8k views

### Numerically solving Helmholtz equation in 2D for arbitrary shapes

I would like to solve the Helmholtz equation with Dirichlet boundary conditions in two dimensions for an arbitrary shape (for a qualitative comparison of the eigenstates to periodic orbits in the ...
4k views

### Symbolic solution(s) to generalized Heat equation

Symbolic solution(s) to Heat equation? or more generally,(eventually) Green functions to known PDEs I am interested in variations of the heat equation: or more generally or even more generally (<...
2k 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 ...
1k views

### How to convert a surface into a solid

Context I am interested in converting surfaces into solids (so I can make a 3D mesh out of them using ToElementMesh) Say I have the following cool surface ...
3k views

### Schrödinger eigenvalue problem in two dimensions (Harmonic Oscillator)

I read here the discussion about how to solve a one-dimensional eigenvalue problem. I am wondering, how can one generalize these methods to two dimensions? For example, how to solve this equation: ...
325 views

### Specific numerical eigenfunctions of Helmholtz equation in 3D for ellipsoids

I am trying to compute the eigenfunctions of an oblate spheroid (a=75 cm and b=60 cm) using Mathematica's FEM package and Chris' answer from here. Specifically, I am looking for eigenfrequencies ...
581 views

### ToElementMesh problem on Ball defined by ImplicitRegion?

Bug introduced in 10.0 and fixed in 10.2 Could any one please confirm the following bug in mathematica 10.0.2 ? If I define this ball ...
291 views

### How to discretize parametric curves for FEM analysis

I would like to know if there is anything available in order to discretize a 3D curve given by parametric equations in order to apply FEM analysis, e.g. to solve the wave equation on a thin wire ...