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

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4
votes
2answers
85 views

MeshRefinementFunction missing points

I'm doing some FEM on a rectangular region with a spherical cavity: ...
12
votes
1answer
196 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
74 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 ...
7
votes
1answer
110 views

Bug? Problem with derivative of interpolating function from FEM

Bug introduced in 10 or earlier and persists through 10.3.1 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 ...
7
votes
0answers
343 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 ...
10
votes
1answer
123 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
80 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
78 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
109 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
263 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
96 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
58 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
72 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
76 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
72 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
124 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
163 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
112 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
94 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
225 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
128 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
66 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
108 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 ...
12
votes
1answer
380 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 ...
2
votes
1answer
125 views

Derivative on uneven grid using interpolate

I have a following problem: I have an uneven 2D grid of points with unknown function value. Let's take some nasty region: ...
0
votes
1answer
149 views

Improving NDSolve computation speed for 3D stationary PDE

Continuing my last question, I am trying to solve 3D Schrodinger equation (with mass equals to 1) and with no potential (I will add a potential later). The analytical solution for this equation is ...
2
votes
1answer
110 views

Swinging Beam example from Help. Not Understanding/Not Working

To help me understand finite element analysis with Mathematica I have been reading the Finite Element Method User Guide in Help and am stuck on the example in Coupled PDEs. Here there is a static beam ...
7
votes
3answers
312 views

FEM Solution desired for “Plate with orifice” deflection: Application of Boundary Conditions and use of Regions

I found the deflection of an orifice plate (circular plate with a hole) subject to uniform pressure using Mathematica's NDSolve functionality. The plate is fixed at its outer circumference and is ...
11
votes
2answers
159 views

Integration of a PDE solution over a custom-defined subdomain

Preamble: In my previous question I raised a problem of a custom-chosen integration of the solution of a PDE. In that case it was an integration along a line lying within the PDE domain. The solution ...
3
votes
1answer
116 views

Increasing NDSolve computation range for 3D stationary PDE

I am trying to solve 3D Schrodinger equation (with mass equals to 1) and with no potential (I will add a potential later). My goal is to set boundary conditions on the outer boundary of a sphere and ...
2
votes
1answer
230 views

Potential flow over cylinder with FEM: Pressure field is flipped

Much in the fashion of a few problems already answered on Mathematica.SE (1, 2), I am trying to solve the Laplace equation in velocity potential $\phi$ to simulate irrotational, inviscid flow over a ...
4
votes
1answer
161 views

NMinimize fails on Mesh?

Context I want to identify the minimum of a solution of a PDE found on a mesh. Problem I do not understand why NMinimize fails on a mesh? As a test case, ...
3
votes
2answers
242 views

Generating Meshes with Conforming Boundaries for FEM

I would like to solve a PDE on an annulus with some boundary condition that relates the inner circle to the outer circle. (For example, periodicity along radial lines). If I use a finite element ...
3
votes
0answers
160 views

StreamPlot of potential flow from a finite element calculation [closed]

I am trying to calculate a potential flow past a thick plate. The finite element calculation seems to go well but I am finding it difficult to get a nice plot of the flow. The stages below are, ...
1
vote
0answers
76 views

Transient PDE with a complex boundary condition [closed]

I am trying to solve a PDE, but one of the boundary conditions is complex, because it includes an integral over the function that I am looking for. The code is shown below ...
1
vote
2answers
120 views

NDSolveValue and DirchletConditions for cylindrical disk

my aim in this is to model the current flow of a cylindrical disk with one end set to potential 0 and the other end set to potential 1. In this section of code I am trying to find the scalar ...
20
votes
2answers
394 views

Getting rid of spikes in the PDE solution

Bug introduced in 10.0 and fixed in 10.3 Note: In 10.0, Rationalize[fd, 0] was needed or mesh generation would fail. Preamble: I am solving a PDE in a domain ...
3
votes
1answer
172 views

Specifying NeumannValue for Axial load instead of transverse load (Plane Stress situation)

I am trying to simulate a bar/link element under axial tensile load. The link is of unit thickness and I may use a plane stress model. A plane stress model is an approximation that may be used for ...
4
votes
1answer
254 views

Use FEM Solver for System of Nonlinear PDEs with Nonlinear Coefficients - Reaction-Diffusion

I am trying to solve a complex transient reaction-diffusion problem numerically in 2D. Let's take a simple system to start, say $$ A+B\rightarrow C \\ C \rightarrow A+B $$ with reaction rate $k_1$ ...
2
votes
1answer
118 views

ToElementMesh fails on DodecahedronIcosahedronCompound

Context I would like to compute the eigenmodes of a DodecahedronIcosahedronCompound. Why? Because it is cool! and I wonder how it ringsā€¦ Starting with: ...
6
votes
1answer
199 views

How to create an ElementMesh of a Sphere

I want to create an ElementMesh of a "sphere". To reduce the computational effort I want to use HexahedronElement; the ...
1
vote
0answers
96 views

How to Implement a “Function Object” suitable for NDSolve and Finite Element Method?

I have a bunch of methods that shoud return an expression that behave like a function, i.e. an expression that, when supplied with suitable arguments, evaluate to something. A simple ...
9
votes
1answer
148 views

Kernel Crash while using “ValuesOnGrid” method of InterpolatingFunction

Bug introduced in 10.0.0 and fixed in 10.2.0 I was experiencing some kernel crash while using "ValuesOnGrid" method of an ...
6
votes
1answer
284 views

3D FEM with holes

I'm trying to create a finite element mesh with some spherical holes. To my mind the behavior is erratic but generally fails. I'm using MMA 10.0.2. In the following 3 different sets of holes are ...
1
vote
1answer
204 views

Generating a boundary mesh from a list of points

I have a list of points from which I am trying to generate a mesh: ...
42
votes
2answers
1k views

Numerically solving Helmholtz equation in 3D for arbitrary shapes

Context While studying manifold Learning I got interested in finding the eigenvectors of the Laplacian. (also in connection to this problem of solving the heat equation) Following this and that ...
15
votes
1answer
289 views

Eigenfunctions of the Laplacian on an arbitrary mesh

So, I've constructed a mesh over which I'd like to find eigenfunctions of Laplace's equation with a free boundary (a zero Neumann boundary condition along the edge). Mostly because I figured an ...
2
votes
1answer
147 views

Solving a time-dependent structural mechanics problem with Finite Element

I'm trying to solve a time-dependent structural mechanics problem with Finite Element. I modified one of the last samples in the "Solving Partial Differential Equations with Finite Elements" Tutorial. ...
2
votes
0answers
304 views

Choosing FEM element type and mesh refinement

I have only recently been introduced to Mathematica's(v10.0) FEM capabilities. I understand that for solving PDEs on non-uniform shapes via NDSolve, Mathematica ...