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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35 views

Interpolation Failing on Data of a Certain Size

I'm trying to interpolate the following unstructured data set so I can compute and plot the gradient. ...
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0answers
49 views

NDSolve Error “message text not found”

I am trying to solve a nonlinear PDE - 1D diffusive heat equation. I'm not sure what is wrong (am new to Mathematica). I'm trying to use https://reference.wolfram.com/language/FEMDocumentation/...
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1answer
118 views

Area of an Annulus (MeshTools<>NIntegrate)

In a very simple example I try to describe an annulus using MeshTools package mesh2D = AnnulusMesh[{0, 0}, { 1 , 2 }, {-Pi, Pi}, {36, 10}]; The area given ...
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1answer
29 views

Creating single AceGen element using the same constitutive model defined for 2 fibre families

I'm currently working with a single constitutive model that describes 2 collagen fibre families that have different element properties. The strain energy density function is W, where there would be 2 ...
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3answers
181 views

Non-Newtonian Momentum Eqn in a rectangular pipe

I am trying to (numerically) solve the momentum eqn for a non-Newtonian fluid in a pipe with rectangular cross section using Mathematica. Here are the assumptions: So, the flow is only in z ...
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53 views

Error when trying to solve elastic PDEs using FEM: “Compile::argcompten: The comparison, LessEqual, is invalid for tensor arguments.”

I'm trying to solve the following linear elastic problem: The pairs of numbers beside each node is the coordinates in meters. The loads are in Newtons. The part of codes that probably have no ...
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1answer
188 views

Transient Heatflow in a Wheel Disc Brake

I try to model the Convection–diffusion equation for a rotating 3D annulus(small thickness): The temperature u[t,x,y,z] is described in cartesian coordinates. ...
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3answers
227 views

Heat Flow in a Pipe

I try to model the transient heat flow in a pipe, assuming that the temperature in radial direction doesn't change: temperature ...
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2answers
170 views

Electrostatics: Finite Elements

I'm messing around with FEM in mathematica and am having trouble solving a very simple problem of the electric field around a unifromly charged sphere. Here is my workflow. ...
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1answer
75 views

NIntegrate over regions, FiniteElement options

I am using NIntegrate to integrate a 3-dimensional region. When I don't set any integration options, I get a warning The global error of the strategy GlobalAdaptive has increased more than 2000 ...
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2answers
129 views

1DPoisson equation with Dirac delta

I was writing my own FEM method to solve the Poisson equation \begin{align} -u'' &= \exp(-c(x-1/2)^2)\\ u(0) &= u(1) = 0 \end{align} where c=100. and I'm reading from the book of Mats G. ...
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2answers
305 views

Generating Mesh of Rotated Graphics

I have a simple geometry that consists of a few rotated rectangles ...
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2answers
126 views

Error trying to solve a 2D elasticity problem using FEM package

I have the following equations $$\frac{\partial{N_x}}{\partial{x}}+\frac{\partial{N_{xy}}}{\partial{y}}=0$$ $$\frac{\partial{N_y}}{\partial{y}}+\frac{\partial{N_{xy}}}{\partial{x}}=0$$ where \begin{...
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1answer
78 views

Eigenvalues and numerical eigenfunctions for similar differential operators

I am looking to numerically approximate the eigenvalues and eigenfunctions for a differential operator I am working with, assuming $\pi$ periodic boundary conditions. Namely, I define the function $...
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1answer
144 views

Poor convergence for first order PDE using FEM (Laplace's equation in a disk)

Consider Laplace's eqn in the unit disk, r^2 D[u[r, t], {r, 2}] + r D[u[r, t], {r, 1}] + D[u[r, t], {t, 2}] == 0. The general analytic solution is easy to work out,...
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2answers
215 views

Solve a one dimensional heat transfer problem with NDSolve

The following problem is a 1-D heat transfer conduction problem: where, I am trying to solve with NDSolve like this way: ...
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1answer
187 views

Curved Dirichlet boundary in FEM

Based on this fascinating blog post (https://blog.wolfram.com/2013/07/09/using-mathematica-to-simulate-and-visualize-fluid-flow-in-a-box/) from a few years ago that shows how to simulate a driven ...
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46 views

internal Neumann boundary for FEM

Following the documentation for NeumannValue (https://reference.wolfram.com/language/ref/NeumannValue.html) gives the impression, that it is only possible to set ...
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2answers
206 views

Solving a steady-state viscous Burger's equation with NDSolve

A steady-state viscous Burger's equation is given by $$ u\,u'=\nu \,u'', \quad x\in (-1,1), $$ $$ u(-1)=1+\delta,\quad u(1)=-1.$$ Here $\nu>0$ is the viscosity, $\delta>0$ is a small ...
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42 views

Is Inactive Form avoidable when using NDSolve for non-linear ODEs

So this is basically the same question as here referring to information provided here. However, I am wondering if this inactive form is always necessary or more of a convenience. For example, ...
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1answer
104 views

Numerical problems when solving a 2-dimensional Fokker-Planck equation

I try to solve a Fokker-Planck equation fpe = D[p[x, y, t], t] + Div[j, {x, y}] == 0; with ...
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1answer
166 views

Heat transport in 1d, two different materials at point contact with NDsolve -

I have two materials touching at a point x=0. 1) The first material lies within the interval [-L1, 0], has diffusion constant D1, and the heat conductivity kappa1. Its left end is kept on time ...
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1answer
81 views

How to use only Neumann boundary conditions and a normalization constraint on a PDE

I'm trying to solve the stationary PDE c = {{5, 0}, {0, 5}}; alpha = {x - 50, y - 50}; pde = Div[-c.Grad[u[x, y], {x, y}] - alpha*u[x, y], {x, y}]; (following ...
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1answer
163 views

Electric field produced by a capacitor consisting of two parallel plates of different lengths

I need to visualize the electrostatic field produced by a capacitor consisting of two parallel 1D plates of different lengths, as shown in the following figure (sorry for the crude drawing), in which ...
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0answers
104 views

Somewhat Singular Sturm-Liouville Equation (With Edition)

I am trying to solve the following Sturm-Liouville equation (i.e., plot the eigenfunctions and calculate the eigenvalues): $$\frac{d}{dx}\left(x²\frac{d}{dx}\right)f(x) + 2f(x) = -\lambda x²f(x)\,,$$ ...
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1answer
112 views

How to solve transient 3D heat equation with robin boundary conditions

Good afternoon! I'm trying to solve the following heat equation: with the following boundary conditions and initial value: Nut I'm getting error while solving it with NDSolve: ...
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1answer
76 views

Finding eigenvalues of the Laplacian on solenoidal (divergence-free) vector fields

In Mathematica it is easy to find eigenvalues of the Laplacian in simple cases. For example, on $\Omega\in \mathbb{R}^2$: ...
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1answer
154 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}...
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1answer
72 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 ...
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2answers
134 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, ...
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2answers
121 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)= ...
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2answers
206 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 ...
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2answers
146 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 ...
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1answer
100 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 ...
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2answers
67 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 ...
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1answer
82 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: ...
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1answer
74 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 ...
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3answers
457 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
57 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
368 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
98 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
67 views

Unexpected error when implementing FEM in MoL SpatialDiscretization

I cannot figure out why the following piece of code ...
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1answer
74 views
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1answer
63 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: ...
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1answer
208 views

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

The thermal conduction problem, described in polarcoordinates can be solved ...
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1answer
82 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
92 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
151 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 ...
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1answer
129 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
93 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)+ (-...