TopologyOpt

christiansen_ε(p, nf, nm) -> Complex

Christiansen refractive index interpolation: n(p) = nf + (nm - nf) * p ε(p) = n(p)²

This gives: p=0 → ε = nf² (fluid) p=1 → ε = nm² (metal)

Derivative: ∂ε/∂p = 2n(p)(nm - nf)

filter_grid(p_vec, sim, control) -> Vector

Filter design vector using 2D convolution.

Arguments

• p_vec — Flat design vector
• sim — Simulation (for grid dimensions)
• control — Control (for filter params)

filter_grid_adjoint(∂g_∂pf, sim, control) -> Vector

Adjoint of filter operation (same as forward for symmetric kernel).

filter_helmholtz!(p_vec, cache, sim, control) -> Vector

Filter design using Helmholtz PDE (3D DOF mode). Caches factorization in cache.F_factor.

filter_helmholtz_adjoint!(∂g_∂pf, cache, sim, control) -> Vector

Adjoint of Helmholtz filter. Since A is symmetric: A^(-T) = A^(-1), so adjoint solve = forward solve.

project_grid(pf_vec, sim, control) -> Vector

Project filtered design to binary-ish values (2D DOF mode).

project_grid_adjoint(∂g_∂pt, pf_vec, control) -> Vector

Adjoint of projection: chain rule through tanh.

project_fe(pf_vec, sim, control) -> ComposedFunction

Convenience wrapper: build FEFunction from vector and apply SSP projection.

project_ssp(pf, control) -> ComposedFunction

Subpixel-smoothed projection on the FEM mesh (SSP is ALWAYS used). Returns a ComposedFunction for lazy evaluation in Gridap.

glc_solid(x, grad; sim, control) -> Float64

Solid linewidth constraint for NLopt. Constraint satisfied when ≤ 0.

glc_void(x, grad; sim, control) -> Float64

Void linewidth constraint for NLopt.

glc_solid_fe(p_vec, grad, obj) -> Float64

Solid linewidth constraint for NLopt (3D DOF mode).

glc_void_fe(p_vec, grad, obj) -> Float64

Void linewidth constraint for NLopt (3D DOF mode).