Questions tagged [finite-element-method]
Tag for the usage of "FiniteElement" Method embedded in NDSolve and implementation of finite element method (fem) in mathematica.
579
questions
5
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1answer
88 views
Numeric Solution for 1-D ODE with only Neumann conditions
I tried to solve a simple ODE with only Neumann conditions like
But obviously this doesn't work.
I must add a useless DirichletCondition to make it work
I have verified that the solution is correct, ...
2
votes
0answers
58 views
Problem Solving Steady State Navier Stokes Equations Using Finite Element Method
I am using MMA 12.0.0 on a Mac running OS version 10.13.6.
Before attempting my own problem I am attempting to follow exactly the code in the FEM Documentation Tutorial, as an exercise:
https://...
2
votes
1answer
106 views
Why can't I solve a system of four third-order partial differential equations using NDSolve?
I solve the problem of optimal control. First, I solve a system of two equations (with respect to the variables p, q, V, n) with already optimal conditions (Kopt and Sopt) to check whether it is ...
1
vote
1answer
78 views
System of pde with Neumann boundary conditions
The Ginzburg-Landau equation for a system of squared superconductor with a slit in presence of a uniform magnetic field can be written as a sort of continuity equation with Neumann boundary conditions ...
17
votes
2answers
324 views
3D Elastic waves in a glass
Take an empty glass, hit the side, the glass will make a sound that can be recorded using
...
5
votes
1answer
172 views
Where to get the detailed code of MMA for grid mesh
I know DelaunayMesh can triangulate the specified area, but I can't see the code and partition idea of this built-in function. I want to know how to get the source ...
2
votes
1answer
47 views
Numerical Issues Using Results of NDSolveValue
I am solving Laplace's Eqn. (Cartesians) in 2D in a region which is infinite in x, semi-infinite in y, and bounded by a function of x (h[x] in my code) close to y=0....
2
votes
1answer
186 views
The NDSolvevalue of MMA can not be used to solve the finite element problems according to the stress boundary conditions
The NDSolvevalue of MMA can well solve the finite element problems according to the displacement boundary conditions
...
2
votes
1answer
85 views
How to change boundary conditions during AceFEM analysis?
I'm trying to prestress a sample by a compressive strain of 10 percent and then stretch it by 30 percent. The way I intend to do this is apply the prestress in one step and then have the code run and ...
1
vote
1answer
50 views
Error message when trying to solve 2 coupled PDEs using NDSolve
I'm currently facing a problem when trying to solve 2 coupled PDEs. I get the warning messages:
NDSolve::fembdcc: Cross-coupling of dependent variables in DirichletCondition[IPF==IPB/10,z==5.] is not ...
1
vote
0answers
81 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 ...
4
votes
1answer
102 views
Solving Laplace's equation in 2D using region primitives
I was looking at examples of solving problems in electromagnetism and ran across this question, which was a great example of just that. However, looking at the Dirichlet condition, both answers define ...
1
vote
0answers
53 views
Converting .stl files to meshes for FEA
I'm trying to conduct finite element analysis on imported .stl models from SketchUp. I can't seem to generate an ElementMesh. I think it may be something to do with intersecting boundaries, and this ...
0
votes
0answers
41 views
How to perform adaptive mesh refinement on a 3D element consisting of 4 superimposed meshes on AceFem?
I'm trying to perform adaptive mesh refinement on a body that is composed of 4 separate meshes joined together. The body is composed of the following individual meshes:
...
3
votes
1answer
101 views
Solving Piecewise Differential Equation using NDSolve (coupling at BC)
I am having some issues in dealing with a system of differential equations. I would like to solve a 1D diffusive heat equation across several regions with different material properties. I now have a ...
1
vote
1answer
87 views
Solving Nonlinear Heat Equation with initial Conditions
I have the following setup for the linear heat equation on an infinite rod (see below). This is a pretty standard setup and the initial condition is $e^{-x^2}$. This initial condition is not special, ...
0
votes
0answers
78 views
Ways to decrease computational time
I have created a 2D axisymmetric simulation of the motion of charged particles in an electric field. The electric field is created by a needle attached to a top plate both of which are at -3800V with ...
16
votes
3answers
426 views
Using Regions, can I model a reflecting wavefront?
I was wondering if I could get Regions and Mathematica's shapes to do all the hard work for me in making a "droplet in a pond" simulation. I do not want the "waves" ...
0
votes
1answer
132 views
Solving a Reaction-diffusion system
I'm just a beginner in Mathematica software. I have version 12.
I am looking for a program that will solve a prey-predator system with diffusion. My problem is that I tried a previously posted ...
3
votes
2answers
80 views
Extracting data from InterpolatingFunction 2D surface plot
I would like to directly extract the surface plot data from the solution to a differential equation (using NDSolve). While there are many examples of this I haven't been able to find an example in 2D.
...
3
votes
1answer
246 views
0
votes
1answer
37 views
Can I convert my SMTShowMesh Object into a mathematica graphics object in AceFem?
My question is related to a string of questions Ive asked in the last few days.
I'm trying to superimpose a vectorplot on a3D plot that I've produced on AceFem using the SMTShowMesh Command. I'm ...
5
votes
1answer
137 views
NDSolve::femcmsd: The spatial derivative order of the PDE may not exceed two
I was in the impression that V12 can now handle higher order PDES but for this particular case it fails to produce any solution.
...
2
votes
1answer
74 views
Plotting fibre direction at each node
I was wondering if there was a way to plot the direction vector of a fibre family at each node in AceGen/AceFem? Below is an example of exactly what I want to do but I do not know how to recreate it.
...
4
votes
1answer
76 views
FEM: does the term $\gamma$ in “The Coefficient Form of Partial Differential Equations” has to be an explicit list?
In the FEM documentation, "The Coefficient Form of Partial Differential Equations" is
I am interested in its simplification to
$$
\nabla \cdot (-c \nabla u + \gamma) = 0
$$
where $c$ should be a ...
3
votes
1answer
99 views
Solution of convection dominated PDE with conditions only on the interior of the domain
I'm Trying to solve the following PDE:
$$ \frac{1}{20}\left(2 x_1^2+x_2^2\right) -25\left( \begin{bmatrix} 0\\ \frac{6 \cos(x_1)}{-37 + 3 \cos(2 x_1)} \end{bmatrix}^\intercal \nabla_{x_1,x_2}V(x_1,...
4
votes
2answers
167 views
FEM: Solving the heat conduction with 2D periodic condition
Suppose you have a region $\Omega = [0,P_1] \times [0,P_2]$ which is composed of, e.g., two materials. One material is distributed as inclusions in an embedding material. We split the region as $\...
7
votes
1answer
185 views
Nonlinear elasticity PDE in Mathematica 12
Mathematica 12, Windows 10.
I am trying to solve a PDE in one spatial dimension $R$ and time $t$. I need a solution for displacement $r(R,t)$, radial Cauchy stress $T_{RR}(R,t)$, and radial growth $\...
6
votes
1answer
74 views
How to help NDSolveValue handle the addition of another dependent variable in a set of reaction-diffusion equations
I am trying to use NDSolveValue to solve a system of coupled reaction-diffusion equations in a 2D space (technically 3D cylindrical coordinates, but due to radial ...
3
votes
1answer
60 views
NDSolve Stiffness and Strange Behaviour with Dirichlet Conditions
I working with the following semiconductor potential equilibrium equation for a diode
$$\psi(x)''=e^{\psi(x)}-e^{-\psi(x)}+10^6\text{sgn}(x-(l+r)/2)$$
where $l$ and $r$ are left and right boundaries ...
7
votes
2answers
113 views
Using mesh cell highlighting to override the default rendering of a region
The default rendering of a region can be rather uninformative. Consider this simple example.
DiscretizeRegion[Rectangle[{0, 0}, {2, 1}], MaxCellMeasure -> 2]
...
3
votes
1answer
55 views
About the accuracy of Method -> FiniteElement in NDSolve, version 12.0
In this question, the equation $uu'=\nu u''$, $x\in (-1,1)$, $u(-1)=1+\delta$, $u(1)=-1$, was considered. The question asked about how to solve this differential equation problem in Mathematica. There ...
2
votes
1answer
94 views
Issues with NDSolve when solving a system of two coupled PDEs
I'm trying to solve a system of non-linear reaction-diffusion-advection PDEs numerically using NDSolve.
The two equations are (taken from here):
where $H(x)$ is ...
1
vote
1answer
148 views
Global Stiffness Matrix Assembly [closed]
I am trying to assemble the global stiffness matrix and global force vector from the local stiffness matrix and local force vector using a function Forcestiffness Assembly as follows:
where
FA[no ...
2
votes
0answers
59 views
NDSolve Error “message text not found” [closed]
I am trying to solve a nonlinear PDE - 1D diffusive heat equation.
I'm not sure what is wrong (am new to Mathematica).
I'm trying to use https://reference.wolfram.com/language/FEMDocumentation/...
5
votes
1answer
142 views
Area of an Annulus (MeshTools<>NIntegrate)
In a very simple example I try to describe an annulus using MeshTools package
mesh2D = AnnulusMesh[{0, 0}, { 1 , 2 }, {-Pi, Pi}, {36, 10}];
The area given ...
1
vote
1answer
36 views
Creating single AceGen element using the same constitutive model defined for 2 fibre families
I'm currently working with a single constitutive model that describes 2 collagen fibre families that have different element properties. The strain energy density function is W, where there would be 2 ...
1
vote
3answers
207 views
Non-Newtonian Momentum Eqn in a rectangular pipe
I am trying to (numerically) solve the momentum eqn for a non-Newtonian fluid in a pipe with rectangular cross section using Mathematica.
Here are the assumptions:
So, the flow is only in z ...
1
vote
0answers
55 views
Error when trying to solve elastic PDEs using FEM: “Compile::argcompten: The comparison, LessEqual, is invalid for tensor arguments.”
I'm trying to solve the following linear elastic problem:
The pairs of numbers beside each node is the coordinates in meters. The loads are in Newtons.
The part of codes that probably have no ...
7
votes
1answer
203 views
Transient Heatflow in a Wheel Disc Brake
I try to model the Convection–diffusion equation for a rotating 3D annulus(small thickness):
The temperature u[t,x,y,z] is described in cartesian coordinates.
...
6
votes
3answers
239 views
Heat Flow in a Pipe
I try to model the transient heat flow in a pipe, assuming that the temperature in radial direction doesn't change:
temperature ...
4
votes
2answers
190 views
Electrostatics: Finite Elements
I'm messing around with FEM in mathematica and am having trouble solving a very simple problem of the electric field around a unifromly charged sphere.
Here is my workflow.
...
1
vote
1answer
87 views
NIntegrate over regions, FiniteElement options
I am using NIntegrate to integrate a 3-dimensional region. When I don't set any integration options, I get a warning
The global error of the strategy GlobalAdaptive has increased more
than 2000 ...
8
votes
2answers
140 views
1DPoisson equation with Dirac delta
I was writing my own FEM method to solve the Poisson equation
\begin{align}
-u'' &= \exp(-c(x-1/2)^2)\\
u(0) &= u(1) = 0
\end{align}
where c=100.
and I'm reading from the book of Mats G. ...
10
votes
2answers
314 views
Generating Mesh of Rotated Graphics
I have a simple geometry that consists of a few rotated rectangles
...
5
votes
2answers
146 views
Error trying to solve a 2D elasticity problem using FEM package
I have the following equations
$$\frac{\partial{N_x}}{\partial{x}}+\frac{\partial{N_{xy}}}{\partial{y}}=0$$
$$\frac{\partial{N_y}}{\partial{y}}+\frac{\partial{N_{xy}}}{\partial{x}}=0$$
where
\begin{...
5
votes
1answer
92 views
Eigenvalues and numerical eigenfunctions for similar differential operators
I am looking to numerically approximate the eigenvalues and eigenfunctions for a differential operator I am working with, assuming $\pi$ periodic boundary conditions.
Namely, I define the function $...
4
votes
1answer
165 views
Poor convergence for first order PDE using FEM (Laplace's equation in a disk)
Consider Laplace's eqn in the unit disk, r^2 D[u[r, t], {r, 2}] + r D[u[r, t], {r, 1}] + D[u[r, t], {t, 2}] == 0. The general analytic solution is easy to work out,...
3
votes
2answers
233 views
Solve a one dimensional heat transfer problem with NDSolve
The following problem is a 1-D heat transfer conduction problem:
where,
I am trying to solve with NDSolve like this way:
...
7
votes
1answer
203 views
Curved Dirichlet boundary in FEM
Based on this fascinating blog post (https://blog.wolfram.com/2013/07/09/using-mathematica-to-simulate-and-visualize-fluid-flow-in-a-box/) from a few years ago that shows how to simulate a driven ...
