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

learn more… | top users | synonyms (1)

2
votes
1answer
52 views

Potential flow over cylinder with FEM: Pressure field is flipped

Much in the fashion of a few problems already answered on Mathematica.SE (1, 2), I am trying to solve the Laplace equation in velocity potential $\phi$ to simulate irrotational, inviscid flow over a ...
3
votes
1answer
103 views

NMinimize fails on Mesh?

Context I want to identify the minimum of a solution of a PDE found on a mesh. Problem I do not understand why NMinimize fails on a mesh? As a test case, ...
3
votes
2answers
128 views

Generating Meshes with Conforming Boundaries for FEM

I would like to solve a PDE on an annulus with some boundary condition that relates the inner circle to the outer circle. (For example, periodicity along radial lines). If I use a finite element ...
3
votes
0answers
70 views

StreamPlot of potential flow from a finite element calculation

I am trying to calculate a potential flow past a thick plate. The finite element calculation seems to go well but I am finding it difficult to get a nice plot of the flow. The stages below are, ...
1
vote
0answers
44 views

Transient PDE with a complex boundary condition

I am trying to solve a PDE, but one of the boundary conditions is complex, because it includes an integral over the function that I am looking for. The code is shown below ...
0
votes
2answers
70 views

NDSolveValue and DirchletConditions for cylindrical disk

my aim in this is to model the current flow of a cylindrical disk with one end set to potential 0 and the other end set to potential 1. In this section of code I am trying to find the scalar ...
17
votes
2answers
249 views

Getting rid of spikes in the PDE solution

Preamble: I am solving a PDE in a domain representing a rectangle 10X10 with several circular holes, say, like this one (n is the number and r is the radius of the holes): ...
3
votes
1answer
95 views

Specifying NeumannValue for Axial load instead of transverse load (Plane Stress situation)

I am trying to simulate a bar/link element under axial tensile load. The link is of unit thickness and I may use a plane stress model. A plane stress model is an approximation that may be used for ...
4
votes
1answer
119 views

Use FEM Solver for System of Nonlinear PDEs with Nonlinear Coefficients - Reaction-Diffusion

I am trying to solve a complex transient reaction-diffusion problem numerically in 2D. Let's take a simple system to start, say $$ A+B\rightarrow C \\ C \rightarrow A+B $$ with reaction rate $k_1$ ...
2
votes
1answer
89 views

ToElementMesh fails on DodecahedronIcosahedronCompound

Context I would like to compute the eigenmodes of a DodecahedronIcosahedronCompound. Why? Because it is cool! and I wonder how it rings… Starting with: ...
5
votes
0answers
83 views

How to create an ElementMesh of a Sphere

I want to create an ElementMesh of a "sphere". To reduce the computational effort I want to use HexahedronElement; the ...
1
vote
0answers
68 views

How to Implement a “Function Object” suitable for NDSolve and Finite Element Method?

I have a bunch of methods that shoud return an expression that behave like a function, i.e. an expression that, when supplied with suitable arguments, evaluate to something. A simple ...
6
votes
1answer
107 views

Kernel Crash while using “ValuesOnGrid” method of InterpolatingFunction

I was experiencing some kernel crash while using "ValuesOnGrid" method of an InterpolatingFunction returned by ...
6
votes
1answer
202 views

3D FEM with holes

I'm trying to create a finite element mesh with some spherical holes. To my mind the behavior is erratic but generally fails. I'm using MMA 10.0.2. In the following 3 different sets of holes are ...
1
vote
1answer
121 views

Generating a boundary mesh from a list of points

I have a list of points from which I am trying to generate a mesh: ...
36
votes
2answers
830 views

Numerically solving Helmholtz equation in 3D for arbitrary shapes

Context While studying manifold Learning I got interested in finding the eigenvectors of the Laplacian. (also in connection to this problem of solving the heat equation) Following this and that ...
15
votes
1answer
214 views

Eigenfunctions of the Laplacian on an arbitrary mesh

So, I've constructed a mesh over which I'd like to find eigenfunctions of Laplace's equation with a free boundary (a zero Neumann boundary condition along the edge). Mostly because I figured an ...
2
votes
1answer
84 views

Solving a time-dependent structural mechanics problem with Finite Element

I'm trying to solve a time-dependent structural mechanics problem with Finite Element. I modified one of the last samples in the "Solving Partial Differential Equations with Finite Elements" Tutorial. ...
2
votes
0answers
141 views

Choosing FEM element type and mesh refinement

I have only recently been introduced to Mathematica's(v10.0) FEM capabilities. I understand that for solving PDEs on non-uniform shapes via NDSolve, Mathematica ...
2
votes
1answer
74 views

ToElementMesh[]

Could you please help with the following: ...
5
votes
0answers
114 views

NDSolve computes wrong solution?

Please excuse me if the question has already been answered somewhere else, but I was not able to find it. Could somebody tell me what I am doing wrong here? The solution of DSolve is of course correct ...
9
votes
2answers
175 views

Build an InterpolatingFunction with ElementMeshInterpolation

Suppose you have a function f[t_, x_, y_] := t (1 - x^2 - y^2) defined for {x,y} in ...
2
votes
0answers
78 views

FEM in Mathematica and AceGen

I just wanted to ask, if anybody has already worked with AceGen AceGen, Wolfram Research AceGen, Homepage and knows what clear advantages AceGen has compared to the new FEM in Mathematica 10 ...
5
votes
1answer
209 views

FEM: user material subroutines (UMAT in ABAQUS), mechanics

Just a quick question (mainly for those who are also familiar with ABAQUS or other comparable FEM programs and non-linear modelling of mechanical behavior, e.g., plasticity). Is there any module in ...
5
votes
2answers
203 views

Kernel quits without error in NDSolveValue

I am using the latest 10.1. The following single line command makes the kernel quit without error message (just a beep): ...
13
votes
1answer
175 views

MinMax function (Mathematica v10.1.0) conflicts with NDSolve`FEM`MinMax?

Bug introduced in 10.1.0 and fixed in 10.2.0 Some problem in v10.1.0 (Windows 8.1 x64) and the new MinMax... ...
3
votes
1answer
75 views

Problem with MeshOrderAlteration to create a 2nd order ElementMesh

After working on this 2D domain, I'm trying to reproduce the same ideas to create a mesh of a sphere composed of QuadElement, instead of more simple and common ...
5
votes
1answer
140 views

NDSolve and FEM support for non conformal meshes of a disk [with Kernel crash]

I want to create an ElementMesh for a disk. For my specific scenario, some author advise to use a regular mesh, where the radial and tangential directions are ...
1
vote
0answers
51 views

Error message for FEMStiffnessElements

I am trying to solve this pde numerically with Mathematica: ...
8
votes
1answer
231 views

FEM: how to choose FEM element type

I am asking myself if there is any simple option for choosing the element type for the mesh generation WITHOUT explicitly creating coordinates and then the mesh. Minimal example: here I would like ...
1
vote
1answer
153 views

PDE solution does not satisfy Neumann boundary conditions using NDSolve

I am trying to solve the free particle Schrodinger equation in 1D (hbar =1, Energy = 1, mass = 1), But specifying conditions only on x==0: ...
4
votes
2answers
117 views

Join Two Element Meshes

Let's say I have two element meshes defined as the following: ...
9
votes
2answers
235 views

Solve a PDE over a region defined by a Bezier patch

I am using NDSolve to find the solution to a PDE over an arbitrary domain. The domain is specified by a Bezier patch. ...
6
votes
1answer
140 views

Long running ToElementMesh with very “large” domains

I'm trying to solve a system of PDE over a large domain. This doesn't means I need to have a huge amount of mesh points and mesh elements to discretize the domain. Just that the domains has a big ...
8
votes
1answer
546 views

FEM - how should I impose periodic boundary conditions in pure space problems?

I have searched other threads, but I was not successful in finding an answer I could understand. Right to the point: how do I impose correctly periodic behavior on the edges of the rectangular ...
3
votes
2answers
133 views

BUG: Problems generating FEM ElementMesh in 1-D

fixed in 10.1 (windows) I'm trying to build an ElementMesh for a simple 1-D problem. First, I build the boundary ...
1
vote
0answers
108 views
1
vote
1answer
90 views
9
votes
4answers
413 views

How discretize a region placing vertices on a specific non-uniform grid

Given a generic region, for example: Ω = ImplicitRegion[ 2 x^2 + 3 y^2 + 2 x y - 2 <= 0 ∧ x^2 + y^2 > .1, {x, y}]; and a non-uniform grid, for ...
3
votes
1answer
223 views

Trouble understanding NeumannValue and Inactive/Formal PDEs

I read all documentation about the Finite Element Method in Mathematica 10, and I read some questions here, but I'm still unable to properly understand how to use the ...
10
votes
1answer
378 views

representation of custom deformation on a meshgrid

I am trying to represent 2D deformations on a rectangular grid. In Mathematica 10, there is a method to solve the elastic differential equations and then represent the deformation as presented here: ...
3
votes
0answers
51 views

Missing links in usage statements

The integration of the documentation center does not seem to be complete on my machine. I often access the documentation center via the usage statement links. ...
7
votes
1answer
235 views

Problem with Neumann condition in quarter disc

Bug persists through version 10.1 So I'm following the available examples in version 10 for FEM, The plane stress operator is shown as this ...
11
votes
2answers
473 views

How to create subregions for the NDSolve FEM Solver

I am trying to create a 2d region consisting of two subregions. The inner region has several holes, where boundary conditions are applied. The figure shows the idea. I have tried to create this ...
2
votes
0answers
114 views

Puzzling NDSolve[] behavior for PDE (smooth solution, inconsistent with boundary conditions)

Consider the following: NDSolve[{D[z[x, y], x, x] + D[z[x, y], y, y] == 0, z[x, 0] == Sin[x], z[0, y] == Cos[y]}, z[x, y], x, y] {{z[x, y] -> ...
2
votes
0answers
224 views

How to solve a PDE with Robin Boundary Condition inside considered region?

I'm trying to solve the heat diffusion equation in cylindrical coordinates. The main problem is that I would like to include the Robin Boundary Condition inside considered region in order to simulate ...
2
votes
0answers
429 views

How to solve a nonlinear coupled PDE with initial and some boundary values

I would like to solve the following nonlinear coupled PDE with a mix of initial conditions and boundary values: ...
27
votes
1answer
945 views

Calculating a potential function using the finite element method

This is my first attempt to use the Finite Element method available in version 10. There are questions and I am very open to suggestions. My example is flow around a cylinder which is a well known ...
1
vote
0answers
70 views

Error when extending 1-dimensional PDE to 2 dimensions

I want to calculate how magnetic flux is trapped in a superconductor near the interface superconductor/vacuum. This problem already was solved analytically by J. Pearl for cylindrical symmetry (if ...
10
votes
2answers
535 views

FEM: Nicer Element Shape for Spherical Region

I'm trying to generate a mesh for later use in the Finite Element Method of the DSolve command. It is basically a parallelepiped with a spherical indentation. I'm ...