MORFE.jl / Tutorials

Tutorials

Every notebook lives in the MORFEExamples repository.

Structures Clamped beam mesh with node 289 highlighted and four backbone curves
Get started

From a mesh to a ROM

Compute the backbone curve of the first bending mode of a clamped beam with geometric nonlinearity.

HyperelastictyGmshCOMSOL~1 min
Structures Top view of the hexahedral mesh of a micromirror: a circular mirror in three rings joined by torsion bars, the clamped frame in purple
Intro · Full example

Dual-axis MEMS micromirror

Choose the clamp and the master mode of a micromirror's mesh, then compute how its frequency changes with the tilt of the mirror.

Anisotropic siliconParaVieworder 5
Navier–Stokes Vorticity of the base flow plus the Hopf mode past the cylinder — the Kármán vortex street
Intro · Full example

Kármán vortex street

Reduce the Navier–Stokes equations to understand how increasing the Reynolds number creates vortex shedding past a cylinder.

Navier–Stokesparametric ROMorder 9
NthOrderModel Phase portrait of the forced Duffing oscillator: the transient spiralling in, and the closed steady-state loop it settles onto
Mid · Core Library

Building a full-order model

MORFE's full-order models have 3 components: the matrices of the linear terms, the nonlinear terms, and (optionally) a external system.

MultilinearMapExternalSystem<15 s
Symbolics.jl u₁ + cu₁ + ku₁ + gu₁³ = r₁ u₂ + cu₂ + ku₂ - ku₁ = 0 r₁ = -Ω r₂ r₂ = Ω r₁
Mid · External Library

Symbolic full-order model

Write the model as an ODE instead of assembling B-matrices and MultilinearMaps by hand. Covers model_from_symbolics, externalsystem_from_symbolics, and a DifferentialEquations.jl-style interface.

NthOrderModelSymbolics.jl
MultiindexSet
Mid · Core Library

Monomials and multiindices

Which monomials does the solve compute? Build the set yourself — generators, anisotropic truncation, deletion, and a spectral bound on the superharmonics — with an interactive lattice at every step.

MultiindexSetGrLex<5 s
Reproducibility

Every tutorial ships with everything needed to run it: the mesh and the MORFE code.

For anything to do with installing or running Julia itself, see the Julia documentation.