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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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
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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
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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 ...
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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
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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
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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
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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
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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
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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
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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
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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
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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 ...
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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 ...
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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
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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
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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, ...
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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
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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
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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
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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
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1answer
246 views

2D Oseen equations

Background info: https://en.wikipedia.org/wiki/Oseen_equations ...
0
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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 ...

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