Julia package for handling various wave-equations and (non-linear) eigenvalue problems.
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WavesAndEigenvalues can be installed from Julia's official package repository using the built-in package manager. Just type ] to enter the package manager and then
pkg> add WavesAndEigenvalues
or
julia> import Pkg; Pkg.add("WavesAndEigenvalues")in the REPL and you are good to go.
The package has evolved from academic research in thermoacoustic-stability analysis. But it is designed fairly general. It currently contains three modules, each of which is targeting at one of the main design goals:
- Provide an elaborate interface to define, solve, and perturb nonlinear eigenvalues (NLEVP)
- Provide a lightweight interface to read unstructured tetrahedral meshes using nastran (
*.bdfand*.nas) or the latest gmsh format (*.msh). (Meshutils) - Provide a convenient interface for solving the (thermo-acoustic) Helmholtz equation. (Helmholtz)
Assume you are a literally a rocket scientist and you want to solve an eigenvalue problem like
[K+ω*C+ω^2*M+n*exp(-iωτ) F] p = 0
Where K, C, M, and F are some matrices, i the imaginary unit, n and τ some parameters, and ω and p unknown eigenpairs.
Then the NLEVP module lets you solve this equation and much more. Actually, any non-linear eigenvalue problem can be solved. Doing science in some other field than rockets or even being a pure mathematician is, thus, no problem at all. Just specify your favourite nonlinear eigenvalue problem and have fun. And fun here includes adjoint-based perturbation of your solution up to arbitrary order!
OK, this was theoretical. But you are a real scientist, so you know that the matrices K, C, M, and F are obtained by discretizing some equation using a specific mesh. You do not want to be too limited to simple geometries so unstructured tetrahedral meshing is the method of choice. Meshutils is the module that gives you the tools to read and process such meshes.
You are a practitioner? Fine, then eigenvalue theory and mesh handling should not bother your every day work too much. You just want to read in a mesh, specify some properties (boundary conditions, speed of sound field...), and get a report on the stability of your configuration? Helmholtz is your module! It even tells you how to optimize your design.