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

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1
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1answer
64 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
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2answers
50 views

Join Two Element Meshes

Let's say I have two element meshes defined as the following: ...
9
votes
2answers
188 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
122 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 ...
5
votes
1answer
158 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 ...
2
votes
1answer
89 views

BUG: Problems generating FEM ElementMesh in 1-D

I'm trying to build an ElementMesh for a simple 1-D problem. First, I build the boundary ElementMesh: ...
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0answers
67 views

Dirichlet conditions being ignored

I have the following domain: ...
1
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1answer
72 views

Toroidal implicit region looks weird

I have the following toroid surface: ...
8
votes
4answers
284 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
146 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
283 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
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0answers
46 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
183 views

Problem with Neumann condition in quarter disc

So I'm following the available examples in version 10 for FEM, The plane stress operator is shown as this ...
10
votes
2answers
339 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
96 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
171 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
259 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: ...
24
votes
1answer
630 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
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0answers
63 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 ...
9
votes
2answers
458 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 ...
0
votes
0answers
55 views

How to set the boundary fixed and apply the Young's modulus in Mathematica's FEM? [duplicate]

Provided the drawing .stl is given, and the Young's modulus is know, how to start a FEM vibration mode test in Mathematica? The boundary is required to be fixed and the interested focus is on the ...
-1
votes
1answer
566 views

Test a wooden board's vibration mode

Here is a wooden board, with dimensions shown on the picture below. How we can use Mathematica's newly build-in finite element analysis features to show the different modes of its vibrations. Assuming ...
1
vote
1answer
609 views

Solving a nonlinear PDE with Mathematica10 FEM Solver

I am trying to solve a system of coupled nonlinear PDEs in a rectangular region with the new FEM solver in Mathematica 10. However, I come across an error stating NDSolveValue::femnonlinear: ...
37
votes
2answers
2k views

Numerically solving Helmholtz equation in 2D for arbitrary shapes

I would like to solve the Helmholtz equation with dirichlet boundary conditions in 2 dimensions for an arbitrary shape. (for a qualitative comparison of the eigenstates to periodic orbits in the ...
13
votes
4answers
1k views

How do I solve a PDE with a strange boundary condition?

How do I solve the PDE with boundary value like this $$u(t,x,y)=0, \textrm{when } F(x,y)=0$$ using DSolve? As a specific example, I want to solve heat equation $$\frac{\partial u}{\partial ...