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

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3
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0answers
19 views

How can I plot a “slice” of the mesh for a 3D plot?

I'm using NDSolveValue to solve the Laplacian equation for this geometry: I want to view the mesh that NDSolveValue is using, so I do the following: ...
3
votes
1answer
42 views

Why is NDSolveValue giving these problems in 3D that it didn't have in 2D?

I'm trying to do the same thing I did in this thread (ignore the actual question I was asking about, I just linked it to show the geometry and equation solving I'm doing), but this time for 3D instead ...
2
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1answer
60 views

Will the solution NDSolveValue finds outside of the region I give it give me bogus results?

I'm using NDSolveValue to solve Laplace's equation for a relatively simple system. I have two rectangles, separated by a small gap, which I define using RegionDifference: ...
0
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0answers
61 views

What code can I use to calculate, integrate, and visualize the electric field for an arbitrary shape? [duplicate]

I'm looking for a Mathematica program/function with which I'd be able to specify two objects in 3D space, each at a different surface potential, and then the program would calculate (using Finite ...
4
votes
1answer
88 views

How do you refine the elements of a 3D mesh?

Response to Answer below. Original Question: I am trying to refine a 3D mesh in a certain region. This seems relevant but does not work for me. I start by making the region which consists of a box ...
3
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0answers
63 views

ColorBars or PlotLegends for ElementMeshSurfacePlot3D

I want to produce a colorbar legend to the output from ElementMeshSurfacePlot3D (Mathematica 10). The pde was solved using NDSolveValue (FEM pdesolution is the resulting interpolating function) over a ...
5
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0answers
133 views

Dealing with a nonlinear PDE using FEM

As far as I can see in the Mathematica documentation center, there are no built-in ways for solving nonlinear PDEs using Finite Element Method (FEM). I am dealing with a simple nonlinear ...
6
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0answers
68 views

benchmark of Mathematica's FEM?

Does anyone have any numbers on how mathematica compares to other commercial (eg ANSYS) or free FEM softwares (eg. FreeFEM++, FEniCS, elmer)? If this is too vague say solving the diffusion equation in ...
3
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2answers
93 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
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1answer
68 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
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1answer
118 views
3
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2answers
73 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
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1answer
156 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
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1answer
103 views
8
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2answers
131 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: ...
5
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2answers
128 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 ...
22
votes
1answer
270 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
140 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 ...
7
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1answer
69 views

Wrong result for mesh generation when using integers for mesh size

Can somebody explain me why this happens? ...
3
votes
1answer
123 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
129 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
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1answer
55 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
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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
137 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
209 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
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2answers
106 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
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1answer
68 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
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1answer
85 views

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

I used the following equations to solve a structural problem: ...
2
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0answers
90 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
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1answer
154 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
68 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
215 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
314 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 ...
5
votes
2answers
122 views

MeshRefinementFunction missing points

I'm doing some FEM on a rectangular region with a spherical cavity: ...
14
votes
1answer
284 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 ...
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0answers
102 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
182 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
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0answers
422 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 ...
12
votes
1answer
198 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 ...
6
votes
1answer
127 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
95 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
125 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
410 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
159 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
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0answers
23 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
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0answers
69 views

Loop Construct with NDSolveValue for Iterative Solution [on hold]

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
99 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
78 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
233 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 ...