Tag for the usage of "FiniteElement" Method embedded in NDSolve and implementation of finite element method (fem) in mathematica.

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3
votes
2answers
79 views

Assigning Element Markers to 3D FEM Mesh

I have created a 3D graphic using GraphicsComplex and then use ToElementMesh to generate a 3D Mesh that I want to solve a PDE on, but I cannot figure out how to apply ElementMarkers to the Boundaries. ...
0
votes
1answer
53 views

Using Neumann boundary conditions

I had a semi-related physics problem I needed to solve analytically (which I have already done), but I am now curious how I would go about numerically solving the entire system in Mathematica. ...
2
votes
1answer
102 views
3
votes
2answers
64 views

DiscretizeRegion does not include the boundary specified in ImplicitRegion (10.1)

I am trying to do some 3D PDE solving, and I keep running into problems with boundary conditions because my meshed boundaries are not what I expected. For example, the following code ...
12
votes
1answer
140 views

How to access FEM shape functions

A couple of days ago I asked here about surface meshes and plotting on surfaces. Now I have another question: How can I access the surface or boundary element shape functions? I would like to ...
6
votes
1answer
99 views
8
votes
2answers
118 views

How to assign Element marker at boundary edges

How to assign marker at the boundary edges as 1, 2, 3, 4 respectively and set all of the inside elements of region as 0? for example: Code: ...
4
votes
2answers
107 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 ...
20
votes
1answer
253 views

How to model wooden joints with mathematica's FEM?

This is a dovetail joint: and I'd like to see the stresses and deformation on the joint.I haven't seen any modeling of disconnected regions with FEM, only connected regions, so I'm curious if you ...
2
votes
1answer
88 views

solving Stokes equations for Force=0 boundary condition

Say you want to solve the movement of a particle in a viscous fluid such that the force on the particle is zero. In general, the solution is trivial since one has no-slip boundary conditions, ie the ...
5
votes
1answer
65 views

Wrong result for mesh generation when using integers for mesh size

Can somebody explain me why this happens? ...
3
votes
1answer
111 views

how to speed up FEM-NDSolve for similar boundary conditions?

I need to solve several stoke's equations for very similar boundary conditions, which represent particles in a fluid with different velocities U[i]. I'm interested in computing the force acting on the ...
8
votes
1answer
116 views

Beam deformation due to localized force distribution

I would like to simulate the deformation of a beam which is fixed on one end and has some localized forces applied along the top. I have been inspired by this Mathematica example: ...
1
vote
1answer
54 views

How to define “DiffusionCoefficients” in InitializePDECoefficients that depend on ElementMarker?

Modelling a Poisson Equation on piecewise constant material, ElementMarkers on the PointElements are used for the boundary ...
0
votes
0answers
25 views

Discretization of a region for NDSolve using [duplicate]

I would like to mesh the region below in order to use it for a calculation by means of NDSolve. Could anyone help me to discretize this region for NDSolve using. Thank you very much. ...
3
votes
4answers
132 views

Invalid region for small angles. To Element Mesh. Finite element method

I would like to mesh the region below in order to use it for a calculation by means of NDSolve. Could anyone help me to discretize this region for NDSolve using. Thank you very much. ...
6
votes
0answers
193 views

Problems with NDSolve for solving coupled Schrödinger-like PDEs with perfectly matched layer boundary condition

I'm trying to solve a full-vectorial wave equation for an arbitrarily shaped wave guide, by using NDSolve and perfectly matched layer (PML) conditions. The PML ...
4
votes
2answers
102 views

Integrating an interpolating function

I have been using the following NDEigensystem command to generate the eigenfunctions of the laplacian with a square domain: ...
2
votes
1answer
66 views

NeumannValue and FiniteElement Methods : BC not respected

I have noticed on several of my personal cases some issue with the BC using NeumannValue. Let me illustrate the problem. I take the 1D example of ...
0
votes
1answer
82 views

How to implement NDsolve for thermo structural code? finite - element - method

I used the following equations to solve a structural problem: ...
3
votes
0answers
116 views

Dealing with two dimensional Black-Scholes partial differential equation

As far as I can see in $\mathtt{http://mathematica.stackexchange.com/}$, there are some questions/answers to solve Black-Scholes PDE, but all for one dimensional case. So, I hope this question be ...
2
votes
0answers
86 views

ElementMesh (rendering?) issue

The appearance of the following ElementMesh is bad as you can see for example on the inside surface of the shell. The same problem happens converting to a ...
3
votes
1answer
148 views

Errors Solving Elliptic PDES with FEM

I am trying to solve the equation below governing transversely isotropic plane strain in cartesian coordinates with the given boundary conditions based on code found here using Mathematica 10.1 on OSX ...
2
votes
1answer
65 views

How to draw the shape of a 2D, 2nd order, element of an ElementMesh

I just want to create a drawing of the shape of 2nd order, two dimensional, finite element like a TriangleElement. Something like ...
3
votes
1answer
204 views

How to solve 3D heat equation with Neumann B.C

I'm trying to solve the 3D heat equation on a cuboid to know if all the perimetric surfaces of a Cuboid achieve the desired temperature of a 873K on deadline time of 2 hours. i have convection on all ...
14
votes
2answers
289 views

Finite Element Method and ElementMeshInterpolation issue in v10.3

Bug introduced in 10.3 I recently installed Mathematica v10.3 and checked a project I was working on few months ago under Mathematica v10.1. In this project I solve a PDE with ...
4
votes
2answers
109 views

MeshRefinementFunction missing points

I'm doing some FEM on a rectangular region with a spherical cavity: ...
14
votes
1answer
278 views

Non Standard Eigenfunction Plots of the Laplacian Over the Unit Square

I have recently been plotting eigenfunctions of the laplacian over the unit square using the NDEigensystem command. However, I have noticed something in the plots ...
1
vote
0answers
98 views

Numerically Solving Helmholtz over the Rectangle - Why does this code only give eigenfunctions of the form $u_{m1}$ [closed]

I have been following the method for numerically solving the Helmholtz equation in this example (the answer by User21) and have come across two problems. I have been implementing the method for a 2x1 ...
8
votes
1answer
175 views

Bug? Problem with derivative of interpolating function from FEM

Bug introduced in 10 or earlier and fixed in version 10.4 I am really not sure if this is a bug or I am missing something very trivial. QUESTION: What I am missing in order to obtain the partial ...
7
votes
0answers
412 views

Problems when solving a nonlinear PDE system with NDSolve

The nonlinear PDE system is actually extracted from a research paper published in 2000 Here is the paper link The authors solved the system by using an ordinary differential equation integrator in ...
11
votes
1answer
192 views

How to enforce a symmetric solution with FEM?

I'm solving the laplace equation in a domain with holes, and I need to compute the integral of the gradient on the boundary of these holes. For that I define a mesh and solve the laplace equation ...
5
votes
1answer
110 views

how to create a FEM mesh with “RegionPlot” where the sample points are a function of the position

I need to resolve the diffusion equation in a domain with circular sources (holes). I've tried defining the whole region with holes but the result is very mesh-dependent and not symmetric, so at the ...
2
votes
1answer
93 views

Failure to create a mesh with ToElementMesh [closed]

When I created mesh by function with ToElementMesh, some errors occured. The code below is a minimal example. I can't understand why it failed. ...
1
vote
1answer
123 views

How to creat mesh on the cube's surface?

Now I'm trying to solve a PDE by FEM, and I need creat the 2D mesh on the cube's surface, the figrue below shows my idea. Both the quadrilateral elements and triangle element are OK. I read the ...
14
votes
1answer
361 views

Stress calculations using finite elements

A standard engineering problem is to calculate stresses in a structure due to applied forces. With the inclusion of the finite element method in version 10 this question attempts to investigate how ...
3
votes
1answer
153 views

Finite Elements 3D

Does anyone knows how to solve the Laplace equation in a Sphere domain and with the following boundary conditions: Consider alpha=0. I have tryed the following code, but i don't belive the boundary ...
0
votes
0answers
22 views

Iterating with NDSolveValue in a Do-loop [duplicate]

I am trying to get a differential solution to converge. There are two separate time periods that I am solving for and the entire solution is periodic. I want to use the output from one as the input ...
0
votes
0answers
66 views

Loop Construct with NDSolveValue for Iterative Solution

I can get this code to run but the plots do not depict the solutions that are being evaluated inside of the Do loop. The plots are only showing the initial ...
2
votes
1answer
76 views

Animating Boundary Elements

I am trying to visualise the eigenvectors of a thick disk. I manage to calculate them and look at one but fail to look at more -probably due to using too much memory. I start by making a mesh and then ...
3
votes
1answer
96 views

Kernel crash when evaluating NDSolveValue

I had a code that was working fine and I tried to add an extra few lines to find the solution of the same equation with different conditions. The original NDSolveValue solutions work fine but when it ...
2
votes
0answers
76 views

Eliminating instabilities in a transient finite element solution at a discontinuity near t = 0

I have found a transient solution to the 1D heat equation where the initial condition is discontinuous. The results are accurate except for when time is small. The initial condition looks like this: ...
3
votes
0answers
215 views

FDTD Electromagnetic Simulations with Mathematica

Mathematica has some Finite Element capabilities (as explained here). Do you think mathematica is a realistic/sensible option for electromagnetic simulations? (aka making a movie of electric fields ...
8
votes
1answer
185 views

Finite element boundary breaking

I am trying to model a cantilever beam which can vibrate. On the left the beam is clamped. I am largely following user21 here and also the example in help. I start by doing a static beam which works ...
1
vote
1answer
143 views

Finite Element Mass and Stiffness Matrices

I am attempting to use the finite element method to solve a vibration problem. I am following user21's answer from here which is very helpful. My problem is that I am confused by the use of the mass ...
3
votes
1answer
111 views

How to specify the plot region for ListPlot3D?

Now I'm trying to solve a PDE and the solving domain is not regular, suppose it is a map. I used the finite element method to solve it and every nodes' value have been got, and now I want to use ...
13
votes
3answers
266 views

Piecewise imposes internal boundaries in NDSolve - is this expected?

In the following code I used True as the predicate for DirichletCondition and found that the boundary condition was applied not ...
2
votes
1answer
197 views

Constant Heat Flux Boundary Condition for the Differential Heat Equation

I am attempting to solve the transient heat equation for a very simple geometry and I am getting a junk solution. I have identified two distinct regions (wall and super-heated fluid layer) with their ...
2
votes
2answers
78 views

mesh vertex coloring

So I created a mesh like this: mesh2 = ToElementMesh[FullRegion[2], {{1, 10}, {1, 10}}, MaxCellMeasure -> 1.]; and want to plot it, coloring the squares: ...
4
votes
1answer
152 views

How to find the number of nodes in finite element model

I am using Mathematica version 10 to solve a 2-D elliptic equation by the finite element method. I created a finite element model with a very fine mesh. Would you please suggest me a command to show ...