Gallery

Laplace(;N = 2, h=1, T = Float64)

Creates a CrystalOperator corresponding to the (central differences) discretization of the Laplace operator $Δ=\sum_j \frac{\partial^2}{\partial x_j^2}$in N dimensions.

• h corresponds to the distance of the grid points.

curlcurl(sigma; T=Float64)

Creates the curlcurl operator. See [Section 6.2, 1] Kahl, K., Kintscher, N. Automated local Fourier analysis (ALFA). Bit Numer Math (2020). https://doi.org/10.1007/s10543-019-00797-w

curlcurl_restriction(sigma; T=Float64)

Creates the restriction operator corresponding to the curl curl operator. See [Section 6.2, 1] Kahl, K., Kintscher, N. Automated local Fourier analysis (ALFA). Bit Numer Math (2020). https://doi.org/10.1007/s10543-019-00797-w

fw_restriction(;m=1, N = 2, T = Float64)

Full weighting restriction operator in N dimensions.

graphene_dirac_restriction(;t = nothing, T=Float64)

Creates a restriction CrystalOperator that conserveres the dirac function. See [Section 6.1, 1] Kahl, K., Kintscher, N. Automated local Fourier analysis (ALFA). Bit Numer Math (2020). https://doi.org/10.1007/s10543-019-00797-w

graphene_tight_binding(;t = nothing, T=Float64)

Creates a CrystalOperator corresponding to the tight-binding Hamiltonian of graphene. The vector t should contain the hopping parameter. See [Section 6.1, 1] Kahl, K., Kintscher, N. Automated local Fourier analysis (ALFA). Bit Numer Math (2020). https://doi.org/10.1007/s10543-019-00797-w