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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62 views

How to use an interpolating function as an intial condition for a PDE?

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: ...
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2answers
75 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
53 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 ...
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2answers
135 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 ...
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1answer
51 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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62 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: ...
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2answers
91 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 ...
1
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1answer
68 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,...
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1answer
44 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. ...
6
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1answer
117 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(...
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3answers
141 views

Problem with boundary condition 2D heat transfer

I want solve this 2D Heat transfer: So at Mathematica: ...
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1answer
67 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
82 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
57 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 ...
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1answer
62 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
65 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 ...
0
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1answer
55 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\}}...
6
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3answers
503 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 ...
3
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1answer
68 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 ...
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1answer
49 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
59 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
78 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 ...
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1answer
74 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: ...
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12answers
2k 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
155 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
59 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 ...
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3answers
281 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 ...
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0answers
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1answer
61 views

How to change the default normalization for NDEigensystem?

I'm currently using NDEigensystem to solve a PDE that describes a particle travelling on a hyperbolic (negatively curved) surface. However, the eigenfunctions that are returned by NDEigensystem are ...
3
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1answer
67 views

How to increase the integration domain of NDEigensystem without a “non-Hermitian” error?

Recently, I've been using NDEigensystem to solve a two-dimensional eigenfunction equation. The region that I'm solving over is as follows. ...
0
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1answer
82 views

Using multiple boundary conditions with NDEigensystem

I'm quite new to Mathematica and to Stack Exchange so I apologise if this question has already been answered. I've recently been trying to solve a partial differential equation to find the ...
4
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1answer
72 views

How to make a 2D region on the surface of 3D volume?

I am trying to define an area on a volume that I can use for a boundary condition. This is a minimum working example to show the problem my real problem involves stress analysis. I define a region ...
2
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1answer
85 views

Using NDEigensystem to find 100 eigenvalues

I'm using "NDEigensystem" to calculate a Sturm-Liouville problem, for which the first 100 eigenvalues are needed. The code is like this: ...
3
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1answer
44 views

NDSolveValue::bcedge: Boundary condition is not specified on a single edge of the boundary of the computational domain

I'm solving a Schrödinger's Equation in 1d, where $\Omega$ is the domain, bcs the periodic boundary condition, init the initial condition. ...
3
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1answer
66 views

Creating a mesh from a very thin layer

I have the following code which works just fine: ...
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0answers
81 views

Problems with the eigenvalues calculated using NDEigenvalue

I'm trying to solve a Sturm-Liouville problem like $\qquad -\psi''(z)+(\frac{1}{z}+2\,z)\psi'(z)=\lambda\,\psi(z)$ using NDEigensystem in order to learn how to ...
3
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2answers
74 views

Solution to eigenvalue BVP using NDEigensystem to high precision

I'm trying to solve linear (non-self-adjoint) boundary-value problems to as high precision as possible (optimally 1e-15). For example, the below code solves for the first 5 eigenvalues of the harmonic ...
3
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1answer
215 views

Solution of Burgers equation with some initial data

Consider the Burgers equation $$\partial_t u + \partial_x\left(u^2/2 \right) = 0, \quad u(0, x) = u_0(x).$$ eq = D[u[t, x], t] + D[u[t,x]^2/2, x] == 0 How ...
2
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1answer
161 views

Coupled PDEs with second order spatial derivative

I'm trying to solve a system of PDE using NDsolve but the following error accors. NDSolveValue::femcmsd: The spatial derivative order of the PDE may not exceed two. Equations: Qm and Q are ...
2
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1answer
91 views

Eigenvalue dependent boundary conditions- mathematica

I am dealing with an eigenvalue problem whose boundary conditions are also eigenvalue dependent. Could anyone please comment whether Mathematica can numerically solve such a problem? For boundary ...
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0answers
59 views

How to draw a triangle shape function plot with shape function area being (s, t,1 - s - t)

I want to draw a dynamic graph showing the varying shape of a triangular element with the change in the point P[x, y] as shown below. I want to find the shape ...
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2answers
143 views

Eigen value solution of coupled ODEs

I want an eigen value solution of following coupled ODEs: But the code showing errors. ...
2
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1answer
88 views

NDSolve error: what does “It may help to rewrite the PDE in inactive form” mean?

I am trying to solve a set of partial differential equations numerically: ...
5
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2answers
115 views

Holes in ElementMesh with ToElementMesh of ImplicitRegion

I am trying to plot a function in a region below a level curve of the function and within a cell. I have been doing this by calculating an ElementMesh using ...
0
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1answer
75 views

NDSolve gives unexpected results when using the method of lines

I've been trying to solve the following PDE using the NDSolve function but it seems something is not working properly. The PDE is a the heat equation on polar coordinates and assuming angular simmetry:...
3
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1answer
63 views

Evaluating Hough functions by using NDEigensystem on the Laplace tidal equation

Currently I am looking into the use of Mathematica to solve the classical tidal equation of M. Laplace: $$\mathcal{F}\Theta+\gamma\Theta=0$$ whose eigenfunctions $\Theta$ are the Hough functions. ...
1
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1answer
71 views

Problem solving PDE with boundary conditions

I have the following PDE: $$ \frac{\partial }{\partial x}\left(G_x \left(\frac{\partial \phi (x,y)}{\partial x}-y\right)\right)+\frac{\partial }{\partial y}\left(G_y \left(\frac{\partial \phi (x,y)}{\...
6
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2answers
337 views

Using NDEigensystem to solve the Mathieu equation

To be able to apply the differential equation capabilities of Mathematica to my graduate thesis, I am trying to apply NDEigensystem to an eigenproblem whose solution I know, but I am having some ...
5
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1answer
820 views

Mathematica 3D Heat Equation Solution

I've been working on trying to analyze the Heat Equation in water both experimentally and theoretically. The model goes as: there's a cuboidal bath (of say, 15x7x5 inches) filled with water, and an ...
8
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3answers
432 views

New things and limitations in Version 12 numerical differential equation solver?

This question is intended to be a place to summarize users' exemplary experience in solving differential equation with the NDSolve family in MMA’s latest version 12....