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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2
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1answer
97 views

Problems with Neumann (zero flux) boundary conditions

I have the following code: ...
1
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1answer
66 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
221 views

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

The thermal conduction problem, described in polarcoordinates can be solved ...
3
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1answer
89 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
115 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
158 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
200 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
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1answer
113 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
296 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, ...
9
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1answer
245 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 ...
7
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1answer
280 views

How to increase NDSolve accuracy for 2nd order ODE?

My attempt to NDSolve a 2nd order nonlinear ODE ...
0
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1answer
119 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
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1answer
204 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
114 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
249 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
118 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
88 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
106 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
124 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
157 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
157 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
88 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
136 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
89 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 ...
11
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2answers
425 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
65 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
115 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: ...
5
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2answers
174 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
77 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
88 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
67 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
148 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
225 views

Problem with boundary condition 2D heat transfer

I want solve this 2D Heat transfer: So at Mathematica: ...
1
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1answer
75 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
239 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 ...
2
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1answer
115 views

Variation of the biharmonic equation with Neumann conditions

I am currently writing a script to plot the solution of a variant of the biharmonic equation. In this case the equation I want to solve is ...
0
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1answer
112 views

Interpolation function error: The quality of the underlying mesh is too low

Consider a dataset BplustoPiXlight.dat (alternative link). I import it and try to interpolate: ...
4
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1answer
75 views

Difficulty in specifying mesh refinement

I am trying to give a region within a 3D volume a finer mesh than the rest of the volume. My problem is more complicated but here is a minimum working example. I define a 3D cuboid and try and have a ...
-1
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1answer
65 views

Coupled PDEs: Wave and String Equations

I need to solve a system of mixed string and wave equations. Omitting some constants it looks like this: $$u_ {\text {yy}} (y, t) - u_ {\text {tt}} (y, t) = \varphi _{t}(x, y, t)$$ $$\nabla _{\{x,y\}}...
9
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3answers
658 views

How to set interface conditions for optical waveguide in NDEigensystem?

I have been working on waveguide mode analysis using FEM in Mathematica for a week, but I haven't succeeded until now. The optical fiber-like waveguide is featured with different refractive index in ...
4
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1answer
183 views

Hat function(UnitTriangle[x]) is really applicable in Finite Element Method?

I am learning finite element method(galerkin method) for solving ode/pde. when searching this topic, I often see examples using the hat functionUnitTriangle[x] as ...
1
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1answer
67 views

ElementMeshInterpolation and C1 splines

I am trying to use NDSolve`FEM`ElementMeshInterpolation on a triangular structured grid constructed from a Delaunay triangulation with zero area triangles dropped. ...
2
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0answers
77 views

Formulating equations for 3D stress in the finite element method

I would like to know how you formulate equations for the finite element method for stress calculations. We know the answer because user21 has put it here. It involves usage of ...
2
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1answer
107 views

NDSolve cannot evolve Gaussian wave packet with small width

I want to solve a 1d wave equation with initial conditions: $$ u(x,0) = f(x) = e^{-(x - x0)^2/2\sigma^2} \ \ \text{and}\\ u_t(x,0) = - f_x(x) $$ The second condition is the advection equation and ...
0
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1answer
87 views

NIntegrate::femrdim: FiniteElement method can only be applied to regions of embedding dimension 1, 2, or 3

As in the title: I'm trying to Nintegrate over an ImplicitRegion, this error appears. No idea what it means. Nothing in the docs. It appears on this line: ...
66
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13answers
3k views

Future enhancements for the finite element method

How should the finite element method (FEM) framework in the language be extended to be more useful? With the release of version 12.0 alI fundamental FEM solvers (linear, nonlinear, stationary, ...
2
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1answer
193 views

Solving a system of PDEs on a piecewise polynomial domain

I wish to solve following system of equations with Dirchlet and Neumann boundary conditions on an piecewise polynomial (cubic spline) shaped domain as showed here. ...
3
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2answers
93 views

Node numbering and element numbering for a mesh

I want to create a mesh with the following The rows and columns control. For example, a mesh of 6 by 3. But the code shown below has no control over rows and columns. Instead, it has some ...
9
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3answers
356 views

Stress analysis in axisymmetric bodies

I would like to do some finite element calculations in axisymmetric cylindrical coordinates. I wish to calculate stress in terms of {r,z} coordinates. The radial ...
0
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0answers
54 views

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