Tagged Questions

Tag for the usage of "FiniteElement" Method embedded in NDSolve and implementation of finite element method (fem) in mathematica.

149 views

Finding eigenvalues for Laplacian operator for 3D shape with Neumann boundary conditions

I've just begun to use the Mathematica so my question may seem to be naive. To get a solution for my problem I looked at the example provided in help. ...
104 views

Approximating Integral under 2D Interpolation function

First, I have already been working on this problem, and have asked a similar question previously here. I am trying to find the integrals of 2D interpolation functions that are output from ...
162 views

Confusion with Neumann and Dirichlet

If I solve Laplace's equation with Neumann boundary conditions then everything is defined via derivatives. Consequently one needs to fix a point with a specific value to get a solution. However if I ...
70 views

Heat Conduction where thermal diffusivity depends on z

I'd like to know why Mathematica is not solving this problem for me. Let's imagine a body in which the thermal diffusivity varies with z (we have a cyllindrical ...
108 views

failure of code with Helmholtz equation with point source

I am new to the finite elements package in Mathematica. I have a system of equations, one of which is a Helmholtz equation with a point source in the interior of a bounded domain. The following is the ...
78 views

Can I use operators of the form $\frac{d^2}{dx^2}+i\frac{d}{dx}$ inside NDEigensystem?

I am currently trying to find the eigenfunctions of Hamiltonians of the form $\hat H=\frac12 \hat p^2 +a\hat p +f(\hat x)$, and I thought I would give NDEigensystem ...
146 views

NDSolveValue Quality Issue

I'm having trouble with the resolution of the NDSolveValue solution. For example this code from here gives the following on my machine (Windows, Version 10.4.1): (Zoomed in to show detail) ...
149 views

Solve 3D Electric Field using FEA

The objective is to solve the 3D electric fields for the geometry below and generate the continuous function eField3D[x_,y_,z_]. The method I was planning on using ...
68 views

Mesh definition in 3d is size dependent

Can somebody tell me if this is a bug? ...
48 views

How do I change nodal coordinates in a 2D mesh without changing anything else?

I have a 2D mesh that I generated via ToElementMesh. It discretizes a square domain with a small hole whose shape comes from a parametric B-spline. I now want to ...
104 views

Using loops to draw multiple polygons and discretizing them

I am trying to plot the first eigenvalue of the Laplacian operator with zero Dirichlet condition on following figure against decreasing values of $\varepsilon$. I used ...
81 views

Writing PDE boundary conditions with derivatives, More general than Neumann

I am solving 2D Laplace equations on f[x,y] with boundary conditions SomeVector[x,y].Grad[f] == 0 This is more general than Neumann. Is there a way to set such boundary conditions for a curved ...
69 views

What is the difference between getting a boundary mesh from ToBoundaryMesh vs doing it with ToElementMesh?

I am trying to figure out how to define and use meshes for FEM and NDSolve. I've figured out that if I want more resolution near my boundaries, I can use ToBoundaryMesh to first create the boundary ...
100 views

Why isn't ToElementMesh figuring out what my boundary is in 3D?

I am trying to change the element mesh for a FEA application I'm doing. I thought I understood it, when I did it in 2D. Here's my shape: ...
60 views

Is there a way to make MaxCellMeasure and MaxBoundaryCellMeasure comparable?

I'm trying to learn a little about meshes used for FEA and such. It seems like a good strategy if you are creating a mesh for a region is to use a finer mesh near features than the mesh used over ...
68 views

How can I plot a “slice” of the mesh for a 3D plot?

I'm using NDSolveValue to solve the Laplacian equation for this geometry: I want to view the mesh that NDSolveValue is using, so I do the following: ...
58 views

Why is NDSolveValue giving these problems in 3D that it didn't have in 2D?

I'm trying to do the same thing I did in this thread (ignore the actual question I was asking about, I just linked it to show the geometry and equation solving I'm doing), but this time for 3D instead ...
72 views

Will the solution NDSolveValue finds outside of the region I give it give me bogus results?

I'm using NDSolveValue to solve Laplace's equation for a relatively simple system. I have two rectangles, separated by a small gap, which I define using RegionDifference: ...
65 views

What code can I use to calculate, integrate, and visualize the electric field for an arbitrary shape? [duplicate]

I'm looking for a Mathematica program/function with which I'd be able to specify two objects in 3D space, each at a different surface potential, and then the program would calculate (using Finite ...
125 views

How do you refine the elements of a 3D mesh?

Response to Answer below. Original Question: I am trying to refine a 3D mesh in a certain region. This seems relevant but does not work for me. I start by making the region which consists of a box ...
164 views

ColorBars or PlotLegends for ElementMeshSurfacePlot3D

I want to produce a colorbar legend to the output from ElementMeshSurfacePlot3D (Mathematica 10). The pde was solved using NDSolveValue (FEM pdesolution is the resulting interpolating function) over a ...
94 views

benchmark of Mathematica's FEM?

Does anyone have any numbers on how mathematica compares to other commercial (eg ANSYS) or free FEM softwares (eg. FreeFEM++, FEniCS, elmer)? If this is too vague say solving the diffusion equation in ...
107 views

Assigning Element Markers to 3D FEM Mesh

I have created a 3D graphic using GraphicsComplex and then use ToElementMesh to generate a 3D Mesh that I want to solve a PDE on, but I cannot figure out how to apply ElementMarkers to the Boundaries. ...
95 views

Using Neumann boundary conditions

I had a semi-related physics problem I needed to solve analytically (which I have already done), but I am now curious how I would go about numerically solving the entire system in Mathematica. ...
137 views

How to include interpolating solution as input into NDSolveValue

I am trying to solve: ...
85 views

DiscretizeRegion does not include the boundary specified in ImplicitRegion (10.1)

I am trying to do some 3D PDE solving, and I keep running into problems with boundary conditions because my meshed boundaries are not what I expected. For example, the following code ...
184 views

How to access FEM shape functions

A couple of days ago I asked here about surface meshes and plotting on surfaces. Now I have another question: How can I access the surface or boundary element shape functions? I would like to ...
108 views

How to go from quadratic Element to Linear Element

I have created a 2D mesh as, ...
148 views

How to assign Element marker at boundary edges

How to assign marker at the boundary edges as 1, 2, 3, 4 respectively and set all of the inside elements of region as 0? for example: Code: ...
194 views

How to create a surface mesh embedded in 3D?

I am working on a problem where I want to optimize current densities on 2D surfaces embedded in 3D to generate magnetic fields. The current density on a surface can be written as a scalar function ...
290 views

How to model wooden joints with mathematica's FEM?

This is a dovetail joint: and I'd like to see the stresses and deformation on the joint.I haven't seen any modeling of disconnected regions with FEM, only connected regions, so I'm curious if you ...
166 views

solving Stokes equations for Force=0 boundary condition

Say you want to solve the movement of a particle in a viscous fluid such that the force on the particle is zero. In general, the solution is trivial since one has no-slip boundary conditions, ie the ...
70 views

Wrong result for mesh generation when using integers for mesh size

Can somebody explain me why this happens? ...
144 views

how to speed up FEM-NDSolve for similar boundary conditions?

I need to solve several stoke's equations for very similar boundary conditions, which represent particles in a fluid with different velocities U[i]. I'm interested in computing the force acting on the ...
157 views

Beam deformation due to localized force distribution

I would like to simulate the deformation of a beam which is fixed on one end and has some localized forces applied along the top. I have been inspired by this Mathematica example: http://www....
64 views

How to define “DiffusionCoefficients” in InitializePDECoefficients that depend on ElementMarker?

Modelling a Poisson Equation on piecewise constant material, ElementMarkers on the PointElements are used for the boundary ...
25 views

Discretization of a region for NDSolve using [duplicate]

I would like to mesh the region below in order to use it for a calculation by means of NDSolve. Could anyone help me to discretize this region for NDSolve using. Thank you very much. Needs["NDSolve<...
146 views

Invalid region for small angles. To Element Mesh. Finite element method

I would like to mesh the region below in order to use it for a calculation by means of NDSolve. Could anyone help me to discretize this region for NDSolve using. Thank you very much. ...
258 views

Problems with NDSolve for solving coupled Schrödinger-like PDEs with perfectly matched layer boundary condition

I'm trying to solve a full-vectorial wave equation for an arbitrarily shaped wave guide, by using NDSolve and perfectly matched layer (PML) conditions. The PML ...
119 views

Integrating an interpolating function

I have been using the following NDEigensystem command to generate the eigenfunctions of the laplacian with a square domain: ...
77 views

NeumannValue and FiniteElement Methods : BC not respected

I have noticed on several of my personal cases some issue with the BC using NeumannValue. Let me illustrate the problem. I take the 1D example of ...
88 views

How to implement NDsolve for thermo structural code? finite - element - method

I used the following equations to solve a structural problem: ...
95 views

ElementMesh (rendering?) issue

The appearance of the following ElementMesh is bad as you can see for example on the inside surface of the shell. The same problem happens converting to a ...
161 views

Errors Solving Elliptic PDES with FEM

I am trying to solve the equation below governing transversely isotropic plane strain in cartesian coordinates with the given boundary conditions based on code found here using Mathematica 10.1 on OSX ...
72 views

How to draw the shape of a 2D, 2nd order, element of an ElementMesh

I just want to create a drawing of the shape of 2nd order, two dimensional, finite element like a TriangleElement. Something like ...
247 views

How to solve 3D heat equation with Neumann B.C

I'm trying to solve the 3D heat equation on a cuboid to know if all the perimetric surfaces of a Cuboid achieve the desired temperature of a 873K on deadline time of 2 hours. i have convection on all ...
329 views

Finite Element Method and ElementMeshInterpolation issue in v10.3

Bug introduced in 10.3 I recently installed Mathematica v10.3 and checked a project I was working on few months ago under Mathematica v10.1. In this project I solve a PDE with ...
136 views

MeshRefinementFunction missing points

I'm doing some FEM on a rectangular region with a spherical cavity: ...