Questions tagged [finite-element-method]
Tag for the usage of "FiniteElement" Method embedded in NDSolve and implementation of finite element method (fem) in mathematica.
3
votes
1answer
42 views
How to increase the integration domain of NDEigensystem without a “non-Hermitian” error?
Recently, I've been using NDEigensystem to solve a two-dimensional eigenfunction equation. The region that I'm solving over is as follows.
...
0
votes
1answer
59 views
Using multiple boundary conditions with NDEigensystem
I'm quite new to Mathematica and to Stack Exchange so I apologise if this question has already been answered.
I've recently been trying to solve a partial differential equation to find the ...
0
votes
0answers
52 views
NDSolve problem with modified heat equation [on hold]
I am having a problem while solving a modified version of the heat equation. The code is as follows:
...
4
votes
1answer
64 views
How to make a 2D region on the surface of 3D volume?
I am trying to define an area on a volume that I can use for a boundary condition. This is a minimum working example to show the problem my real problem involves stress analysis.
I define a region ...
2
votes
1answer
58 views
Using NDEigensystem to find 100 eigenvalues
I'm using "NDEigensystem" to calculate a Sturm-Liouville problem, for which the first 100 eigenvalues are needed. The code is like this:
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3
votes
1answer
32 views
NDSolveValue::bcedge: Boundary condition is not specified on a single edge of the boundary of the computational domain
I'm solving a Schrödinger's Equation in 1d, where $\Omega$ is the domain, bcs the periodic boundary condition, init the initial condition.
...
2
votes
1answer
52 views
1
vote
0answers
73 views
Problems with the eigenvalues calculated using NDEigenvalue
I'm trying to solve a Sturm-Liouville problem like
$\qquad -\psi''(z)+(\frac{1}{z}+2\,z)\psi'(z)=\lambda\,\psi(z)$
using NDEigensystem in order to learn how to ...
3
votes
2answers
68 views
Solution to eigenvalue BVP using NDEigensystem to high precision
I'm trying to solve linear (non-self-adjoint) boundary-value problems to as high precision as possible (optimally 1e-15). For example, the below code solves for the first 5 eigenvalues of the harmonic ...
3
votes
1answer
198 views
Solution of Burgers equation with some initial data
Consider the Burgers equation
$$\partial_t u + \partial_x\left(u^2/2 \right) = 0, \quad u(0, x) = u_0(x).$$
eq = D[u[t, x], t] + D[u[t,x]^2/2, x] == 0
How ...
2
votes
1answer
141 views
Coupled PDEs with second order spatial derivative
I'm trying to solve a system of PDE using NDsolve but the following error accors.
NDSolveValue::femcmsd: The spatial derivative order of the PDE may not
exceed two.
Equations:
Qm and Q are ...
2
votes
1answer
75 views
Eigenvalue dependent boundary conditions- mathematica
I am dealing with an eigenvalue problem whose boundary conditions are also eigenvalue dependent.
Could anyone please comment whether Mathematica can numerically solve such a problem? For boundary ...
0
votes
0answers
44 views
How to draw a triangle shape function plot with shape function area being (s, t,1 - s - t)
I want to draw a dynamic graph showing the varying shape of a triangular element with the change in the point P[x, y] as shown below.
I want to find the shape ...
1
vote
2answers
130 views
Eigen value solution of coupled ODEs
I want an eigen value solution of following coupled ODEs: But the code showing errors.
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2
votes
1answer
68 views
NDSolve error: what does “It may help to rewrite the PDE in inactive form” mean?
I am trying to solve a set of partial differential equations numerically:
...
5
votes
2answers
94 views
Holes in ElementMesh with ToElementMesh of ImplicitRegion
I am trying to plot a function in a region below a level curve of the function and within a cell. I have been doing this by calculating an ElementMesh using ...
0
votes
1answer
55 views
NDSolve gives unexpected results when using the method of lines
I've been trying to solve the following PDE using the NDSolve function but it seems something is not working properly. The PDE is a the heat equation on polar coordinates and assuming angular simmetry:...
3
votes
1answer
59 views
Evaluating Hough functions by using NDEigensystem on the Laplace tidal equation
Currently I am looking into the use of Mathematica to solve the classical tidal equation of M. Laplace:
$$\mathcal{F}\Theta+\gamma\Theta=0$$
whose eigenfunctions $\Theta$ are the Hough functions. ...
1
vote
1answer
61 views
Problem solving PDE with boundary conditions
I have the following PDE:
$$
\frac{\partial }{\partial x}\left(G_x \left(\frac{\partial \phi (x,y)}{\partial x}-y\right)\right)+\frac{\partial }{\partial y}\left(G_y \left(\frac{\partial \phi (x,y)}{\...
6
votes
2answers
324 views
Using NDEigensystem to solve the Mathieu equation
To be able to apply the differential equation capabilities of Mathematica to my graduate thesis, I am trying to apply NDEigensystem to an eigenproblem whose solution I know, but I am having some ...
5
votes
1answer
783 views
Mathematica 3D Heat Equation Solution
I've been working on trying to analyze the Heat Equation in water both experimentally and theoretically.
The model goes as: there's a cuboidal bath (of say, 15x7x5 inches) filled with water, and an ...
8
votes
3answers
400 views
New things and limitations in Version 12 numerical differential equation solver?
This question is intended to be a place to summarize users' exemplary experience in solving differential equation with the NDSolve family in MMA’s latest version 12....
3
votes
0answers
45 views
Interface points of NDEigensystem
When solving an eigenvalue problem with "NDEigensystem", e.g. a 1D Eigenvalue problem with the interval composed of different materials, which should be solved by the pure numerical method such as FEM,...
5
votes
2answers
366 views
Numerical methods to solve a continuity equation
What numerical methods can be used to study the initial value problem for the continuity equation where $ u = u(t, x) $
$$
u_t + \nabla\cdot(\boldsymbol b u) = 0, \qquad t \in [0,T], \quad x=(x_1,x_2)...
23
votes
1answer
2k views
How do I use the new nonlinear finite element in Mathematica 12 for this equation?
With Mathematica 12 we get new technology for nonlinear finite elements. Out of curiosity, I just wanted to solve the following equation
$$
\frac{d}{dx} \left( c(x) \left[\frac{d}{dx} u(x)\right]^p \...
2
votes
1answer
69 views
Meshing control of NDEigensystem
I have to solve an Eigenvalue problem originating from the Electrodynamics. It is a 2-D problem with a rectangular region. More specifically, there is a hole on a rectangle made by magnetic material. ...
3
votes
1answer
34 views
Is there a way to automatically use triangular elements in ToElementMesh [closed]
I have some simple code to generate a mesh over a rectangle.
...
1
vote
1answer
79 views
Periodic boundary conditions with multiple variables
I am trying to numerically solve the following first order coupled differential equations numerically, where i is an integer (can be set to zero), ...
4
votes
1answer
89 views
Sign of conservative convection coefficient in a formal (Inactive) PDE
Consider the PDE
$$\nabla \cdot (
- \color{blue}{\texttt{c}} \;\nabla u
- \color{blue}{\texttt{alpha}} \; u) = 0
\tag{std}\label{std}
$$
where
...
1
vote
1answer
35 views
Uneven distribution of nodes by ToElementMesh[]
We are using FEM package to generate mesh in a circular sector. Somehow mesh becomes dense in upper right corner. Is there any way to circumvent this uneven distribution?
...
1
vote
1answer
99 views
Solving Laplace equation in spherical coordinates
I was trying to solve Laplace's equation for a spherical capacitor, which is not difficult by hand, just to figure out the commands so I can eventually try something more complicated. Then, I ran into ...
6
votes
2answers
243 views
Specific numerical eigenfunctions of Helmholtz equation in 3D for ellipsoids
I am trying to compute the eigenfunctions of an oblate spheroid (a=75 cm and b=60 cm) using Mathematica's FEM package and Chris' answer from here. Specifically, I am looking for eigenfrequencies ...
2
votes
2answers
120 views
Contact with rigid obstacle in AceFEM
Does anyone of you know how to specify the simulation when a deformable body is affected by contact with some rigid body? I think it should be possible, but I am unable to find it in the manual.
16
votes
4answers
622 views
How to apply different equations to different parts of a geometry in PDE?
I want to solve two coupled partial differential equations on two dimension.
There are two variables v and m. The geometry is a ...
4
votes
1answer
152 views
Neumann boundary condition is not satisfied
I want to solve the diffusion equation on a disk centered at (0,0) with a radius of 1. I also want the flux at a radius of 0.8 to be zero. I have this initial condition at time zero:
...
7
votes
2answers
317 views
How to diminish computation time when nonlinearity appears in 2D heat conduction equation?
I am trying to simulate heating and melting of the steel plate by means of FEM.The model is based on nonlinear heat conduction equation in axial symmetry case.
The problem statement is the next:
$$
\...
2
votes
1answer
93 views
NDSolve with Finite Element ignoring terms in partial differential equations?
Solving a 1D dispersive wave equation with NDSolve and the finite element method seems to give completely wrong results. Consider the 1D PDE below
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3
votes
1answer
129 views
How to specify non-reflective boundary conditions when NDSolving two coupled first order PDEs?
Due to a lack of fruitful answers after 3 days, this question has been reformulated in a more direct way compared to its first version.
Consider the telegraph equation problem expressed as a system ...
6
votes
0answers
66 views
Direction of NeumannValue on boundary
When solving partial differential equations NeumannValue is used to specify the flux across the boundary. For normal fluxes the detailed notes state
They appear on the boundary ∂Ω of the region Ω ...
10
votes
2answers
122 views
ToElementMesh of Region with Hole
When I try to mesh the following region it fails. Why? Is there a workaround?
...
1
vote
1answer
89 views
Absorbing/Derivative Boundary Conditions
I am attempting to solve a differential equation, however I am having issues implementing boundary conditions that reduce the impact of reflections/instabilities.
I've had a look at similar ...
13
votes
2answers
555 views
Meshing the cow
As a simple example for applying stl-files I took "cow" out of MMA example data. I'm able to discretize the Graphic without problems
...
2
votes
1answer
85 views
Access to the temporary solution in NDSolve with StepMonitor
I want to step-monitor at each time step of a spatio-temporal NDSolve (using the finite element method) the maximum bending of the function sampled over the curent mesh. For this I first need access ...
5
votes
3answers
245 views
How to create “Volumemesh” from closed “surfacemesh”?
Given a surface region (MesgRegion netz2D), for example
...
3
votes
2answers
85 views
Making NDSolve choosing by itself a spatial meshing leading to correct integrated results
In a previous post, I was asking how to force a fine spatial meshing in NDSolve using the FiniteElement method. The solution was
...
4
votes
3answers
84 views
Forcing at least $n$ spatial steps in solving a 1D spatio-temporal PDE problem with NDSolve
I want to solve the telegraph equation with a spatial discretization forced at 200 points. I tried:
...
10
votes
4answers
398 views
Poisson equation with pure Neumann boundary conditions
Dear Mathematica users,
I would like to numerically solve a, as the title says, Poisson equation with pure Neumann boundary conditions
$-\nabla^2(\psi)=f$
$\nabla(\psi)\cdot \text{n}=g$
Is it ...
2
votes
1answer
136 views
Numerically solving the Laplace equation in a 2d cylinder
Consider the following Laplace equation and boundary condition $$\begin{equation}\begin{cases} \Delta \theta(r,\phi)=0
\\ \int d \vec{\ell}\cdot\nabla \theta(r,\phi)=2\pi \end{cases} \end{equation}$$...
7
votes
1answer
161 views
Absorbing Boundary Condition for Complex/Coupled PDE
Context: This question is relevant to the physical problem of an excited leaky cavity. The boundary condition on the inside of the cavity is Dirichlet. The other end of the cavity is partially blocked ...
18
votes
3answers
410 views
