Questions tagged [finite-element-method]

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

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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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 ...
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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 ...
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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 ...
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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
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1answer
63 views

Unexpected error when implementing FEM in MoL SpatialDiscretization

I cannot figure out why the following piece of code ...
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1answer
59 views
1
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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
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1answer
190 views

Thermal conduction (Annulus, 2D): Missing boundary conditions

The thermal conduction problem, described in polarcoordinates can be solved ...
3
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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: ...
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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
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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
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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 ...
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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
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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
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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
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1answer
164 views

How to increase NDSolve accuracy for 2nd order ODE?

My attempt to NDSolve a 2nd order nonlinear ODE ...
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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: <...
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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
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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
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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 ...
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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
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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
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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
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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
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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
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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
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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
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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 ...
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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
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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
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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): ...
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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
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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
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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
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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
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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
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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
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3answers
160 views

Problem with boundary condition 2D heat transfer

I want solve this 2D Heat transfer: So at Mathematica: ...
1
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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
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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 ...