Linked Questions
10 questions linked to/from Numerically solving Helmholtz equation in 3D for arbitrary shapes
73
votes
3answers
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 ...
44
votes
3answers
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 (<...
6
votes
2answers
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 ...
16
votes
3answers
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
...
11
votes
1answer
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:
$$...
6
votes
2answers
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 ...
6
votes
2answers
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
...
3
votes
2answers
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 ...
2
votes
1answer
571 views
Gradients of the NDSolve PDE solution
I would like to understand, how to obtain gradients of the PDE solution obtained with NDSolve. To be precise let us consider a Laplace equation from one of the examples:
...
3
votes
1answer
485 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.
...