition in NDSolve to overcome a computational overflow
I am trying to implement and evaluate the function GeneratePsiOfX. The definition of GeneratePsiOfX is:
...
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0
votes
1
answer
119
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Finite Element NDSolve with input data at node points
I am trying to solve a steady-state advection-diffusion problem of the following form:
$-D \nabla^2 T + \nabla \cdot (\mathbf{u} T) = -1$. I will be solving this problem in a 3D geometry (typically ...
- 75
3
votes
1
answer
120
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Solve PDE with consraints
I am trying to solve the following problem of the free fall dynamics under gravity of a inextensible horizontal string attached at its end, in a 2D vertical plane. If I'm right, that is the governing ...
- 14k
1
vote
1
answer
213
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Properly Updating Particle Motion in 3D Electric Field Simulation
I have a code (very bottom of post) which plots a static electric field as it passed through some metal sheet with an aperture in it.
I seek to observe the motion of some N charged particles (point ...
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0
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77
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Transient darcy flow equation
I can solve the following stationary Darcy problem:
$div(\nabla u)=1$
with
$ u = 0 \in \Gamma_d$
...
- 2,820
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votes
0
answers
62
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Meshing Error on Imported obj file
I am trying to import a .obj file to be used in a static electric field simulation. I am able to successfully run the simulation with certain other aperture geometries (see here: < https://www....
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1
vote
0
answers
73
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Simulating the Response of Charged Particles to Apertures with Inhomogeneous Electric Fields Passing through them
I have produced a simulation which allows me to observe a static electric field produced by a charged plate as it passes through some complex apertures in a different, oppositely charged metal plate.
...
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3
votes
2
answers
109
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Defining Dirichlet Boundary Conditions on an Imported 3D Object with Apertures in it
I am trying to simulate a static electric field (in 2d and 3d) as it passes through a couple of apertures in a 3D "metal sheet" (model imported as a .obj file) given here:
https://www....
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5
votes
1
answer
84
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NDEigensystem: 1D problem with discontinuous coefficients
I am trying to use NDEigensystem to solve the 1D problem
-cs[x]^2 vx''[x] = w^2 vx[x]
with vx[x] and w the eigenfunction and eigenvalue. The coefficient cs[x] is discontinuous at x = -xp, +xp and vx[x]...
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0
votes
1
answer
181
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How to solve 2D Heat equation on rectangle with NDSolve?
I am trying to solve the 2D heat equation $$\Delta u =u_t$$ with Dirichlet boundary conditions on the rectangle $(0,a)\times (0,b)$ and with initial condition $u(x,y,0)=g(x,y)$.
This is my code
...
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6
votes
2
answers
328
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NDSolve for Laplace equation on disk is not working
I want to solve the laplace equation on the disk using NDSolve.
Particularly I want to solve the problem $$\frac{\partial^2 u }{\partial r^2 } +r^{-1}\frac{\partial u }{\partial r }+r^{-2}\frac{\...
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1
vote
1
answer
132
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PDE with tangential derivative condition along boundary. NDSolve not working
I'm considering the following PDE
$$
\begin{align}
\left[\cos\theta\frac{\partial}{\partial r}-\frac{\sin\theta}{r}\frac{\partial}{\partial\theta}\right]\left[\sin\theta\frac{\partial}{\partial r}+\...
- 681
8
votes
1
answer
490
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Droplet of water-alcohol mixture spreading due to evaporation-caused surface tension gradient
I am trying to solve a coupled system of PDEs for 2 functions h[t,r] and c[t,r], with initial conditions of ...
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4
votes
0
answers
111
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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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