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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19
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3answers
348 views

Inverting differential equation using finite element methods

tl;dr; How to use FEM tools to extract models needed to invert PDEs. Context In astrophysics, one is interested in so-called 'cosmic archeology' which involves recovering the origin of a given ...
-1
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0answers
58 views

How to solve the natural frequency of cantilever beam by mathematical method

I want to calculate the natural frequency of the cantilever beam according to the theoretical method. I find a post on how to solve the free vibration frequency of a cantilever beam with the finite ...
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0answers
66 views

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 ...
4
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1answer
56 views

Piecewise Continuous Linear Basis on a Triangular Mesh

Question Given a FEM mesh, I would like to define a set of basis functions anchored to the mesh, so that any piecewise linear continuous function on the mesh can be expanded over that set. Such a ...
6
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1answer
157 views

Laplace equation with robin boundary conditions

I want to solve the following steady state heat transfer problem with robin boundary condition at the bottom: The following is the code for the transient solution, but how should I change the code ...
6
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2answers
83 views

Penalty function on discrete mesh using Laplace-Beltrami operator?

Context I am interested in extending to the ill-condionned regime the inversion of linear equations arising from inverting differential equations which have been solved via 0-splines over a mesh ...
7
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1answer
1k views

How to solve heat equation with Robin type conditions with NDSolve?

Could you help me please to solve following problem! I need to solve one-dimensional heat equation with Robin type boundary conditions. But Mathematica find only constant solution with no dependence ...
66
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13answers
3k views

Future enhancements for the finite element method

How should the finite element method (FEM) framework in the language be extended to be more useful? With the release of version 12.0 alI fundamental FEM solvers (linear, nonlinear, stationary, ...
3
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1answer
70 views

How to numerically obtain the first ten eigenvalues of a 3D Sturm-Liouville problem

I'm trying to numerically obtain the first ten eigenvalues of a 3D S-L problem via NDEigenvalues but with no success. The problem is given by ...
3
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0answers
59 views

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 $b$, ...
1
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1answer
55 views

Define indicator function of mesh elements

Context I would like to (partially) answer my own question here (ok its a bit cheesy but...) Question I am interested in defining an indicator function which value would be 1 on a cell and ...
8
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1answer
132 views

Why can't I use Inactive[D] in NDSolve?

I have a 2D rectangular domain with -L/2 < x < L/2 and 0 < y < D0, which is divided into two parts, with a ...
23
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2answers
463 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 ...
8
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2answers
207 views

Unexpected 'switch' of partial derivatives when differentiating InterpolatingFunction

Bug introduced in 11.3 or earlier and persisting through 12.1.0 or later In short, there is a simple initial boundary-value problem for which NDSolveValue produces an InterpolatingFunction ...
0
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2answers
75 views

Poisson equation and FEM [closed]

I am trying to solve $u_{xx}+u_{yy}=-[(3x+x^2)y(1-y)+(3y+y^2)x(1-x)] e^{x+y},$ for $0<x<1,0<y<1,$ and homogeneous Dirichlet boundary conditions $u(x,y)=x(1-x)y(1-y)e^{x+y}$ by an ...
4
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1answer
92 views

Using FEM and NDSolve

I have to solve the ODE $u''[t]+u'[t]+\sin {(5t)} u[t]=t^3-t$, with $u[0]=0,u[1]=0,$ with a finite element method and then with NDSolve. Finally, I have to ...
3
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1answer
72 views

Plotting a differential equation with boundary conditions

I have a problem with numerical calculation and plotting of differential equation. Now I set a complicated region to set a boundary condition: ...
5
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1answer
199 views

Understanding PeriodicBoundaryConditions

Every thing works fine in a simple example with periodic boundary condition u[ 2,y]==u[0,y] from documentation of ...
2
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2answers
100 views

An ImplicitRegion with a boundary which is an Interpolated Function is not a ConstantRegion

I create an ImplicitRegion from a box-shaped region with one face replaced by a function h[x,y]. If h[x,y] is a "normal" function, e.g. ...
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4answers
562 views
7
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1answer
521 views

Is it possible to create .stp 3D model from Graphics3D ?

I want to create some 3D solid model by Mathematica, and then export it into stp (step) format for further finite element or finite volume analysis in Fluent/ANSYS or Abaqus. But so far to me, it ...
11
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3answers
1k views

How to create a surface mesh embedded in 3D?

I am working on a problem where I want to optimize current densities on 2D surfaces embedded in 3D to generate magnetic fields. The current density on a surface can be written as a scalar function ...
6
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1answer
136 views

Solving Laplace's equation in 2D using region primitives

Fixed in 12.1 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 ...
11
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3answers
308 views

Why the mesh generated for NDSolve is different from the final plotted mesh?

When I try the following code to solve the Laplace's equation, the mesh generated by bmesh = ToElementMesh[bmesh] is different from the mesh shown in ...
9
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2answers
200 views

FEM Mesh related errors

Bug introduced in 12.0. Fixed in 12.1.0. I try to solve the simple heat transfer equation but there are some errors at the stage of the pre-processing. ...
1
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0answers
94 views

normal derivative for Laplace equation

I am try to evaluate the Neumann boundary conditions for Laplace equation which define as: dy/dn, where n the external normal vector to the boundary, I have: ...
35
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3answers
4k views

Nonlinear FEM Solver for Navier-Stokes equations in 2D

it's me again. I'm trying to obtain a numerical solution to Navier-Stokes equations in 2D in a non-rectangular region. So far, this guide was very helpful, but he is using finite differences, which is ...
0
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0answers
67 views

NDSolve: Which method for fast moving/spreading wavepackets?

I want to model a wave-packet interacting with a non-linear potential. ...
19
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1answer
949 views

Couple a PDE and ODE in NDSolve

I would like to solve an example of non-stationary heat transfer with a coupled PDE and ODE. Let's assume that we have 1 dimensional bar of length $L$ with uniform initial temperature. The right end ...
3
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0answers
66 views

Numerical solution for PDE [duplicate]

I have got the help from the expert ''Nasser'' to write the code for the PDE with variable coefficients and mixed boundary conditions define on a square domain: ...
2
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1answer
115 views

Variation of the biharmonic equation with Neumann conditions

I am currently writing a script to plot the solution of a variant of the biharmonic equation. In this case the equation I want to solve is ...
7
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1answer
94 views

FEM: how to find 2D flow under external forcing?

I'm trying to sovle a 2D Navier-Stokes equation in a rectangular region with no-flow boundary conditions and an external rotating force $f(x,y)=(-y,x)$. I've got the error message: NDSolveValue::...
5
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1answer
132 views

Problem Solving Steady-State Euler Equations in 2D Using FEM

I am working with gas flows, and my Reynolds number is very large (>10^6). Still as a toy exercise, I solve the steady-state Navier Stokes equations for my volume and it seems to work ok for Reynolds ...
3
votes
1answer
43 views

Exporting data from an Interpolating Function

Apologies if this question is repetitive, but I have browsed the questions already posed on exporting data from NDSolve and haven't been able to successfully apply the information I found to my own ...
48
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3answers
4k views

Mathematica vs. Comsol for finite element analysis?

Being relatively new to finite element analysis, I was wondering how expert users assess Mathematica's capabilities in solving PDEs via the finite element method compared to other commercial tools (e....
2
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2answers
180 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 ...
22
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3answers
11k views

How to solve ODE with boundary at infinity

y''[x] - x y[x] == 0 y[0] == AiryAi[0], y[∞] == 0 The analytic solution to this ODE is the Airy function y[x] == AiryAi[x] ...
3
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1answer
84 views

How to tell mathematica polar coordinates belong to mesh?

Context I want to solve a PDE via FEM on a Disk. If I use a Square I can write ...
17
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3answers
731 views

Gravitational potential created by a thin disc using FEM and NDSolve

Context I would like to compute the torque that a (thin) disc applies onto a ring. I.e. I would like to try to understand what is the impact of this outer ring on the inner disc in the simulation ...
4
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2answers
193 views

Not sure how to set up the Laplacian/Poisson Equation

As stated, I am having trouble trying to set up a Laplacian/Poisson Equation. I have boundary conditions with this too, and I've tried using the DirichletCondition function, but I don't know what I'm ...
2
votes
1answer
121 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 ...
5
votes
1answer
101 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
82 views

Problem Solving Steady State Navier Stokes Equations Using Finite Element Method [closed]

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://...
1
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1answer
87 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 ...
2
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1answer
190 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 ...
5
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1answer
178 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 ...
3
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1answer
53 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....
1
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1answer
353 views

Boundary Problems

I am trying to study what happens to a wave as it passes different boundaries. This is the working wave equation defined on a plane ...
10
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3answers
641 views

How can i construct a 3D surface pass through a curve defined by formula and some other controllable points?

For example, If a have a curve defined by x^2+y^2=1 and z=0, and some isolated points having z coordinates, Can I construct a 3D surface passed through? It's better if I can change the surface shape ...
2
votes
1answer
89 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 ...

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