Modal Analisys

[WesleyFransin]

I've been wondering whether it is possible to solve the eigenvalue problem (modal analysis) with the current tools available in Gridap. I tried exploring the docs and messing around with the library, but since I'm reasonably new to this world, I couldn't figure it out.
Could someone please shed a light on this problem?

[colinthart]

Here's a simple example that solves for eigenmodes of the Laplace equation on a rectangular domain with zero Dirichlet boundary conditions. Because we don't care about the right hand side vector and only need the assembled matrix, I set b(v) = 0.

using Gridap

N = 20
model = CartesianDiscreteModel((0, π, 0, π / 2), (N, N / 2))

reffe = ReferenceFE(lagrangian, Float64, 1)
V = FESpace(model, reffe; conformity=:H1, dirichlet_tags="boundary")
U = V

x = Triangulation(model)
dx = Measure(x, 2)

a(u, v) = ∫(∇(u) ⋅ ∇(v))dx
b(v) = 0.0

A = AffineFEOperator(a, b, U, V).op.matrix

using Arpack

nev = 10
λ, ϕ = eigs(A; nev=nev, which=:SM)

writevtk(
    x,
    "modes";
    cellfields=["mode$i" => FEFunction(U, real(ϕ[:, i])) for i in 1:nev],
)

λ[1:nev]

[fverdugo]

Just a minor syntax improvement:

you can replace

A = AffineFEOperator(a, b, U, V).op.matrix

with

feop = AffineFEOperator(a, b, U, V)
A = get_matrix(feop)

or

using Gridap.FESpaces
A = assemble_matrix(a,U,V)