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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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 ...
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 ...
84 views

In a simple example I try to solve the heat equation using NDSolve and Method->"FiniteElement". I know that NDSolve gives ...
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 ...
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: ...
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 ...
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 ...
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 ...
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 ...
94 views

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, ...
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 ...
164 views

How to increase NDSolve accuracy for 2nd order ODE?

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

Problem with boundary condition 2D heat transfer

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