Questions tagged [finite-element-method]
Tag for the usage of "FiniteElement" Method embedded in NDSolve and implementation of finite element method (fem) in mathematica.
517
questions
2
votes
0answers
22 views
Solving the Stokes equation for planar Marangoni flow with FEM
Background
I would like to numerically solve the stationary Stokes equation from fluid dynamics
$\eta_i \nabla^2 \vec{u}_i - \nabla p = 0$
with the incompressibility condition
$\nabla \cdot \vec{u}...
2
votes
1answer
63 views
Laplace equation DirichletCondition ignored
My goal is to find out force between two parallel identical disks with Voltage difference.
To solve this, I tried to use laplace equation.
And below is my code.
where R is radius of disks, d is ...
4
votes
1answer
81 views
How to mesh a region with inclusions touching the boundary
Suppose you have a region composed of two materials. You define the inclusions of material 1 through, e.g., disks, ellipsoids, ...
2
votes
2answers
109 views
Finding eigenvectors of a differential operator
How can I find the eigenvalues and eigenvectors(numerically) of the below matrix equation:
$
\qquad \hat{A}\left({\begin{array}{c}
y_1(x,\theta)\\
y_2(x,\theta) \\
\end{array} } \right)=
...
9
votes
2answers
158 views
The FEMDampingElements operator failed
I am using Mathematica's (v12.0) NDSolveValue method to solve a finite element method problem (Navier-Stokes equations for a compressible gas). During the initialization process at t==0, I repeatedly ...
4
votes
2answers
126 views
NDSolve::ntdvdae: Cannot solve to find an explicit formula for the derivatives
I am facing these error messages,
NDSolve::ntdvdae: Cannot solve to find an explicit formula for the
derivatives. NDSolve will try solving the system as
differential-algebraic equations.
plus
...
4
votes
1answer
84 views
Adaptive Meshrefinement NDSolve&FiniteElements
In a simple example I try to solve the heat equation using NDSolve and Method->"FiniteElement". I know that NDSolve gives ...
3
votes
2answers
54 views
Checking NDEigensystem Results
I'm looking to verify the output of a call to NDEigensystem. I'm doing this by plotting the operator acting on the Interpolating Function outputs versus the ...
3
votes
1answer
68 views
Coupling DirichletCondition of one dependent variable to the value of the second
Maybe due to my limited experience with PDEs solving I could not find the answer to the following issue. Let's say we have a simple advection along a line:
...
0
votes
1answer
72 views
Nonatomic expression expected at position 1 in First[None]
This is a follow-up question to an earlier question:Solving a system of PDEs on a piecewise polynomial domain.
I tried to solve the system of equations from one of my previous post with the different ...
6
votes
3answers
447 views
Compare FEM mesh with the mesh created within Mathematica
This is a follow-up question to an earlier question: Make uniform mesh with quad elements
Question: How to solve system of equations with NDsolve on the mesh created in Ansys in order to compare it ...
1
vote
1answer
49 views
How do I formulate a Dirichlet boundary condition for which the boundary depends on the other variable?
I am trying to solve the Poisson equation on a cylindrical grid.
$$
\frac{1}{r^2} \frac{\partial}{\partial r} r^2 \frac{\partial f(r, \theta)}{\partial r} = n(r, \theta)
$$
Analytically, there is ...
3
votes
3answers
357 views
Nearly equally spaced 3D-mesh
How to mesh a volume (3D region) with nearly equaly spaced vertices?
Example: Disk with radius 50 and height 15
...
2
votes
0answers
94 views
Why doesn't NDEigenSystem give smooth eigenfunctions? [closed]
I'm looking for smooth solutions of the 1D Helmholtz equation
$\left[\frac{d^{2}}{dx^{2}}+k_{0}^{2}\epsilon(x)\right]\phi=0$
with homogeneous Dirichlet boundary conditions, where the permittivity $\...
3
votes
1answer
63 views
Unexpected error when implementing FEM in MoL SpatialDiscretization
I cannot figure out why the following piece of code
...
2
votes
1answer
59 views
1
vote
1answer
62 views
Why does domain size change results of NDSolve? / How to overcome this?
this is a follow-up on a previous question which was answered, but it turned out that I was running in circles...
I have the following code:
...
5
votes
1answer
190 views
Thermal conduction (Annulus, 2D): Missing boundary conditions
The thermal conduction problem, described in polarcoordinates can be solved
...
3
votes
1answer
67 views
Unable to use ElementMarker in DirichletCondition with structured quad mesh
I would like to use ElementMarker in a DirichletCondition on a structured quad mesh, but I am receiving the error:
...
1
vote
1answer
80 views
Solving system of PDEs with NDSolve
I am trying to solve a system of coupled PDEs with zero-flux boundary conditions on a large domain.
I have two problems:
1) Is there a possibility to use results of NDSolve as inititial conditions? ...
5
votes
1answer
140 views
One dimensional heat exchange on a ring: Periodic solution
Subsequent I consider the transient heat exchange problem of a ring in polar coordinates.
The ring is heated in a small range 0<\[CurlyPhi]<20° and cooled ...
5
votes
1answer
127 views
Understanding PeriodicBoundaryConditions
Every thing works fine in a simple example with periodic boundary condition u[ 2,y]==u[0,y] from documentation of ...
3
votes
1answer
86 views
Problem with complex eigenvalues in periodic Sturm-Liouville problem
I'm having trouble using NDEigenvalues to obtain the first few eigenvalues for a differential operator on the circle of radius one-half.
$\qquad Lf(x) = f''(x)+ (-...
6
votes
1answer
219 views
Controlling dynamic time step size in NDSolveValue
Statement of problem
I'm writing a script to calculate the temperature of a 2D system with time-dependent heat deposition. The heat deposition is a square wave pulse of duration w = 10^-6 seconds, ...
8
votes
1answer
184 views
Finite element for coupled 1D and 3D equations
This is a renewed post for this question, since the old post is already 2 years old and the problem hasn't been solved completely.
The problem is to solve heat conduction with robin type boundary ...
5
votes
1answer
164 views
How to increase NDSolve accuracy for 2nd order ODE?
My attempt to NDSolve a 2nd order nonlinear ODE
...
0
votes
1answer
85 views
PDE-DirichletCondition needs to be linear
I am trying to solve the following multi-field problem in MMA 12, however, this probelm cannot be solved, i.e., error:
DirichletCondition [...] needs to be linear.
I attached the code here:
<...
2
votes
1answer
160 views
Solving multi-field problems in MMA 11.3
Based on the PDE model proposed by @Schumacher Solving a second order coupled PDE system, the one dimensional multi-field Problem I would like to solve such benchmark test:
namely:
u(x): ...
4
votes
1answer
86 views
control FEM grid size for 1D regions
I need to manage the mesh size for finite element method solution to a differential equation, where properties change over two regions. This is for one dimension. I created a boundary mesh of three ...
8
votes
2answers
209 views
Make uniform mesh with quad elements
I have the following code that generates a finite element mesh with triangular elements which by using command ToQuadMesh I convert to the quadrilateral elements, but I am not able to make the uniform ...
1
vote
1answer
103 views
How to solve wave equation with finite elements when material properties vary continuously over a region
I am solving the one-dimensional wave equation over regions where the bulk modulus (and thus the wave speed) vary continuously over a region. The current version seems to assume that the material ...
2
votes
1answer
57 views
Cross coupling in DirichletCondition not supported — conflict with documentation?
Mathematica 12.0.0.0 happily solves the trivial coupled differential system as follows:
...
6
votes
2answers
91 views
How to refine a linear FEM mesh in three regions?
I am trying to solve the one-dimensional wave equation with a frequency dependent source function over three intervals with varying velocity. I need to refine the mesh over the low velocity regions ...
4
votes
1answer
97 views
Line-Dirichlet Boundary NDSolve
I have defined such a Dirichlet boundary conditions which fixes the nodes in a line, however, the results show that only two nodes are fixed, not the nodes in a line,
Code:
...
2
votes
1answer
142 views
MMA 12: Transient plane stress problem
Based on the numerical example enter link description here which is proposed by @Hugh and @user21, then, I continue to
solve transient plane stress problems (...
4
votes
1answer
138 views
Wave equation: Understanding PeriodicBoundaryCondition
Inspired by the interesting question 202542 I try to solve the wave equation with coupled boundary conditions
u[x,t==1 ]==u[x,t==x/2]
I tried
...
3
votes
0answers
80 views
How to use an interpolating function as an intial condition for a PDE? [closed]
I want to be able to approximate a PDE, but my eigenfunction is an Interpolating function. Is there a way I can use an interpolating function as an initial condition in the PDE.
For Example:
...
5
votes
2answers
120 views
Using NDSolve on wave PDE on string, when solution given at 2 different times instead of initial velocity?
This is a PDE taken from a Maple document. Mathematica DSolve currently unable to solve it.
I wanted to verify Maple solution using NDSolve. This is string of length 1, fixed on the left, and free ...
1
vote
1answer
77 views
Solidification Problems in MMA
can we define such intial value and BCs for a solidification problem in MMA using Finite Element:
1.) initial value:=1 for a plate
2.) in this plate we have to define dirichlet bcs for a whole ...
10
votes
2answers
306 views
Solving Cahn-Hilliard equation: LinearSolve: Linear equation encountered that has no solution
I have built the Cahn-Hilliard Eqs. in MMA (Mixed Formulation, second order), However, it doesnot work in MMA using Finite Element.
LinearSolve: Linear equation encountered that has no solution.
And ...
1
vote
1answer
61 views
Random intial conditions using finite element method
How can we define the initial value for Cahn-Hilliard problem (links) using FEM in MMA?
Complete test code (I am using MIXED formulation for C1 Problem):
...
2
votes
0answers
79 views
Non constant coefficient in heat equation
I have to solve the following heat equation over a cylindrical domain.
In cylindrical coordinates the PDE Equation reads:
...
4
votes
2answers
110 views
Automatic solution to label boundary elements with BoundaryMarkerFunction
Preparations
Mathematica 11.3, Windows.
Let us say I have a rectangular region with 10 little holes inside. Their coordinates are given by positionList. The ...
2
votes
1answer
70 views
AceGen incremental values of degrees of freedom
I need to operate with incremental values of my rotational degrees of freedom in my FE code. But I wish this incremental rotations to be dependent on the actual rotations, that I use as degrees of ...
2
votes
1answer
77 views
Does 2D time dependent Schrödinger equation example work?
I have entered the example: www.wolfram.com/mathematica/new-in-10/pdes-and-finite-elements/solve-a-wave-equation-in-2d.html
into 12.0, and gotten an error message in the uifWave assignment. It says,...
3
votes
1answer
51 views
Problem with interpolating function returned by NDEigensystem
I'm trying to evaluate interpolating function returned by NDEigensystem at a point but Mathematica won't evaluate it.
...
7
votes
1answer
128 views
How to solve this 1st-order linear ODE system with a few discrete eigenvalues?
I am trying to solve the eigensystem of a 1st-order linear ODE system in the region $(-\infty,\infty)$ and with Dirichlet boundary condition at the infinities
$$
-i\partial_xu(x)+f^*(x)v(x)=\lambda u(...
2
votes
3answers
160 views
Problem with boundary condition 2D heat transfer
I want solve this 2D Heat transfer:
So at Mathematica:
...
1
vote
1answer
73 views
Errors from NDSolve [closed]
I'm trying to solve a system of PDEs with periodic boundary conditions using NDSolve. This works if I don't specify an initial condition (but is uninteresting, ...
3
votes
1answer
138 views
Mathematica cannot compile complex-valued interpolated PDE coefficients? (NDSolve, Finite Elements)
Bug introduced in 11.1 or earlier, fixed in 11.3 or earlier.
The following PDE
pde = I Cos[x y] D[u[x, y], x] + Laplacian[u[x, y], {x, y}] == 0;
Is happily ...
