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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12 votes
3 answers
779 views

FEM doesn't output exactly the same solution for exactly the same code?

Consider this toy example: ...
  • 59.4k
4 votes
0 answers
121 views

Inactive PDE terms in FEM without Neumann boundary conditions

I am solving a Poisson-like set of PDEs for u[x,y] and v[x,y] in the square region ...
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9 votes
2 answers
322 views

How can we apply specific boundary conditions with NDEigensystem?

I'm solving an eigenvalue problem with special b.c. mentioned in the paper Edge states in gated bilayer-monolayer graphene ribbons and bilayer domain walls. (See Eq.(3)(6)(7) and the paragraph after (...
1 vote
1 answer
94 views

Define a function on a MeshRegion

This looks like a simple question with the answer to be easily found, but unfortunately I could not find it either on the web or in the documentation browser. Let us assume we have a MeshRegion ...
1 vote
1 answer
74 views

Numbering of auxiliary symbols in AceGen generated code

I have a general question regarding the numbering of auxiliary symbols in AceGen. Consider this example (taken from the AceGen manual, only the language is switched to ...
3 votes
1 answer
107 views

Understand NDEigensystem::stlin

I am trying to solve Eq.3 and reproduce Fig.2 of this paper using NDEigensystem but fail, what is wrong with my code? ...
2 votes
0 answers
78 views

3D BoundaryMeshRegion Minkowski difference via RegionErosion Failure

I need to be able to produce Minkowski difference of an arbitrary BoundaryMeshRegion and a cylinder. ...
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4 votes
1 answer
63 views

Total number of corner nodes and middle nodes in a given mesh with 2nd order triangular elements

I have created a mesh consisting of 2nd order triangular elements, on the domain as follows. ...
7 votes
1 answer
302 views

Refining mesh size leads to absurd results for a coupled heat transfer FEM model

I have been recently solving a conjugate heat transfer problem, which involves fully-reversing or reciprocating flow of fluid over a heated block of solid. The problem is 2D and the temperature field ...
  • 297
3 votes
0 answers
74 views

What is the correct way to create an animation in parallel using the result of NDSolve?

For example, in the following code ParallelTable takes 23 minutes: ...
  • 329
2 votes
2 answers
135 views

NDSolve Extrapolating boundary conditions for FiniteElements

I'm trying to solve a 1+1 (1d time + 1d space) partial differential diffusion equation. My NDSolve call look basically like this: ...
  • 21
1 vote
0 answers
54 views

Problem meshing hexahedron

I have observed the following problem when meshing with the Hexahedra function. A rectangular body can be meshed by ToElementMesh and ToBoundaryMesh. A non-rectangular solid cannot. The difference ...
  • 634
3 votes
1 answer
89 views

Making a mesh from a set of points

In conjunction with this question I find I am having difficulty making a mesh using a given set of points. The overarching objective is to make an interpolation function from an irregular set of ...
  • 15.6k
2 votes
1 answer
131 views

Directly calculating the cyclic steady state of a time-periodic conjugate heat transfer problem

Context The following transient problem is the reciprocating (i.e., fully reversing) flow of a fluid $0<x<L, 0<y<d$ over a thick heated block $0<x<L, -e<y<0$ until the system ...
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3 votes
1 answer
126 views

Conjugate heat transfer modelling of reciprocating flow crashes for long flow times

The following transient problem is essentially the reciprocating (i.e., fully reversing) flow of a fluid over a thick heated block until the system reaches a cyclic steady-state (i.e., the system ...
  • 297
1 vote
0 answers
73 views

Some conceptual doubts about steady and transient solvers of the NS + energy equations

Recently, I have been solving some transient and steady, flow and heat transfer problems in Mathematica. The transient problem is essentially the reciprocating (i.e., fully reversing) flow of a fluid ...
  • 297
1 vote
1 answer
139 views

How to solve a reaction-diffusion?

I would like to solve a PDE system reaction-diffusion type (2D spatial + 1 temporal) coupled as described below. Another question of this same system was solved here: System of nonlinear PDE 2D (...
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3 votes
2 answers
75 views

How to create an ElementMesh with at least two triangle elements at each corner?

Based on this simple example of a triangle mesh ...
2 votes
1 answer
67 views

Confusion in Eigenvalue and eigenfunction distribution using NDEigensystem [duplicate]

I have been using NDEigensystem to solve the Schrodinger equation for different potentials. However, whenever the potential has its minimum in the negative y-axis, ...
  • 1,094
0 votes
1 answer
156 views

On the Dirichlet integral

Continuing this topic, once the Dini-Neumann problem is solved: $$ \begin{cases} \Delta f = 0 & \text{on} \; \Omega \\ \frac{\text{d}}{\text{d} n} f = y\,n_x - x\,n_y & \text{on} \; \partial\...
  • 4,392
6 votes
1 answer
292 views

Numerical solution of a partial derivative problem

WARNING: a couple of days ago I posted a similar question, but due to the impossibility of DirichletCondition[] to handle "cross-coupling of dependent ...
  • 4,392
3 votes
2 answers
146 views

Solving a system of differential and integral equations in Mathematica

Here is a system of differential equation I am trying to solve: $$ u''(x) - a(x) u(x) + b(x) v(x) = 0 \quad (1)$$ $$ \gamma v''(x) + a(x) u(x) - b(x) v(x) = 0 \quad (2) $$ where $a(x)$, $b(x)$ are ...
2 votes
0 answers
70 views

Make NDSolve return solution over only part of domain

Consider the following pair of PDEs, for which I will solve in the mesh built below. The mesh needs to be much larger than the region of interest to mimic boundary conditions "at infinity". ...
3 votes
1 answer
205 views

Strange chattering in derivative of InterpolatingFunction returned by NDSolve using FEM

When using the Finite Element Method of NDSolve to solve a set of ODE, the resulting InterpolatingFunction showcases a strange chattering in its derivatives. This ...
  • 933
5 votes
1 answer
223 views

Solving Coupled nonlinear Differential Equations For Eigenvalue And Eigen functions

I tried to solve coupled nonlinear differential equations from this paper https://sci-hub.hkvisa.net/10.1016/j.jcp.2019.109058 to see eigenvalues and eigenfunctions in different dimensions. At first, ...
1 vote
0 answers
58 views

Using FEM to solve 1D coupled PDES [duplicate]

I have been attempting to numerically simulate the electron and lattice temperature of a two-layer metal subject to laser heating (1d two-temperature model). I have read related questions such as ...
2 votes
1 answer
81 views

Step size of InterpolatingFunction returned from NDSolve using FEM

I would like to retrieve the step size information of an InterpolatingFunction returned from NDSolve while using the Finite Element Method (FEM) (...
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2 votes
0 answers
58 views

Coupled PDEs with different dimensions and boundary conditions

The geometry of the problem is described by a cylinder inside a rectangular domain. The equations describes the region in between them. I have 2 PDEs for U(x,y,z) in the bulk region and V(z) for -0.5&...
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4 votes
1 answer
107 views

FEM breaks because of Abs(f'(x))

I am trying to solve a 1d differential equation in Mathematica using the finite element method. I have successfully implemented the problem in a commercial software called COMSOL, but I like to use ...
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5 votes
1 answer
121 views

Steady state heat equation/Laplace's equation special geometry

I would like to solve the Laplace's equation in between the square domain and a disk. However, using the code below, I was able to generate mesh but not able to obtain results with correct boundary ...
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2 votes
1 answer
72 views

How to use ElementMeshInterpolation to interpolate to deformed mesh?

I'm solving a problem in solid mechanics, but I ran into problems when I tried to plot some stuff over the deformed mesh, because the plots are cut off. They end when the undeformed mesh ends. ...
  • 330
3 votes
1 answer
92 views

AceFEM higher order elements fail basic test

I was trying to perform a simple test, as some results that we obtained from AceFEM were not matching with the results we obtained from other methods. Here, I have a simple biaxial test on a cube of ...
  • 33
2 votes
2 answers
111 views

3D FEM - How to define Point-Markers for an ElementMesh object created with ElementMeshRegionProduct

I want to create a 3D grid based on a 2D mesh, on the surface of which I want to assign point-marker for certain regions. The mesh created in the sample code is a fluidic Y-structure, at whose inputs (...
  • 31
2 votes
0 answers
64 views

Problems with using NDSolveValue to solve two-dimensional Fokker-Planck equation

When I use NDSolveValue to solve the following two-dimensional Fokker-Planck equation, it works well: ...
6 votes
1 answer
189 views

Finite element method solution data, Mathematica 13.1

I just upgraded to Mathematica 13.1 and encountered the following issue (this is just code from the first few lines of the FEM programming documentation): ...
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4 votes
2 answers
214 views

Animating a potential function (eigenfunctions of Laplace's equation) - something has changed

I had this working with Kuba's help some time ago see here but something has changed. I am using version 13.0. The animation lay out has changed to this configuration where the animation bar is ...
  • 15.6k
4 votes
3 answers
254 views

Multiply differential operator matrix and shape function matrix

I'm new to Mathematica. Say $N(\xi, \eta)$ (NSHAPE in code below) is a 2x6 matrix: $$ N(\xi,\eta) = \left[ \begin{array}{cccccc} 1 -\xi -\eta & 0 & \xi &...
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0 votes
0 answers
100 views

How to modify global stiffness matrix before solving it by SMTNewtonIteration[]?

I'm trying to use the Model Order Reduction technique to reduce the stiffness matrix in AceFEM/AceGen. But there is a problem with the manipulation of the global stiffness before solving it by ...
1 vote
0 answers
48 views

How to find the relationship between parameters and eigenvalue via DEigensystem or NDEigensystem?

I have a system with some parameters(like masses,couplings). But it seems DEigensystem/NDEigensystem only works when theses parameters are specified? My code is below: ...
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0 votes
0 answers
27 views

NDSolveValue with derivative boundary conditions not working [duplicate]

I have some nonlinear PDE that I'm trying to solve. I have defined the equation, eqJ, and am running the following code: ...
  • 1
-1 votes
1 answer
119 views

How to find complex eigenvalues via NDEigensystem? [closed]

I'm using NDEigenvalue to solve following uncoupled eigenvalue problem: ...
  • 205
2 votes
2 answers
256 views

How should I define the boundary conditions of free end and fixed end scenarios for 1D Wave Equation?

The 1D wave equation is $$\frac{\partial^2 u(x,t)}{\partial t^2} = c^2 \frac{\partial^2 u(x,t)}{\partial x^2}$$ where $c$ is the wave speed, $c^2=E/\rho$, $E$ is the Young's modulus and $\rho$ is the ...
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1 vote
0 answers
129 views

Solid mechanics - traction boundary condition in the reference configuration

Both SolidBoundaryLoadValue or NeumannValue can be used to specify the traction boundary condition, because ...
  • 330
4 votes
1 answer
141 views

Nonlinear PDE with a trivial and nontrivial solutions: how to?

I am solving the following PDE: eqMain = D[z[x, y], {x, 2}] + D[ z[x, y], {y, 2}] - (a - x/(x^2 + y^2 + 0.0001))*z[x, y] - z[x, y]^3==0; with the zero ...
4 votes
1 answer
142 views

Problem with NDSolve for 1st order non-linear system of PDEs

I wish to solve the PDE system \begin{align} x_u^2+y_u^2+\left(xx_u+yy_u \right)^2&=1\\ x_v^2+y_v^2+\left(xx_v+yy_v \right)^2&=1 \end{align} subjected to $x(0,v)=0$ and $y(u,0)=0$. However, ...
6 votes
2 answers
252 views

SolidMechanicsStress returns, that the stress is equal to zero

Bug introduced in 13.1 and fixed in 13.2.0 I am trying to compute a deformation and a stress of a material with a custom material law. I have successfully computed the deformation using ...
  • 330
3 votes
1 answer
217 views

Solving 3D Nonlinear Integral Partial Differential Equation

I am trying to solve Equation number (1.2) numerically in MATHEMATICA. This equation is solved in the papers https://arxiv.org/pdf/2205.05193.pdf, https://arxiv.org/pdf/2202.13264.pdf, and https://...
10 votes
3 answers
326 views

Can NDSolve be initialized with a close solution?

I have a set of 4 first order ODE with 4 initial conditions to be met. It models a simple damped pendulum like the one described here. What changes is the damping term and I switched to first order ...
  • 933
4 votes
1 answer
113 views

Is it possible to remove an element during computation in AceFEM?

The title says it all. I know there have been a lot of enhancements in the recent versions of AceGen/AceFEM. I would like to know if there is a possibility of removing an element during computation (...
  • 1,243
10 votes
1 answer
184 views

1D diffusion problem: Troublesome NeumannValue

Bug introduced in 13.1 or earlier and fixed in 13.2.0 Mathematica solves the diffusion problem (two Neumann-conditions) ...

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