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17
votes
1answer
248 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
42 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
349 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
52 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 ...
-3
votes
1answer
259 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
211 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: ...
35
votes
2answers
1k 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 ...
12
votes
4answers
832 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 ...