Homogeneous case with Dirichelt boundary condition

Problem

We consider homogeneous case with Dirichlet boundary condition on the boundaries of the closed waveguide

Code

We load the packages we need.

using Ferrite
using ClosedWaveguideDispersion

function n(x)
    return 1.0
end

n (generic function with 1 method)

We need to implement a new function to impose the periodic boundary condition and the Dirichlet boundary condition.

function my_bdcs(dh::DofHandler; period=1.0)
    cst = ConstraintHandler(dh)

    # Periodic boundary condition on the left and right
    # side of the periodic cell
    pfacets = collect_periodic_facets(dh.grid, "right", "left", x -> x + Ferrite.Vec{2}((period, 0.0)))
    pbc = PeriodicDirichlet(:u, pfacets)
    add!(cst, pbc)

    # Set Dirichlet boundary condition on the top and bottom boundaries of the periodic cell
    dfacets = union(getfacetset(dh.grid, "bottom"), getfacetset(dh.grid, "top"))
    dbc = Dirichlet(:u, dfacets, x -> 0)
    add!(cst, dbc)

    close!(cst)

    return cst
end

p = 1.0;
h = 1.0;
N = 100;

Set up the grid.

grid = setup_grid(lc=0.05, period=p, height=h)

Ferrite.Grid{2, Ferrite.Triangle, Float64} with 944 Ferrite.Triangle cells and 513 nodes

Basic steps needed by Ferrite.jl

ip = Lagrange{RefTriangle, 1}()
cv = setup_fevs(ip)
dh = setup_dofs(grid, ip)

# Set the boundary conditions
cst = my_bdcs(dh, period=p)

# Allocate the matrices
A = allocate_matries(dh, cst)
B = allocate_matries(dh, cst)

# Discretize the Brillouin zone
bz = collect(range(-π/p, π/p, N))

# Calculate the dispersion diagram
μ = calc_diagram(cv, dh, cst, A, B, n, bz, nevs=6)

# Plot the dispersion diagram
plot_diagram(bz, μ, period=p)

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